Higgs Field
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The Higgs boson, sometimes called the Higgs particle, is an
elementary particle In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. The Standard Model presently recognizes seventeen distinct particles—twelve fermions and five bosons. As a c ...
in the
Standard Model The Standard Model of particle physics is the Scientific theory, theory describing three of the four known fundamental forces (electromagnetism, electromagnetic, weak interaction, weak and strong interactions – excluding gravity) in the unive ...
of
particle physics Particle physics or high-energy physics is the study of Elementary particle, fundamental particles and fundamental interaction, forces that constitute matter and radiation. The field also studies combinations of elementary particles up to the s ...
produced by the quantum excitation of the Higgs field, one of the
fields Fields may refer to: Music *Fields (band), an indie rock band formed in 2006 * Fields (progressive rock band), a progressive rock band formed in 1971 * ''Fields'' (album), an LP by Swedish-based indie rock band Junip (2010) * "Fields", a song by ...
in
particle physics Particle physics or high-energy physics is the study of Elementary particle, fundamental particles and fundamental interaction, forces that constitute matter and radiation. The field also studies combinations of elementary particles up to the s ...
theory. In the Standard Model, the Higgs particle is a massive
scalar boson A scalar boson is a boson whose spin equals zero. A ''boson'' is a particle whose wave function is symmetric under particle exchange and therefore follows Bose–Einstein statistics. The spin–statistics theorem implies that all bosons have a ...
that
couples Couple or couples may refer to: *Couple, a set of two of items of a type *Couple (mechanics), a pair of force which are equal in magnitude but opposite in direction and separated by a perpendicular distance so that their line of action do not c ...
to (interacts with) particles whose mass arises from their interactions with the Higgs Field, has zero spin, even (positive) parity, no
electric charge Electric charge (symbol ''q'', sometimes ''Q'') is a physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative''. Like charges repel each other and ...
, and no colour charge. It is also very unstable, decaying into other particles almost immediately upon generation. The Higgs field is a
scalar field In mathematics and physics, a scalar field is a function associating a single number to each point in a region of space – possibly physical space. The scalar may either be a pure mathematical number ( dimensionless) or a scalar physical ...
with two neutral and two electrically charged components that form a complex doublet of the
weak isospin In particle physics, weak isospin is a quantum number relating to the electrically charged part of the weak interaction: Particles with half-integer weak isospin can interact with the bosons; particles with zero weak isospin do not. Weak isospin ...
SU(2) symmetry. Its " sombrero potential" leads it to take a nonzero value everywhere (including otherwise empty space), which
breaks Break or Breaks or The Break may refer to: Time off from duties * Recess (break), time in which a group of people is temporarily dismissed from its duties * Break (work), time off during a shift/recess ** Coffee break, a short mid-morning rest ...
the
weak isospin In particle physics, weak isospin is a quantum number relating to the electrically charged part of the weak interaction: Particles with half-integer weak isospin can interact with the bosons; particles with zero weak isospin do not. Weak isospin ...
symmetry of the
electroweak interaction In particle physics, the electroweak interaction or electroweak force is the unified description of two of the fundamental interactions of nature: electromagnetism (electromagnetic interaction) and the weak interaction. Although these two force ...
and, via the
Higgs mechanism In the Standard Model of particle physics, the Higgs mechanism is essential to explain the Mass generation, generation mechanism of the property "mass" for gauge bosons. Without the Higgs mechanism, all bosons (one of the two classes of particles ...
, gives a rest mass to all massive elementary particles of the Standard Model, including the Higgs boson itself. The existence of the Higgs field became the last unverified part of the Standard Model of particle physics, and for several decades was considered "the central problem in particle physics". Both the field and the
boson In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value (0, 1, 2, ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have half odd-intege ...
are named after physicist
Peter Higgs Peter Ware Higgs (29 May 1929 – 8 April 2024) was a British theoretical physicist, professor at the University of Edinburgh,Griggs, Jessica (Summer 2008The Missing Piece ''Edit'' the University of Edinburgh Alumni Magazine, p. 17 and Nobel ...
, who in 1964, along with five other scientists in three teams, proposed the
Higgs mechanism In the Standard Model of particle physics, the Higgs mechanism is essential to explain the Mass generation, generation mechanism of the property "mass" for gauge bosons. Without the Higgs mechanism, all bosons (one of the two classes of particles ...
, a way for some particles to acquire mass. All fundamental particles known at the time should be massless at very high energies, but fully explaining how some particles gain mass at lower energies had been extremely difficult. If these ideas were correct, a particle known as a scalar boson (with certain properties) should also exist. This particle was called the Higgs boson and could be used to test whether the Higgs field was the correct explanation. After a 40-year search, a subatomic particle with the expected properties was discovered in 2012 by the
ATLAS An atlas is a collection of maps; it is typically a bundle of world map, maps of Earth or of a continent or region of Earth. Advances in astronomy have also resulted in atlases of the celestial sphere or of other planets. Atlases have traditio ...
and CMS experiments at the
Large Hadron Collider The Large Hadron Collider (LHC) is the world's largest and highest-energy particle accelerator. It was built by the CERN, European Organization for Nuclear Research (CERN) between 1998 and 2008, in collaboration with over 10,000 scientists, ...
(LHC) at
CERN The European Organization for Nuclear Research, known as CERN (; ; ), is an intergovernmental organization that operates the largest particle physics laboratory in the world. Established in 1954, it is based in Meyrin, western suburb of Gene ...
near
Geneva Geneva ( , ; ) ; ; . is the List of cities in Switzerland, second-most populous city in Switzerland and the most populous in French-speaking Romandy. Situated in the southwest of the country, where the Rhône exits Lake Geneva, it is the ca ...
, Switzerland. The new particle was subsequently confirmed to match the expected properties of a Higgs boson. Physicists from two of the three teams, Peter Higgs and
François Englert François, Baron Englert (; born 6 November 1932) is a Belgian theoretical physicist and 2013 Nobel Prize laureate. Englert is professor emeritus at the Université libre de Bruxelles (ULB), where he is a member of the Service de Physique Thé ...
, were awarded the
Nobel Prize in Physics The Nobel Prize in Physics () is an annual award given by the Royal Swedish Academy of Sciences for those who have made the most outstanding contributions to mankind in the field of physics. It is one of the five Nobel Prizes established by the ...
in 2013 for their theoretical predictions. Although Higgs's name has come to be associated with this theory, several researchers between about 1960 and 1972 independently developed different parts of it. In the media, the Higgs boson has often been called the "God particle" after the 1993 book '' The God Particle'' by Nobel Laureate
Leon Lederman Leon, Léon (French) or León (Spanish) may refer to: Places Europe * León, Spain, capital city of the Province of León * Province of León, Spain * Kingdom of León, an independent state in the Iberian Peninsula from 910 to 1230 and again fro ...
. The name has been criticised by physicists, including Peter Higgs.


Introduction


Standard Model

Physicists explain the fundamental particles and
forces In physics, a force is an influence that can cause an object to change its velocity unless counterbalanced by other forces. In mechanics, force makes ideas like 'pushing' or 'pulling' mathematically precise. Because the magnitude and directi ...
of the universe in terms of the
Standard Model The Standard Model of particle physics is the Scientific theory, theory describing three of the four known fundamental forces (electromagnetism, electromagnetic, weak interaction, weak and strong interactions – excluding gravity) in the unive ...
– a widely accepted framework based on
quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ...
that predicts almost all known particles and forces aside from
gravity In physics, gravity (), also known as gravitation or a gravitational interaction, is a fundamental interaction, a mutual attraction between all massive particles. On Earth, gravity takes a slightly different meaning: the observed force b ...
with great accuracy. (A separate theory,
general relativity General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...
, is used for gravity.) In the Standard Model, the particles and forces in nature (aside from gravity) arise from properties of quantum fields known as gauge invariance and
symmetries Symmetry () in everyday life refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is invariant under some transformations ...
. Forces in the Standard Model are transmitted by particles known as
gauge boson In particle physics, a gauge boson is a bosonic elementary particle that acts as the force carrier for elementary fermions. Elementary particles whose interactions are described by a gauge theory interact with each other by the exchange of gauge ...
s.


Gauge-invariant theories and symmetries

: ''"It is only slightly overstating the case to say that physics is the study of symmetry"'' – Philip Anderson, Nobel Prize Physics Gauge-invariant theories are theories with a useful feature, namely that changes to certain quantities make no difference to experimental outcomes. For example, increasing the
electric potential Electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as electric potential energy per unit of electric charge. More precisely, electric potential is the amount of work (physic ...
of an
electromagnet An electromagnet is a type of magnet in which the magnetic field is produced by an electric current. Electromagnets usually consist of wire (likely copper) wound into a electromagnetic coil, coil. A current through the wire creates a magnetic ...
by 100 volts does not itself cause any change to the
magnetic field A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular ...
that it produces. Similarly, the measured
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...
in vacuum remains unchanged, whatever the location in time and space, and whatever the local
gravitational field In physics, a gravitational field or gravitational acceleration field is a vector field used to explain the influences that a body extends into the space around itself. A gravitational field is used to explain gravitational phenomena, such as ...
. In these theories, the gauge is a quantity that can be changed with no resultant effect. This independence of the results from some changes is called gauge invariance, and these changes reflect symmetries of the underlying physics. These symmetries provide constraints on the fundamental forces and particles of the physical world. Gauge invariance is therefore an important property within particle physics theory. The gauge symmetries are closely connected to
conservation law In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves over time. Exact conservation laws include conservation of mass-energy, conservation of linear momen ...
s and are described mathematically using
group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ( ...
. Quantum field theory and the Standard Model are both gauge-invariant theories – meaning that the gauge symmetries allow theoretical derivation of properties of the universe.


Gauge boson rest mass problem

Quantum field theories based on gauge invariance had been used with great success in understanding the
electromagnetic In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interacti ...
and
strong force In nuclear physics and particle physics, the strong interaction, also called the strong force or strong nuclear force, is one of the four known fundamental interactions. It confines quarks into protons, neutrons, and other hadron particles, an ...
s, but by around 1960, all attempts to create a ''gauge invariant'' theory for the weak force (and its combination with the electromagnetic force, known together as the
electroweak interaction In particle physics, the electroweak interaction or electroweak force is the unified description of two of the fundamental interactions of nature: electromagnetism (electromagnetic interaction) and the weak interaction. Although these two force ...
) had consistently failed. As a result of these failures, gauge theories began to fall into disrepute. The problem was that symmetry requirements for these two forces incorrectly predicted that the weak force's gauge bosons ( W and Z) would have zero mass (in the specialized terminology of particle physics, "mass" refers specifically to a particle's
rest mass The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an object or system of objects that is independent of the overall motion of the system. More precisely, ...
). But experiments showed the W and Z gauge bosons had non-zero (rest) mass. Further, many promising solutions seemed to require the existence of extra particles known as
Goldstone boson In physics, Goldstone bosons or Nambu–Goldstone bosons (NGBs) are bosons that appear necessarily in models exhibiting spontaneous breakdown of continuous symmetries. They were discovered by Yoichiro Nambu within the context of the BCS superco ...
s, but evidence suggested these did not exist. This meant that either gauge invariance was an incorrect approach, or something unknown was giving the weak force's W and Z bosons their mass, and doing it in a way that did not imply the existence of Goldstone bosons. By the late 1950s and early 1960s, physicists were at a loss as to how to resolve these issues, or how to create a comprehensive theory for particle physics.


Symmetry breaking

In the late 1950s,
Yoichiro Nambu was a Japanese-American physicist and professor at the University of Chicago. Known for his groundbreaking contributions to theoretical physics, Nambu was the originator of the theory of spontaneous symmetry breaking, a concept that revoluti ...
recognised that
spontaneous symmetry breaking Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state spontaneously ends up in an asymmetric state. In particular, it can describe systems where the equations of motion o ...
, a process whereby a symmetric system becomes asymmetric, could occur under certain conditions. Symmetry breaking is when some variable takes on a value that does not reflect the symmetries that the underlying laws have, such as when the space of all stable configurations possesses a given symmetry but the stable configurations do not individually possess that symmetry. In 1962, physicist Philip Anderson, an expert in
condensed matter physics Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid State of matter, phases, that arise from electromagnetic forces between atoms and elec ...
, observed that symmetry breaking plays a role in
superconductivity Superconductivity is a set of physical properties observed in superconductors: materials where Electrical resistance and conductance, electrical resistance vanishes and Magnetic field, magnetic fields are expelled from the material. Unlike an ord ...
, and suggested that it could also be part of the answer to the problem of gauge invariance in particle physics. Specifically, Anderson suggested that the
Goldstone boson In physics, Goldstone bosons or Nambu–Goldstone bosons (NGBs) are bosons that appear necessarily in models exhibiting spontaneous breakdown of continuous symmetries. They were discovered by Yoichiro Nambu within the context of the BCS superco ...
s that would result from symmetry breaking might instead, in some circumstances, be "absorbed" by the massless
W and Z bosons In particle physics, the W and Z bosons are vector bosons that are together known as the weak bosons or more generally as the intermediate vector bosons. These elementary particles mediate the weak interaction; the respective symbols are , , an ...
. If so, perhaps the Goldstone bosons would not exist, and the W and Z bosons could gain mass, solving both problems at once. Similar behaviour was already theorised in superconductivity. In 1964, this was shown to be theoretically possible by physicists Abraham Klein and Benjamin Lee, at least for some limited ( non-relativistic) cases.


Higgs mechanism

Following the 1963 and early 1964 papers, three groups of researchers independently developed these theories more completely, in what became known as the 1964 PRL symmetry breaking papers. All three groups reached similar conclusions and for all cases, not just some limited cases. They showed that the conditions for electroweak symmetry would be "broken" if an unusual type of field existed throughout the universe, and indeed, there would be no Goldstone bosons and some existing bosons would acquire mass. The field required for this to happen (which was purely hypothetical at the time) became known as the ''Higgs field'' (after
Peter Higgs Peter Ware Higgs (29 May 1929 – 8 April 2024) was a British theoretical physicist, professor at the University of Edinburgh,Griggs, Jessica (Summer 2008The Missing Piece ''Edit'' the University of Edinburgh Alumni Magazine, p. 17 and Nobel ...
, one of the researchers) and the mechanism by which it led to symmetry breaking became known as the ''
Higgs mechanism In the Standard Model of particle physics, the Higgs mechanism is essential to explain the Mass generation, generation mechanism of the property "mass" for gauge bosons. Without the Higgs mechanism, all bosons (one of the two classes of particles ...
''. A key feature of the necessary field is that the field would have ''less'' energy when it had a non-zero value than when it was zero, unlike every other known field; therefore, the Higgs field has a non-zero value (or '' vacuum expectation'') everywhere. This non-zero value could in theory break electroweak symmetry. It was the first proposal that was able to show, within a gauge invariant theory, how the weak force gauge bosons could have mass despite their governing symmetry. Although these ideas did not gain much initial support or attention, by 1972 they had been developed into a comprehensive theory and gave "sensible" results that accurately described particles known at the time, and which, with exceptional accuracy, predicted several other particles, which were discovered during the following years. During the 1970s, these theories rapidly became the
Standard Model The Standard Model of particle physics is the Scientific theory, theory describing three of the four known fundamental forces (electromagnetism, electromagnetic, weak interaction, weak and strong interactions – excluding gravity) in the unive ...
of particle physics.


Higgs field

To allow symmetry breaking, the Standard Model includes a field of the kind needed to "break" electroweak symmetry and give particles their correct mass. This field, which became known as the Higgs field, was hypothesized to exist throughout space, and to break some symmetry laws of the
electroweak interaction In particle physics, the electroweak interaction or electroweak force is the unified description of two of the fundamental interactions of nature: electromagnetism (electromagnetic interaction) and the weak interaction. Although these two force ...
, triggering the Higgs mechanism. It would therefore cause the W and Z gauge bosons of the weak force to be massive at all temperatures below an extremely high value. When the weak force bosons acquire mass, this affects the distance they can freely travel, which becomes very small, also matching experimental findings. Furthermore, it was later realised that the same field would also explain, in a different way, why other fundamental constituents of matter (including
electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...
s and
quark A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nucleus, atomic nuclei ...
s) have mass. Unlike all other known fields, such as the
electromagnetic field An electromagnetic field (also EM field) is a physical field, varying in space and time, that represents the electric and magnetic influences generated by and acting upon electric charges. The field at any point in space and time can be regarde ...
, the Higgs field is a
scalar field In mathematics and physics, a scalar field is a function associating a single number to each point in a region of space – possibly physical space. The scalar may either be a pure mathematical number ( dimensionless) or a scalar physical ...
, and has a non-zero average value in
vacuum A vacuum (: vacuums or vacua) is space devoid of matter. The word is derived from the Latin adjective (neuter ) meaning "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressur ...
.


The "central problem"

Prior to the discovery of the Higgs Boson, there was no direct evidence that the Higgs field exists, but even without direct evidence, the accuracy of predictions within the Standard Model led scientists to believe the theory might be correct. By the 1980s, the question of whether the Higgs field exists, and whether the entire Standard Model is correct, had come to be regarded as one of the most important unanswered questions in particle physics. The existence of the Higgs field became the last unverified part of the Standard Model of particle physics, and for several decades was considered "the central problem in particle physics". For many decades, scientists had no way to determine whether the Higgs field exists because the technology needed for its detection did not exist at that time. If the Higgs field did exist, then it would be unlike any other known fundamental field, but it also was possible that these key ideas, or even the entire Standard Model, were somehow incorrect. The hypothesised Higgs theory made several key predictions. One crucial prediction was that a matching
particle In the physical sciences, a particle (or corpuscle in older texts) is a small localized object which can be described by several physical or chemical properties, such as volume, density, or mass. They vary greatly in size or quantity, from s ...
, called the Higgs boson, should also exist. Proving the existence of the Higgs boson would prove the existence of the Higgs field, and therefore finally prove the Standard Model. Therefore, there was an extensive search for the Higgs boson as a way to prove the Higgs field itself exists.


Search and discovery

Although the Higgs field would exist and be nonzero everywhere, proving its existence was far from easy. In principle, it can be proved to exist by detecting its excitations, which manifest as Higgs particles (Higgs bosons), but these are extremely difficult to produce and detect due to the energy required to produce them and their very rare production even if there is sufficient energy available. It was, therefore, several decades before the first evidence of the Higgs boson would be found. Particle colliders, detectors, and computers capable of looking for Higgs bosons took more than 30 years to develop. The importance of this fundamental question led to a 40-year search, and the construction of one of the world's most expensive and complex experimental facility to date,
CERN The European Organization for Nuclear Research, known as CERN (; ; ), is an intergovernmental organization that operates the largest particle physics laboratory in the world. Established in 1954, it is based in Meyrin, western suburb of Gene ...
's
Large Hadron Collider The Large Hadron Collider (LHC) is the world's largest and highest-energy particle accelerator. It was built by the CERN, European Organization for Nuclear Research (CERN) between 1998 and 2008, in collaboration with over 10,000 scientists, ...
(LHC), in an attempt to create Higgs bosons and other particles for observation and study. On 4 July 2012, the discovery of a new particle with a mass between was announced; physicists suspected that it was the Higgs boson. Since then, the particle has been shown to behave, interact, and decay in many of the ways predicted for Higgs particles by the Standard Model, including having even parity and zero spin, two fundamental attributes of a Higgs boson. This also means it is the first elementary scalar particle discovered in nature. By March 2013, the existence of the Higgs boson was confirmed, and therefore the concept of some type of Higgs field throughout space is strongly supported. The presence of the field, now confirmed by experimental investigation, explains why some fundamental particles have (a rest) mass, despite the
symmetries Symmetry () in everyday life refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is invariant under some transformations ...
controlling their interactions implying that they should be "massless". It also resolves several other long-standing problems, such as the reason for the extremely short distance travelled by the weak force bosons, and therefore the weak force's extremely short range. As of 2018, in-depth research shows the particle continuing to behave in line with predictions for the Standard Model's Higgs boson. More studies are needed to verify with higher precision that the discovered particle has all of the properties predicted or whether, as described by some theories, multiple Higgs bosons exist. The nature and properties of this field are now being investigated further, using more data collected at the LHC.


Interpretation

Various analogies have been used to describe the Higgs field and boson, including analogies with well-known symmetry-breaking effects such as the
rainbow A rainbow is an optical phenomenon caused by refraction, internal reflection and dispersion of light in water droplets resulting in a continuous spectrum of light appearing in the sky. The rainbow takes the form of a multicoloured circular ...
and prism,
electric field An electric field (sometimes called E-field) is a field (physics), physical field that surrounds electrically charged particles such as electrons. In classical electromagnetism, the electric field of a single charge (or group of charges) descri ...
s, and ripples on the surface of water. Other analogies based on the resistance of macroscopic objects moving through media (such as people moving through crowds, or some objects moving through
syrup In cooking, syrup (less commonly sirup; from ; , beverage, wine and ) is a condiment that is a thick, viscous liquid consisting primarily of a Solution (chemistry), solution of sugar in water, containing a large amount of dissolved sugars but ...
or
molasses Molasses () is a viscous byproduct, principally obtained from the refining of sugarcane or sugar beet juice into sugar. Molasses varies in the amount of sugar, the method of extraction, and the age of the plant. Sugarcane molasses is usuall ...
) are commonly used but misleading, since the Higgs field does not actually resist particles, and the effect of mass is not caused by resistance.


Overview of Higgs boson and field properties

In the Standard Model, the Higgs boson is a massive
scalar boson A scalar boson is a boson whose spin equals zero. A ''boson'' is a particle whose wave function is symmetric under particle exchange and therefore follows Bose–Einstein statistics. The spin–statistics theorem implies that all bosons have a ...
whose mass must be found experimentally. Its mass has been determined to be by CMS (2022) and by ATLAS (2023). It is the only particle that remains massive even at very high energies. It has zero spin, even (positive) parity, no
electric charge Electric charge (symbol ''q'', sometimes ''Q'') is a physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative''. Like charges repel each other and ...
, no colour charge, and it
couples Couple or couples may refer to: *Couple, a set of two of items of a type *Couple (mechanics), a pair of force which are equal in magnitude but opposite in direction and separated by a perpendicular distance so that their line of action do not c ...
to (interacts with) mass. It is also very unstable, decaying into other particles almost immediately via several possible pathways. The Higgs field is a
scalar field In mathematics and physics, a scalar field is a function associating a single number to each point in a region of space – possibly physical space. The scalar may either be a pure mathematical number ( dimensionless) or a scalar physical ...
, with two neutral and two electrically charged components that form a complex doublet of the
weak isospin In particle physics, weak isospin is a quantum number relating to the electrically charged part of the weak interaction: Particles with half-integer weak isospin can interact with the bosons; particles with zero weak isospin do not. Weak isospin ...
SU(2) symmetry. Unlike any other known quantum field, it has a sombrero potential. This shape means that below extremely high cross-over temperature of such as those seen during the first picosecond (10−12 s) of the
Big Bang The Big Bang is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models based on the Big Bang concept explain a broad range of phenomena, including th ...
, the Higgs field in its
ground state The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state ...
has less energy when it is nonzero, resulting in a nonzero
vacuum expectation value In quantum field theory, the vacuum expectation value (VEV) of an operator is its average or expectation value in the vacuum. The vacuum expectation value of an operator O is usually denoted by \langle O\rangle. One of the most widely used exa ...
. Therefore, in today's universe the Higgs field has a nonzero value everywhere (including in otherwise empty space). This nonzero value in turn breaks the weak isospin SU(2) symmetry of the
electroweak interaction In particle physics, the electroweak interaction or electroweak force is the unified description of two of the fundamental interactions of nature: electromagnetism (electromagnetic interaction) and the weak interaction. Although these two force ...
everywhere. (Technically the non-zero expectation value converts the Lagrangian's Yukawa coupling terms into mass terms.) When this happens, three components of the Higgs field are "absorbed" by the SU(2) and U(1)
gauge boson In particle physics, a gauge boson is a bosonic elementary particle that acts as the force carrier for elementary fermions. Elementary particles whose interactions are described by a gauge theory interact with each other by the exchange of gauge ...
s (the
Higgs mechanism In the Standard Model of particle physics, the Higgs mechanism is essential to explain the Mass generation, generation mechanism of the property "mass" for gauge bosons. Without the Higgs mechanism, all bosons (one of the two classes of particles ...
) to become the longitudinal components of the now-massive
W and Z bosons In particle physics, the W and Z bosons are vector bosons that are together known as the weak bosons or more generally as the intermediate vector bosons. These elementary particles mediate the weak interaction; the respective symbols are , , an ...
of the weak force. The remaining electrically neutral component either manifests as a Higgs boson, or may couple separately to other particles known as
fermion In particle physics, a fermion is a subatomic particle that follows Fermi–Dirac statistics. Fermions have a half-integer spin (spin 1/2, spin , Spin (physics)#Higher spins, spin , etc.) and obey the Pauli exclusion principle. These particles i ...
s (via Yukawa couplings), causing these to acquire mass as well.


Significance

Evidence for the Higgs field and its properties has been extremely significant for many reasons. The primary importance of the Higgs boson is that it completes the mechanism by which the heavy electroweak bosons acquire mass, and it is fortunate that the mass is such that it is able to be examined using existing experimental technology, as a way to confirm and study the entire Higgs field theory. Conversely, evidence that the Higgs field and boson did ''not'' exist within the expected mass range would have also been significant.


Particle physics


Validation of the Standard Model

The Higgs boson validates the
Standard Model The Standard Model of particle physics is the Scientific theory, theory describing three of the four known fundamental forces (electromagnetism, electromagnetic, weak interaction, weak and strong interactions – excluding gravity) in the unive ...
mechanism of mass generation for the weak bosons, and can provide masses to the fermions. As more precise measurements of its properties are made, more advanced extensions may be suggested or excluded. As experimental means to measure the Higgs field behaviour and interactions are developed, this fundamental field may be better understood. If the Higgs boson had not been discovered, the Standard Model would have needed to be modified or superseded. Related to this, it is a widely held belief among many physicists that there is likely to be "new"
physics beyond the Standard Model Physics beyond the Standard Model (BSM) refers to the theoretical developments needed to explain the deficiencies of the Standard Model, such as the inability to explain the fundamental parameters of the standard model, the strong CP problem, neut ...
, and the Standard Model will at some point be extended or superseded. The discovery of the Higgs boson, as well as the many measured collisions occurring at the LHC, provide physicists with a sensitive tool to search their data for any evidence of the failure of the Standard Model, and might provide considerable evidence to guide researchers into future theoretical developments.


Symmetry breaking of the electroweak interaction

Below an extremely high temperature, electroweak symmetry breaking causes the
electroweak interaction In particle physics, the electroweak interaction or electroweak force is the unified description of two of the fundamental interactions of nature: electromagnetism (electromagnetic interaction) and the weak interaction. Although these two force ...
to manifest in part as the short-ranged weak force, which is carried by massive
gauge boson In particle physics, a gauge boson is a bosonic elementary particle that acts as the force carrier for elementary fermions. Elementary particles whose interactions are described by a gauge theory interact with each other by the exchange of gauge ...
s. In the
history of the universe Big History is an academic discipline that examines history from the Big Bang to the present. Big History resists specialization and searches for universal patterns or trends. It examines long time frames using a multidisciplinary approach ...
, electroweak symmetry breaking is believed to have happened at about after the
Big Bang The Big Bang is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models based on the Big Bang concept explain a broad range of phenomena, including th ...
, when the universe was at a temperature . This symmetry breaking is required for
atom Atoms are the basic particles of the chemical elements. An atom consists of a atomic nucleus, nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished fr ...
s and other structures to form, as well as for nuclear reactions in stars, such as the
Sun The Sun is the star at the centre of the Solar System. It is a massive, nearly perfect sphere of hot plasma, heated to incandescence by nuclear fusion reactions in its core, radiating the energy from its surface mainly as visible light a ...
. The Higgs field is responsible for this symmetry breaking.


Particle mass acquisition

The Higgs field is pivotal in generating the masses of
quark A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nucleus, atomic nuclei ...
s and charged leptons (through Yukawa coupling) and the W and Z gauge bosons (through the Higgs mechanism), although it was the generation of mass for the weak bosons which is the most significant factor – providing terms in the Standard Model Lagrangian that allow for the generation of fermion masses, was a useful, but less significant by product. The fermion masses must be entered by hand, essentially determining the relative strength of the coupling of the fermion to the Higgs field. The Higgs field does not "create" mass out of nothing, nor is the Higgs field responsible for the mass of all particles. For example, approximately 99% of the mass of
baryon In particle physics, a baryon is a type of composite particle, composite subatomic particle that contains an odd number of valence quarks, conventionally three. proton, Protons and neutron, neutrons are examples of baryons; because baryons are ...
s (
composite particle This is a list of known and hypothesized microscopic particles in particle physics, condensed matter physics and cosmology. Standard Model elementary particles Elementary particles are particles with no measurable internal structure; that is, ...
s such as the
proton A proton is a stable subatomic particle, symbol , Hydron (chemistry), H+, or 1H+ with a positive electric charge of +1 ''e'' (elementary charge). Its mass is slightly less than the mass of a neutron and approximately times the mass of an e ...
and
neutron The neutron is a subatomic particle, symbol or , that has no electric charge, and a mass slightly greater than that of a proton. The Discovery of the neutron, neutron was discovered by James Chadwick in 1932, leading to the discovery of nucle ...
), is due instead to quantum chromodynamic binding energy, which is the sum of the kinetic energies of quarks and the energies of the massless
gluon A gluon ( ) is a type of Massless particle, massless elementary particle that mediates the strong interaction between quarks, acting as the exchange particle for the interaction. Gluons are massless vector bosons, thereby having a Spin (physi ...
s mediating the
strong interaction In nuclear physics and particle physics, the strong interaction, also called the strong force or strong nuclear force, is one of the four known fundamental interaction, fundamental interactions. It confines Quark, quarks into proton, protons, n ...
inside the baryons. In Higgs-based theories, the property of "mass" is a manifestation of
potential energy In physics, potential energy is the energy of an object or system due to the body's position relative to other objects, or the configuration of its particles. The energy is equal to the work done against any restoring forces, such as gravity ...
transferred to fundamental particles when they interact ("couple") with the Higgs field.


Scalar fields and extension of the Standard Model

The Higgs field is the only scalar (spin-0) field to be detected; all the other fundamental fields in the Standard Model are spin-
fermions In particle physics, a fermion is a subatomic particle that follows Fermi–Dirac statistics. Fermions have a half-integer spin ( spin , spin , etc.) and obey the Pauli exclusion principle. These particles include all quarks and leptons and ...
or spin-1 bosons. According to Rolf-Dieter Heuer, director general of CERN when the Higgs boson was discovered, this existence proof of a scalar field is almost as important as the Higgs's role in determining the mass of other particles. It suggests that other hypothetical scalar fields suggested by other theories, from the inflaton to quintessence, could perhaps exist as well.


Cosmology


Inflaton

There has been considerable scientific research on possible links between the Higgs field and the inflatona hypothetical field suggested as the explanation for the expansion of space during the first fraction of a second of the
universe The universe is all of space and time and their contents. It comprises all of existence, any fundamental interaction, physical process and physical constant, and therefore all forms of matter and energy, and the structures they form, from s ...
(known as the "
inflationary epoch __NOTOC__ In physical cosmology, the inflationary epoch was the period in the evolution of the early universe when, according to inflation theory, the universe underwent an extremely rapid exponential expansion. This rapid expansion increased th ...
"). Some theories suggest that a fundamental scalar field might be responsible for this phenomenon; the Higgs field is such a field, and its existence has led to papers analysing whether it could also be the ''inflaton'' responsible for this
exponential Exponential may refer to any of several mathematical topics related to exponentiation, including: * Exponential function, also: **Matrix exponential, the matrix analogue to the above *Exponential decay, decrease at a rate proportional to value * Ex ...
expansion of the universe during the
Big Bang The Big Bang is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models based on the Big Bang concept explain a broad range of phenomena, including th ...
. Such theories are highly tentative and face significant problems related to unitarity, but may be viable if combined with additional features such as large non-minimal coupling, a Brans–Dicke scalar, or other "new" physics, and they have received treatments suggesting that Higgs inflation models are still of interest theoretically.


Nature of the universe, and its possible fates

In the Standard Model, there exists the possibility that the underlying state of our universe – known as the "vacuum" – is long-lived, but not completely stable. In this scenario, the universe as we know it could effectively be destroyed by collapsing into a more stable vacuum state. This was sometimes misreported as the Higgs boson "ending" the universe. If the masses of the Higgs boson and
top quark The top quark, sometimes also referred to as the truth quark, (symbol: t) is the most massive of all observed elementary particles. It derives its mass from its coupling to the Higgs field. This coupling is very close to unity; in the Standard ...
are known more precisely, and the Standard Model provides an accurate description of particle physics up to extreme energies of the
Planck scale In particle physics and physical cosmology, Planck units are a system of units of measurement defined exclusively in terms of four universal physical constants: '' c'', '' G'', '' ħ'', and ''k''B (described further below). Expressing one of ...
, then it is possible to calculate whether the vacuum is stable or merely long-lived. A Higgs mass of seems to be extremely close to the boundary for stability, but a definitive answer requires much more precise measurements of the pole mass of the top quark. New physics can change this picture. If measurements of the Higgs boson suggest that our universe lies within a false vacuum of this kind, then it would implymore than likely in many billions of years The article quotes
Fermilab Fermi National Accelerator Laboratory (Fermilab), located in Batavia, Illinois, near Chicago, is a United States Department of Energy United States Department of Energy National Labs, national laboratory specializing in high-energy particle phys ...
's Joseph Lykken: " e parameters for our universe, including the Higgs nd top quark's massessuggest that we're just at the edge of stability, in a "metastable" state. Physicists have been contemplating such a possibility for more than 30 years. Back in 1982, physicists Michael Turner and Frank Wilczek wrote in ''Nature'' that "without warning, a bubble of true vacuum could nucleate somewhere in the universe and move outwards ..."
that the universe's forces, particles, and structures could cease to exist as we know them (and be replaced by different ones), if a true vacuum happened to nucleate. It also suggests that the Higgs self-coupling and its function could be very close to zero at the Planck scale, with "intriguing" implications, including theories of gravity and Higgs-based inflation. A future electron–positron collider would be able to provide the precise measurements of the top quark needed for such calculations.


Vacuum energy and the cosmological constant

More speculatively, the Higgs field has also been proposed as the energy of the vacuum, which at the extreme energies of the first moments of the
Big Bang The Big Bang is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models based on the Big Bang concept explain a broad range of phenomena, including th ...
caused the universe to be a kind of featureless symmetry of undifferentiated, extremely high energy. In this kind of speculation, the single unified field of a
Grand Unified Theory A Grand Unified Theory (GUT) is any Mathematical model, model in particle physics that merges the electromagnetism, electromagnetic, weak interaction, weak, and strong interaction, strong fundamental interaction, forces (the three gauge theory, ...
is identified as (or modelled upon) the Higgs field, and it is through successive symmetry breakings of the Higgs field, or some similar field, at
phase transition In physics, chemistry, and other related fields like biology, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic Sta ...
s that the presently known forces and fields of the universe arise. The relationship (if any) between the Higgs field and the presently observed vacuum energy density of the universe has also come under scientific study. As observed, the present vacuum energy density is extremely close to zero, but the energy densities predicted from the Higgs field, supersymmetry, and other current theories are typically many orders of magnitude larger. It is unclear how these should be reconciled. This
cosmological constant In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: ), alternatively called Einstein's cosmological constant, is a coefficient that Albert Einstein initially added to his field equations of general rel ...
problem remains a major unanswered problem in physics.


History


Theorisation

Particle physicists study
matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic pa ...
made from fundamental particles whose interactions are mediated by exchange particles
gauge boson In particle physics, a gauge boson is a bosonic elementary particle that acts as the force carrier for elementary fermions. Elementary particles whose interactions are described by a gauge theory interact with each other by the exchange of gauge ...
sacting as
force carrier In quantum field theory, a force carrier is a type of particle that gives rise to forces between other particles. They serve as the quanta of a particular kind of physical field. Force carriers are also known as messenger particles, intermedia ...
s. At the beginning of the 1960s a number of these particles had been discovered or proposed, along with theories suggesting how they relate to each other, some of which had already been reformulated as field theories in which the objects of study are not particles and forces, but quantum fields and their
symmetries Symmetry () in everyday life refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is invariant under some transformations ...
. However, attempts to produce quantum field models for two of the four known
fundamental forces In physics, the fundamental interactions or fundamental forces are interactions in nature that appear not to be reducible to more basic interactions. There are four fundamental interactions known to exist: * gravity * electromagnetism * weak int ...
– the
electromagnetic force In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interac ...
and the weak nuclear force – and then to unify these interactions, were still unsuccessful. One known problem was that gauge invariant approaches, including non-abelian models such as
Yang–Mills theory Yang–Mills theory is a quantum field theory for nuclear binding devised by Chen Ning Yang and Robert Mills in 1953, as well as a generic term for the class of similar theories. The Yang–Mills theory is a gauge theory based on a special un ...
(1954), which held great promise for unified theories, also seemed to predict known massive particles as massless.
Goldstone's theorem In physics, Goldstone bosons or Nambu–Goldstone bosons (NGBs) are bosons that appear necessarily in models exhibiting spontaneous breakdown of continuous symmetries. They were discovered by Yoichiro Nambu within the context of the BCS superc ...
, relating to continuous symmetries within some theories, also appeared to rule out many obvious solutions, since it appeared to show that zero-mass particles known as
Goldstone boson In physics, Goldstone bosons or Nambu–Goldstone bosons (NGBs) are bosons that appear necessarily in models exhibiting spontaneous breakdown of continuous symmetries. They were discovered by Yoichiro Nambu within the context of the BCS superco ...
s would also have to exist that simply were "not seen". According to Guralnik, physicists had "no understanding" how these problems could be overcome. Particle physicist and mathematician Peter Woit summarised the state of research at the time: The Higgs mechanism is a process by which
vector boson In particle physics, a vector boson is a boson whose spin equals one. Vector bosons that are also elementary particles are gauge bosons, the force carriers of fundamental interactions. Some composite particles are vector bosons, for instance any ...
s can acquire
rest mass The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an object or system of objects that is independent of the overall motion of the system. More precisely, ...
''without'' explicitly breaking gauge invariance, as a byproduct of
spontaneous symmetry breaking Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state spontaneously ends up in an asymmetric state. In particular, it can describe systems where the equations of motion o ...
. Initially, the mathematical theory behind spontaneous symmetry breaking was conceived and published within particle physics by
Yoichiro Nambu was a Japanese-American physicist and professor at the University of Chicago. Known for his groundbreaking contributions to theoretical physics, Nambu was the originator of the theory of spontaneous symmetry breaking, a concept that revoluti ...
in 1960 (and somewhat anticipated by Ernst Stueckelberg in 1938), and the concept that such a mechanism could offer a possible solution for the "mass problem" was originally suggested in 1962 by Philip Anderson, who had previously written papers on broken symmetry and its outcomes in superconductivity. Anderson concluded in his 1963 paper on the Yang–Mills theory, that "considering the superconducting analog ... ese two types of bosons seem capable of canceling each other out ... leaving finite mass bosons"),Talk given by Peter Higgs at King's College, London, England, expanding on a paper originally presented in 2001. The original 2001 paper may be found in: and in March 1964, Abraham Klein and Benjamin Lee showed that Goldstone's theorem could be avoided this way in at least some non-relativistic cases, and speculated it might be possible in truly relativistic cases. These approaches were quickly developed into a full relativistic model, independently and almost simultaneously, by three groups of physicists: by
François Englert François, Baron Englert (; born 6 November 1932) is a Belgian theoretical physicist and 2013 Nobel Prize laureate. Englert is professor emeritus at the Université libre de Bruxelles (ULB), where he is a member of the Service de Physique Thé ...
and Robert Brout in August 1964; by
Peter Higgs Peter Ware Higgs (29 May 1929 – 8 April 2024) was a British theoretical physicist, professor at the University of Edinburgh,Griggs, Jessica (Summer 2008The Missing Piece ''Edit'' the University of Edinburgh Alumni Magazine, p. 17 and Nobel ...
in October 1964; and by Gerald Guralnik, Carl Hagen, and Tom Kibble (GHK) in November 1964. Higgs also wrote a short, but important, response published in September 1964 to an objection by Gilbert, which showed that if calculating within the radiation gauge, Goldstone's theorem and Gilbert's objection would become inapplicable. Higgs later described Gilbert's objection as prompting his own paper. Properties of the model were further considered by Guralnik in 1965, by Higgs in 1966, by Kibble in 1967, and further by GHK in 1967. The original three 1964 papers demonstrated that when a
gauge theory In physics, a gauge theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, does not change under local transformations according to certain smooth families of operations (Lie groups). Formally, t ...
is combined with an additional charged scalar field that spontaneously breaks the symmetry, the gauge bosons may consistently acquire a finite mass. In 1967,
Steven Weinberg Steven Weinberg (; May 3, 1933 – July 23, 2021) was an American theoretical physicist and Nobel laureate in physics for his contributions with Abdus Salam and Sheldon Glashow to the unification of the weak force and electromagnetic inter ...
and
Abdus Salam Mohammad Abdus Salam Salam adopted the forename "Mohammad" in 1974 in response to the anti-Ahmadiyya decrees in Pakistan, similarly he grew his beard. (; ; 29 January 192621 November 1996) was a Pakistani theoretical physicist. He shared the 1 ...
independently showed how a Higgs mechanism could be used to break the electroweak symmetry of Sheldon Glashow's unified model for the weak and electromagnetic interactions, (itself an extension of work by Schwinger), forming what became the
Standard Model The Standard Model of particle physics is the Scientific theory, theory describing three of the four known fundamental forces (electromagnetism, electromagnetic, weak interaction, weak and strong interactions – excluding gravity) in the unive ...
of particle physics. Weinberg was the first to observe that this would also provide mass terms for the fermions. At first, these seminal papers on spontaneous breaking of gauge symmetries were largely ignored, because it was widely believed that the (non-Abelian gauge) theories in question were a dead-end, and in particular that they could not be renormalised. In 1971–72,
Martinus Veltman Martinus Justinus Godefriedus "Tini" Veltman (; 27 June 1931 – 4 January 2021) was a Dutch theoretical physicist. He shared the 1999 Nobel Prize in Physics with his former PhD student Gerardus 't Hooft for their work on particle theory. Bio ...
and
Gerard 't Hooft Gerardus "Gerard" 't Hooft (; born July 5, 1946) is a Dutch theoretical physicist and professor at Utrecht University, the Netherlands. He shared the 1999 Nobel Prize in Physics with his thesis advisor Martinus J. G. Veltman "for elucidating t ...
proved renormalisation of Yang–Mills was possible in two papers covering massless, and then massive, fields. Their contribution, and the work of others on the renormalisation groupincluding "substantial" theoretical work by Russian physicists
Ludvig Faddeev Ludvig Dmitrievich Faddeev (also ''Ludwig Dmitriyevich''; ; 23 March 1934 – 26 February 2017) was a Soviet Union, Soviet and Russian Mathematical physics, mathematical physicist. He is known for the discovery of the Faddeev equations in the qu ...
, Andrei Slavnov, Efim Fradkin, and Igor Tyutinwas eventually "enormously profound and influential", but even with all key elements of the eventual theory published there was still almost no wider interest. For example,
Coleman Coleman may refer to: Places Antarctica * Coleman Glacier (Antarctica) * Coleman Peak, Ross Island Canada * Coleman, Alberta * Coleman, Ontario * Coleman, Prince Edward Island United Kingdom * Coleman, Leicester, England United States * C ...
found in a study that "essentially no-one paid any attention" to Weinberg's paper prior to 1971 and discussed by
David Politzer Hugh David Politzer (; born August 31, 1949) is an American theoretical physicist Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and pred ...
in his 2004 Nobel speech.now the most cited in particle physics
span>. Letters from the PastA PRL Retrospective (50 year celebration, 2008).
and even in 1970 according to Politzer, Glashow's teaching of the weak interaction contained no mention of Weinberg's, Salam's, or Glashow's own work. In practice, Politzer states, almost everyone learned of the theory due to physicist Benjamin Lee, who combined the work of Veltman and 't Hooft with insights by others, and popularised the completed theory. In this way, from 1971, interest and acceptance "exploded" and the ideas were quickly absorbed in the mainstream. The resulting electroweak theory and Standard Model have Standard Model#Tests and predictions, accurately predicted (among other things) weak neutral currents, three bosons, the
top Top most commonly refers to: * Top, a basic term of orientation, distinguished from bottom, front, back, and sides * Spinning top, a ubiquitous traditional toy * Top (clothing), clothing designed to be worn over the torso * Mountain top, a moun ...
and
charm quark The charm quark, charmed quark, or c quark is an elementary particle found in composite subatomic particles called hadrons such as the J/psi meson and the charmed baryons created in particle accelerator collisions. Several bosons, including th ...
s, and with great precision, the mass and other properties of some of these. Many of those involved eventually won Nobel Prizes or other renowned awards. A 1974 paper and comprehensive review in ''
Reviews of Modern Physics ''Reviews of Modern Physics'' (often abbreviated RMP) is a quarterly Peer review, peer-reviewed scientific journal published by the American Physical Society. It was established in 1929 and the current editor-in-chief is Michael Thoennessen. The jo ...
'' commented that "while no one doubted the athematicalcorrectness of these arguments, no one quite believed that nature was diabolically clever enough to take advantage of them", adding that the theory had so far produced accurate answers that accorded with experiment, but it was unknown whether the theory was fundamentally correct. By 1986 and again in the 1990s it became possible to write that understanding and proving the Higgs sector of the Standard Model was "the central problem today in particle physics". Cited by Peter Higgs in his talk "My Life as a Boson", 2001, ref#25.


Summary and impact of the PRL papers

The three papers written in 1964 were each recognised as milestone papers during ''
Physical Review Letters ''Physical Review Letters'' (''PRL''), established in 1958, is a peer-reviewed, scientific journal that is published 52 times per year by the American Physical Society. The journal is considered one of the most prestigious in the field of physics ...
'' 50th anniversary celebration. Their six authors were also awarded the 2010 J. J. Sakurai Prize for Theoretical Particle Physics for this work.American Physical Society (A controversy also arose the same year, because in the event of a Nobel Prize only up to three scientists could be recognised, with six being credited for the papers.) Two of the three PRL papers (by Higgs and by GHK) contained equations for the hypothetical field that eventually would become known as the Higgs field and its hypothetical
quantum In physics, a quantum (: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a property can be "quantized" is referred to as "the hypothesis of quantization". This me ...
, the Higgs boson. Higgs's subsequent 1966 paper showed the decay mechanism of the boson; only a massive boson can decay and the decays can prove the mechanism. In the paper by Higgs the boson is massive, and in a closing sentence Higgs writes that "an essential feature" of the theory "is the prediction of incomplete multiplets of scalar and
vector boson In particle physics, a vector boson is a boson whose spin equals one. Vector bosons that are also elementary particles are gauge bosons, the force carriers of fundamental interactions. Some composite particles are vector bosons, for instance any ...
s". ( Frank Close comments that 1960s gauge theorists were focused on the problem of massless ''vector'' bosons, and the implied existence of a massive ''scalar'' boson was not seen as important; only Higgs directly addressed it.) In the paper by GHK the boson is massless and decoupled from the massive states. In reviews dated 2009 and 2011, Guralnik states that in the GHK model the boson is massless only in a lowest-order approximation, but it is not subject to any constraint and acquires mass at higher orders, and adds that the GHK paper was the only one to show that there are no massless
Goldstone boson In physics, Goldstone bosons or Nambu–Goldstone bosons (NGBs) are bosons that appear necessarily in models exhibiting spontaneous breakdown of continuous symmetries. They were discovered by Yoichiro Nambu within the context of the BCS superco ...
s in the model and to give a complete analysis of the general Higgs mechanism. All three reached similar conclusions, despite their very different approaches: Higgs's paper essentially used classical techniques, Englert and Brout's involved calculating vacuum polarisation in perturbation theory around an assumed symmetry-breaking vacuum state, and GHK used operator formalism and conservation laws to explore in depth the ways in which Goldstone's theorem was avoided. Some versions of the theory predicted more than one kind of Higgs fields and bosons, and alternative "Higgsless" models were considered until the discovery of the Higgs boson.


Experimental search

To produce Higgs bosons, two beams of particles are accelerated to very high energies and allowed to collide within a
particle detector In experimental and applied particle physics, nuclear physics, and nuclear engineering, a particle detector, also known as a radiation detector, is a device used to detect, track, and/or identify ionizing elementary particle, particles, such as t ...
. Occasionally, although rarely, a Higgs boson will be created fleetingly as part of the collision byproducts. Because the Higgs boson decays very quickly, particle detectors cannot detect it directly. Instead the detectors register all the decay products (the ''decay signature'') and from the data the decay process is reconstructed. If the observed decay products match a possible decay process (known as a ''decay channel'') of a Higgs boson, this indicates that a Higgs boson may have been created. In practice, many processes may produce similar decay signatures. Fortunately, the Standard Model precisely predicts the likelihood of each of these, and each known process, occurring. So, if the detector detects more decay signatures consistently matching a Higgs boson than would otherwise be expected if Higgs bosons did not exist, then this would be strong evidence that the Higgs boson exists. Because Higgs boson production in a particle collision is likely to be very rare (1 in 10 billion at the LHC), and many other possible collision events can have similar decay signatures, the data of hundreds of trillions of collisions needs to be analysed and must "show the same picture" before a conclusion about the existence of the Higgs boson can be reached. To conclude that a new particle has been found,
particle physicist Particle physics or high-energy physics is the study of fundamental particles and fundamental interaction, forces that constitute matter and radiation. The field also studies combinations of elementary particles up to the scale of protons and ...
s require that the
statistical analysis Statistical inference is the process of using data analysis to infer properties of an underlying probability distribution.Upton, G., Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP. . Inferential statistical analysis infers properties of ...
of two independent particle detectors each indicate that there is less than a one-in-a-million chance that the observed decay signatures are due to just background random Standard Model eventsi.e., that the observed number of events is more than five
standard deviation In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its Expected value, mean. A low standard Deviation (statistics), deviation indicates that the values tend to be close to the mean ( ...
s (sigma) different from that expected if there was no new particle. More collision data allows better confirmation of the physical properties of any new particle observed, and allows physicists to decide whether it is indeed a Higgs boson as described by the Standard Model or some other hypothetical new particle. To find the Higgs boson, a powerful
particle accelerator A particle accelerator is a machine that uses electromagnetic fields to propel electric charge, charged particles to very high speeds and energies to contain them in well-defined particle beam, beams. Small accelerators are used for fundamental ...
was needed, because Higgs bosons might not be seen in lower-energy experiments. The collider needed to have a high
luminosity Luminosity is an absolute measure of radiated electromagnetic radiation, electromagnetic energy per unit time, and is synonymous with the radiant power emitted by a light-emitting object. In astronomy, luminosity is the total amount of electroma ...
in order to ensure enough collisions were seen for conclusions to be drawn. Finally, advanced computing facilities were needed to process the vast amount of data (25 
petabyte The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable un ...
s per year as of 2012) produced by the collisions. For the announcement of 4 July 2012, a new collider known as the
Large Hadron Collider The Large Hadron Collider (LHC) is the world's largest and highest-energy particle accelerator. It was built by the CERN, European Organization for Nuclear Research (CERN) between 1998 and 2008, in collaboration with over 10,000 scientists, ...
was constructed at
CERN The European Organization for Nuclear Research, known as CERN (; ; ), is an intergovernmental organization that operates the largest particle physics laboratory in the world. Established in 1954, it is based in Meyrin, western suburb of Gene ...
with a planned eventual collision energy of 14  TeVover seven times any previous colliderand over 300 trillion () LHC proton–proton collisions were analysed by the LHC Computing Grid, the world's largest computing grid (as of 2012), comprising over 170 computing facilities in a worldwide network across 36 countries.


Search before 4 July 2012

The first extensive search for the Higgs boson was conducted at the
Large Electron–Positron Collider The Large Electron–Positron Collider (LEP) was one of the largest particle accelerators ever constructed. It was built at CERN, a multi-national centre for research in nuclear and particle physics near Geneva, Switzerland. LEP collided electr ...
(LEP) at CERN in the 1990s. At the end of its service in 2000, LEP had found no conclusive evidence for the Higgs. This implied that if the Higgs boson were to exist it would have to be heavier than . The search continued at
Fermilab Fermi National Accelerator Laboratory (Fermilab), located in Batavia, Illinois, near Chicago, is a United States Department of Energy United States Department of Energy National Labs, national laboratory specializing in high-energy particle phys ...
in the United States, where the
Tevatron The Tevatron was a circular particle accelerator (active until 2011) in the United States, at the Fermilab, Fermi National Accelerator Laboratory (called ''Fermilab''), east of Batavia, Illinois, and was the highest energy particle collider unt ...
the collider that discovered the
top quark The top quark, sometimes also referred to as the truth quark, (symbol: t) is the most massive of all observed elementary particles. It derives its mass from its coupling to the Higgs field. This coupling is very close to unity; in the Standard ...
in 1995 – had been upgraded for this purpose. There was no guarantee that the Tevatron would be able to find the Higgs, but it was the only supercollider that was operational since the
Large Hadron Collider The Large Hadron Collider (LHC) is the world's largest and highest-energy particle accelerator. It was built by the CERN, European Organization for Nuclear Research (CERN) between 1998 and 2008, in collaboration with over 10,000 scientists, ...
(LHC) was still under construction and the planned Superconducting Super Collider had been cancelled in 1993 and never completed. The Tevatron was only able to exclude further ranges for the Higgs mass, and was shut down on 30 September 2011 because it no longer could keep up with the LHC. The final analysis of the data excluded the possibility of a Higgs boson with a mass between and . In addition, there was a small (but not significant) excess of events possibly indicating a Higgs boson with a mass between and . The
Large Hadron Collider The Large Hadron Collider (LHC) is the world's largest and highest-energy particle accelerator. It was built by the CERN, European Organization for Nuclear Research (CERN) between 1998 and 2008, in collaboration with over 10,000 scientists, ...
at
CERN The European Organization for Nuclear Research, known as CERN (; ; ), is an intergovernmental organization that operates the largest particle physics laboratory in the world. Established in 1954, it is based in Meyrin, western suburb of Gene ...
in Switzerland, was designed specifically to be able to either confirm or exclude the existence of the Higgs boson. Built in a 27 km tunnel under the ground near
Geneva Geneva ( , ; ) ; ; . is the List of cities in Switzerland, second-most populous city in Switzerland and the most populous in French-speaking Romandy. Situated in the southwest of the country, where the Rhône exits Lake Geneva, it is the ca ...
originally inhabited by LEP, it was designed to collide two beams of protons, initially at energies of per beam (7 TeV total), or almost 3.6 times that of the Tevatron, and upgradeable to (14 TeV total) in future. Theory suggested if the Higgs boson existed, collisions at these energy levels should be able to reveal it. As one of the most complicated scientific instruments ever built, its operational readiness was delayed for 14 months by a magnet quench event nine days after its inaugural tests, caused by a faulty electrical connection that damaged over 50 superconducting magnets and contaminated the vacuum system. Data collection at the LHC finally commenced in March 2010. By December 2011 the two main particle detectors at the LHC,
ATLAS An atlas is a collection of maps; it is typically a bundle of world map, maps of Earth or of a continent or region of Earth. Advances in astronomy have also resulted in atlases of the celestial sphere or of other planets. Atlases have traditio ...
and CMS, had narrowed down the mass range where the Higgs could exist to around (ATLAS) and (CMS). There had also already been a number of promising event excesses that had "evaporated" and proven to be nothing but random fluctuations. However, from around May 2011, both experiments had seen among their results, the slow emergence of a small yet consistent excess of gamma and 4-lepton decay signatures and several other particle decays, all hinting at a new particle at a mass around . By around November 2011, the anomalous data at was becoming "too large to ignore" (although still far from conclusive), and the team leaders at both ATLAS and CMS each privately suspected they might have found the Higgs. On 28 November 2011, at an internal meeting of the two team leaders and the director general of CERN, the latest analyses were discussed outside their teams for the first time, suggesting both ATLAS and CMS might be converging on a possible shared result at , and initial preparations commenced in case of a successful finding. While this information was not known publicly at the time, the narrowing of the possible Higgs range to around and the repeated observation of small but consistent event excesses across multiple channels at both ATLAS and CMS in the region (described as "tantalising hints" of around 2–3 sigma) were public knowledge with "a lot of interest". It was therefore widely anticipated around the end of 2011, that the LHC would provide sufficient data to either exclude or confirm the finding of a Higgs boson by the end of 2012, when their 2012 collision data (with slightly higher 8 TeV collision energy) had been examined.


Discovery of candidate boson at CERN

On 22 June 2012
CERN The European Organization for Nuclear Research, known as CERN (; ; ), is an intergovernmental organization that operates the largest particle physics laboratory in the world. Established in 1954, it is based in Meyrin, western suburb of Gene ...
announced an upcoming seminar covering tentative findings for 2012, and shortly afterwards (from around 1 July 2012 according to an analysis of the spreading rumour in social media) rumours began to spread in the media that this would include a major announcement, but it was unclear whether this would be a stronger signal or a formal discovery. Speculation escalated to a "fevered" pitch when reports emerged that
Peter Higgs Peter Ware Higgs (29 May 1929 – 8 April 2024) was a British theoretical physicist, professor at the University of Edinburgh,Griggs, Jessica (Summer 2008The Missing Piece ''Edit'' the University of Edinburgh Alumni Magazine, p. 17 and Nobel ...
, who proposed the particle, was to be attending the seminar, and that "five leading physicists" had been invitedgenerally believed to signify the five living 1964 authorswith Higgs, Englert, Guralnik, Hagen attending and Kibble confirming his invitation (Brout having died in 2011). On 4 July 2012 both of the CERN experiments announced they had independently made the same discovery: CMS of a previously unknown boson with mass and ATLAS of a boson with mass . Using the combined analysis of two interaction types (known as 'channels'), both experiments independently reached a local significance of 5 sigmaimplying that the probability of getting at least as strong a result by chance alone is less than one in three million. When additional channels were taken into account, the CMS significance was reduced to 4.9 sigma. The two teams had been working 'blinded' from each other from around late 2011 or early 2012, meaning they did not discuss their results with each other, providing additional certainty that any common finding was genuine validation of a particle. This level of evidence, confirmed independently by two separate teams and experiments, meets the formal level of proof required to announce a confirmed discovery. On 31 July 2012, the ATLAS collaboration presented additional data analysis on the "observation of a new particle", including data from a third channel, which improved the significance to 5.9 sigma (1 in 588 million chance of obtaining at least as strong evidence by random background effects alone) and mass , and CMS improved the significance to 5-sigma and mass .


New particle tested as a possible Higgs boson

Following the 2012 discovery, it was still unconfirmed whether the particle was a Higgs boson. On one hand, observations remained consistent with the observed particle being the Standard Model Higgs boson, and the particle decayed into at least some of the predicted channels. Moreover, the production rates and branching ratios for the observed channels broadly matched the predictions by the Standard Model within the experimental uncertainties. However, the experimental uncertainties currently still left room for alternative explanations, meaning an announcement of the discovery of a Higgs boson would have been premature. To allow more opportunity for data collection, the LHC's proposed 2012 shutdown and 2013–14 upgrade were postponed by seven weeks into 2013. In November 2012, in a conference in Kyoto researchers said evidence gathered since July was falling into line with the basic Standard Model more than its alternatives, with a range of results for several interactions matching that theory's predictions. Physicist Matt Strassler highlighted "considerable" evidence that the new particle is not a
pseudoscalar In linear algebra, a pseudoscalar is a quantity that behaves like a scalar, except that it changes sign under a parity inversion while a true scalar does not. A pseudoscalar, when multiplied by an ordinary vector, becomes a '' pseudovector'' ...
negative parity particle (consistent with this required finding for a Higgs boson), "evaporation" or lack of increased significance for previous hints of non-Standard Model findings, expected Standard Model interactions with
W and Z bosons In particle physics, the W and Z bosons are vector bosons that are together known as the weak bosons or more generally as the intermediate vector bosons. These elementary particles mediate the weak interaction; the respective symbols are , , an ...
, absence of "significant new implications" for or against
supersymmetry Supersymmetry is a Theory, theoretical framework in physics that suggests the existence of a symmetry between Particle physics, particles with integer Spin (physics), spin (''bosons'') and particles with half-integer spin (''fermions''). It propo ...
, and in general no significant deviations to date from the results expected of a Standard Model Higgs boson. However some kinds of extensions to the Standard Model would also show very similar results; so commentators noted that based on other particles that are still being understood long after their discovery, it may take years to be sure, and decades to fully understand the particle that has been found. These findings meant that as of January 2013, scientists were very sure they had found an unknown particle of mass ~ , and had not been misled by experimental error or a chance result. They were also sure, from initial observations, that the new particle was some kind of boson. The behaviours and properties of the particle, so far as examined since July 2012, also seemed quite close to the behaviours expected of a Higgs boson. Even so, it could still have been a Higgs boson or some other unknown boson, since future tests could show behaviours that do not match a Higgs boson, so as of December 2012 CERN still only stated that the new particle was "consistent with" the Higgs boson, and scientists did not yet positively say it was the Higgs boson. Despite this, in late 2012, widespread media reports announced (incorrectly) that a Higgs boson had been confirmed during the year. In January 2013, CERN director-general Rolf-Dieter Heuer stated that based on data analysis to date, an answer could be possible 'towards' mid-2013,Interview by AP, at the World Economic Forum, 26 January 2013. and the deputy chair of physics at
Brookhaven National Laboratory Brookhaven National Laboratory (BNL) is a United States Department of Energy national laboratories, United States Department of Energy national laboratory located in Upton, New York, a hamlet of the Brookhaven, New York, Town of Brookhaven. It w ...
stated in February 2013 that a "definitive" answer might require "another few years" after the collider's 2015 restart. In early March 2013, CERN Research Director Sergio Bertolucci stated that confirming spin-0 was the major remaining requirement to determine whether the particle is at least some kind of Higgs boson.


Confirmation of existence and current status

On 14 March 2013 CERN confirmed the following:
CMS and ATLAS have compared a number of options for the spin-parity of this particle, and these all prefer no spin and even parity wo fundamental criteria of a Higgs boson consistent with the Standard Model This, coupled with the measured interactions of the new particle with other particles, strongly indicates that it is a Higgs boson.
This also makes the particle the first elementary scalar particle to be discovered in nature. The following are examples of tests used to confirm that the discovered particle is the Higgs boson:


Findings since 2013

In July 2017, CERN confirmed that all measurements still agree with the predictions of the Standard Model, and called the discovered particle simply "the Higgs boson". As of 2019, the
Large Hadron Collider The Large Hadron Collider (LHC) is the world's largest and highest-energy particle accelerator. It was built by the CERN, European Organization for Nuclear Research (CERN) between 1998 and 2008, in collaboration with over 10,000 scientists, ...
has continued to produce findings that confirm the 2013 understanding of the Higgs field and particle. The LHC's experimental work since restarting in 2015 has included probing the Higgs field and boson to a greater level of detail, and confirming whether less common predictions were correct. In particular, exploration since 2015 has provided strong evidence of the predicted direct decay into
fermion In particle physics, a fermion is a subatomic particle that follows Fermi–Dirac statistics. Fermions have a half-integer spin (spin 1/2, spin , Spin (physics)#Higher spins, spin , etc.) and obey the Pauli exclusion principle. These particles i ...
s such as pairs of
bottom quark The bottom quark, beauty quark, or b quark, is an elementary particle of the third generation. It is a heavy quark with a charge of −  ''e''. All quarks are described in a similar way by electroweak interaction and quantum chromodynamic ...
s (3.6 ''σ'')described as an "important milestone" in understanding its short lifetime and other rare decaysand also to confirm decay into pairs of tau leptons (5.9 ''σ''). This was described by CERN as being "of paramount importance to establishing the coupling of the Higgs boson to leptons and represents an important step towards measuring its couplings to third generation fermions, the very heavy copies of the electrons and quarks, whose role in nature is a profound mystery". Published results as of 19 March 2018 at 13 TeV for ATLAS and CMS had their measurements of the Higgs mass at and respectively. In July 2018, the ATLAS and CMS experiments reported observing the Higgs boson decay into a pair of bottom quarks, which makes up approximately 60% of all of its decays.


Theoretical issues


Theoretical need for the Higgs

Gauge invariance is an important property of modern particle theories such as the
Standard Model The Standard Model of particle physics is the Scientific theory, theory describing three of the four known fundamental forces (electromagnetism, electromagnetic, weak interaction, weak and strong interactions – excluding gravity) in the unive ...
, partly due to its success in other areas of fundamental physics such as
electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interacti ...
and the
strong interaction In nuclear physics and particle physics, the strong interaction, also called the strong force or strong nuclear force, is one of the four known fundamental interaction, fundamental interactions. It confines Quark, quarks into proton, protons, n ...
(
quantum chromodynamics In theoretical physics, quantum chromodynamics (QCD) is the study of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type of ...
). However, before Sheldon Glashow extended the electroweak unification models in 1961, there were great difficulties in developing gauge theories for the weak nuclear force or a possible unified
electroweak interaction In particle physics, the electroweak interaction or electroweak force is the unified description of two of the fundamental interactions of nature: electromagnetism (electromagnetic interaction) and the weak interaction. Although these two force ...
.
Fermion In particle physics, a fermion is a subatomic particle that follows Fermi–Dirac statistics. Fermions have a half-integer spin (spin 1/2, spin , Spin (physics)#Higher spins, spin , etc.) and obey the Pauli exclusion principle. These particles i ...
s with a mass term would violate gauge symmetry and therefore cannot be gauge invariant. (This can be seen by examining the Dirac Lagrangian for a fermion in terms of left and right handed components; we find none of the spin-half particles could ever flip helicity as required for mass, so they must be massless.)
W and Z bosons In particle physics, the W and Z bosons are vector bosons that are together known as the weak bosons or more generally as the intermediate vector bosons. These elementary particles mediate the weak interaction; the respective symbols are , , an ...
are observed to have mass, but a boson mass term contains terms which clearly depend on the choice of gauge, and therefore these masses too cannot be gauge invariant. Therefore, it seems that ''none'' of the standard model fermions ''or'' bosons could "begin" with mass as an inbuilt property except by abandoning gauge invariance. If gauge invariance were to be retained, then these particles had to be acquiring their mass by some other mechanism or interaction. Additionally, solutions based on spontaneous symmetry breaking appeared to fail, seemingly an inevitable result of
Goldstone's theorem In physics, Goldstone bosons or Nambu–Goldstone bosons (NGBs) are bosons that appear necessarily in models exhibiting spontaneous breakdown of continuous symmetries. They were discovered by Yoichiro Nambu within the context of the BCS superc ...
. Because there is no potential energy cost to moving around the complex plane's "circular valley" responsible for spontaneous symmetry breaking, the resulting quantum excitation is pure kinetic energy, and therefore a massless boson ("Goldstone boson"), which in turn implies a new long range force. But no new long range forces or massless particles were detected either. So whatever was giving these particles their mass had to not "break" gauge invariance as the basis for other parts of the theories where it worked well, ''and'' had to not require or predict unexpected massless particles or long-range forces which did not actually seem to exist in nature. A solution to all of these overlapping problems came from the discovery of a previously unnoticed borderline case hidden in the mathematics of Goldstone's theorem, that under certain conditions it ''might'' theoretically be possible for a symmetry to be broken ''without'' disrupting gauge invariance and ''without'' any new massless particles or forces, and having "sensible" ( renormalisable) results mathematically. This became known as the
Higgs mechanism In the Standard Model of particle physics, the Higgs mechanism is essential to explain the Mass generation, generation mechanism of the property "mass" for gauge bosons. Without the Higgs mechanism, all bosons (one of the two classes of particles ...
. The Standard Model hypothesises a field which is responsible for this effect, called the Higgs field (symbol: \phi), which has the unusual property of a non-zero amplitude in its
ground state The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state ...
; i.e., a non-zero
vacuum expectation value In quantum field theory, the vacuum expectation value (VEV) of an operator is its average or expectation value in the vacuum. The vacuum expectation value of an operator O is usually denoted by \langle O\rangle. One of the most widely used exa ...
. It can have this effect because of its unusual "sombrero" shaped potential whose lowest "point" is not at its "centre". In simple terms, unlike all other known fields, the Higgs field requires ''less'' energy to have a non-zero value than a zero value, so it ends up having a non-zero value ''everywhere''. Below a certain extremely high energy level the existence of this non-zero vacuum expectation spontaneously breaks electroweak
gauge symmetry In physics, a gauge theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, does not change under local transformations according to certain smooth families of operations (Lie groups). Formally, t ...
which in turn gives rise to the Higgs mechanism and triggers the acquisition of mass by those particles interacting with the field. This effect occurs because
scalar field In mathematics and physics, a scalar field is a function associating a single number to each point in a region of space – possibly physical space. The scalar may either be a pure mathematical number ( dimensionless) or a scalar physical ...
components of the Higgs field are "absorbed" by the massive bosons as
degrees of freedom In many scientific fields, the degrees of freedom of a system is the number of parameters of the system that may vary independently. For example, a point in the plane has two degrees of freedom for translation: its two coordinates; a non-infinite ...
, and couple to the fermions via Yukawa coupling, thereby producing the expected mass terms. When symmetry breaks under these conditions, the
Goldstone boson In physics, Goldstone bosons or Nambu–Goldstone bosons (NGBs) are bosons that appear necessarily in models exhibiting spontaneous breakdown of continuous symmetries. They were discovered by Yoichiro Nambu within the context of the BCS superco ...
s that arise ''interact'' with the Higgs field (and with other particles capable of interacting with the Higgs field) instead of becoming new massless particles. The intractable problems of both underlying theories "neutralise" each other, and the residual outcome is that elementary particles acquire a consistent mass based on how strongly they interact with the Higgs field. It is the simplest known process capable of giving mass to the
gauge boson In particle physics, a gauge boson is a bosonic elementary particle that acts as the force carrier for elementary fermions. Elementary particles whose interactions are described by a gauge theory interact with each other by the exchange of gauge ...
s while remaining compatible with
gauge theories In physics, a gauge theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, does not change under local transformations according to certain smooth families of operations (Lie groups). Formally, t ...
. Its
quantum In physics, a quantum (: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a property can be "quantized" is referred to as "the hypothesis of quantization". This me ...
would be a
scalar boson A scalar boson is a boson whose spin equals zero. A ''boson'' is a particle whose wave function is symmetric under particle exchange and therefore follows Bose–Einstein statistics. The spin–statistics theorem implies that all bosons have a ...
, known as the Higgs boson.


Simple explanation of the theory, from its origins in superconductivity

The proposed Higgs mechanism arose as a result of theories proposed to explain observations in
superconductivity Superconductivity is a set of physical properties observed in superconductors: materials where Electrical resistance and conductance, electrical resistance vanishes and Magnetic field, magnetic fields are expelled from the material. Unlike an ord ...
. A superconductor does not allow penetration by external magnetic fields (the
Meissner effect In condensed-matter physics, the Meissner effect (or Meißner–Ochsenfeld effect) is the expulsion of a magnetic field from a superconductor during its transition to the superconducting state when it is cooled below the critical temperature. Th ...
). This strange observation implies that somehow, the electromagnetic field becomes short ranged during this phenomenon. Successful theories arose to explain this during the 1950s, first for fermions ( Ginzburg–Landau theory, 1950), and then for bosons (
BCS theory In physics, the Bardeen–Cooper–Schrieffer (BCS) theory (named after John Bardeen, Leon Cooper, and John Robert Schrieffer) is the first microscopic theory of superconductivity since Heike Kamerlingh Onnes's 1911 discovery. The theory descr ...
, 1957). In these theories, superconductivity is interpreted as arising from a charged condensate field. Initially, the condensate value does not have any preferred direction, implying it is scalar, but its phase is capable of defining a gauge, in gauge based field theories. To do this, the field must be charged. A charged scalar field must also be complex (or described another way, it contains at least two components, and a symmetry capable of rotating each into the other(s)). In naïve gauge theory, a gauge transformation of a condensate usually rotates the phase. But in these circumstances, it instead fixes a preferred choice of phase. However, it turns out that fixing the choice of gauge so that the condensate has the same phase everywhere also causes the electromagnetic field to gain an extra term. This extra term causes the electromagnetic field to become short range. Once attention was drawn to this theory within particle physics, the parallels were clear. A change of the usually long range electromagnetic field to become short ranged, within a gauge invariant theory, was exactly the needed effect sought for the weak force bosons (because a long range force has massless gauge bosons, and a short ranged force implies massive gauge bosons, suggesting that a result of this interaction is that the field's gauge bosons acquired mass, or a similar and equivalent effect). The features of a field required to do this were also quite well defined – it would have to be a charged scalar field, with at least two components, and complex in order to support a symmetry able to rotate these into each other.


Alternative models

The Minimal Standard Model as described above is the simplest known model for the Higgs mechanism with just one Higgs field. However, an extended Higgs sector with additional Higgs particle doublets or triplets is also possible, and many extensions of the Standard Model have this feature. The non-minimal Higgs sector favoured by theory are the two-Higgs-doublet models (2HDM), which predict the existence of a quintet of scalar particles: two CP-even neutral Higgs bosons h0 and H0, a CP-odd neutral Higgs boson A0, and two charged Higgs particles H±.
Supersymmetry Supersymmetry is a Theory, theoretical framework in physics that suggests the existence of a symmetry between Particle physics, particles with integer Spin (physics), spin (''bosons'') and particles with half-integer spin (''fermions''). It propo ...
("SUSY") also predicts relations between the Higgs-boson masses and the masses of the gauge bosons, and could accommodate a neutral Higgs boson. The key method to distinguish between these different models involves study of the particles' interactions ("coupling") and exact decay processes ("branching ratios"), which can be measured and tested experimentally in particle collisions. In the Type-I 2HDM model one Higgs doublet couples to up and down quarks, while the second doublet does not couple to quarks. This model has two interesting limits, in which the lightest Higgs couples to just fermions ("gauge- phobic") or just gauge bosons ("fermiophobic"), but not both. In the Type-II 2HDM model, one Higgs doublet only couples to up-type quarks, the other only couples to down-type quarks. The heavily researched
Minimal Supersymmetric Standard Model The Minimal Supersymmetric Standard Model (MSSM) is an extension to the Standard Model that realizes supersymmetry. MSSM is the minimal supersymmetrical model as it considers only "the inimumnumber of new particle states and new interactions ...
(MSSM) includes a Type-II 2HDM Higgs sector, so it could be disproven by evidence of a Type-I 2HDM Higgs. In other models the Higgs scalar is a composite particle. For example, in technicolour the role of the Higgs field is played by strongly bound pairs of fermions called techniquarks. Other models feature pairs of
top quark The top quark, sometimes also referred to as the truth quark, (symbol: t) is the most massive of all observed elementary particles. It derives its mass from its coupling to the Higgs field. This coupling is very close to unity; in the Standard ...
s (see top quark condensate). In yet other models, there is no Higgs field at all and the electroweak symmetry is broken using extra dimensions.


Further theoretical issues and hierarchy problem

The Standard Model leaves the mass of the Higgs boson as a
parameter A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when ...
to be measured, rather than a value to be calculated. This is seen as theoretically unsatisfactory, particularly as quantum corrections (related to interactions with
virtual particle A virtual particle is a theoretical transient particle that exhibits some of the characteristics of an ordinary particle, while having its existence limited by the uncertainty principle, which allows the virtual particles to spontaneously emer ...
s) should apparently cause the Higgs particle to have a mass immensely higher than that observed, but at the same time the Standard Model requires a mass of the order of to ensure unitarity (in this case, to unitarise longitudinal vector boson scattering). Reconciling these points appears to require explaining why there is an almost-perfect cancellation resulting in the visible mass of ~ , and it is not clear how to do this. Because the weak force is about 1032 times stronger than gravity, and (linked to this) the Higgs boson's mass is so much less than the Planck mass or the
grand unification energy The grand unification energy \Lambda_, or the GUT scale, is the energy level above which, it is believed, the electromagnetism, electromagnetic force, weak interaction, weak force, and strong interaction, strong force become equal in strength and un ...
, it appears that either there is some underlying connection or reason for these observations which is unknown and not described by the Standard Model, or some unexplained and extremely precise fine-tuning of parametershowever at present neither of these explanations is proven. This is known as a
hierarchy problem In theoretical physics, the hierarchy problem is the problem concerning the large discrepancy between aspects of the weak force and gravity. There is no scientific consensus on why, for example, the weak force is 1024 times stronger than gravi ...
. More broadly, the hierarchy problem amounts to the worry that a future theory of fundamental particles and interactions should not have excessive fine-tunings or unduly delicate cancellations, and should allow masses of particles such as the Higgs boson to be calculable. The problem is in some ways unique to spin-0 particles (such as the Higgs boson), which can give rise to issues related to quantum corrections that do not affect particles with spin. A number of solutions have been proposed, including
supersymmetry Supersymmetry is a Theory, theoretical framework in physics that suggests the existence of a symmetry between Particle physics, particles with integer Spin (physics), spin (''bosons'') and particles with half-integer spin (''fermions''). It propo ...
, conformal solutions and solutions via extra dimensions such as braneworld models. There are also issues of quantum triviality, which suggests that it may not be possible to create a consistent quantum field theory involving elementary scalar particles. Triviality constraints can be used to restrict or predict parameters such as the Higgs boson mass. This can also lead to a predictable Higgs mass in asymptotic safety scenarios.


Properties


Properties of the Higgs field

In the Standard Model, the Higgs field is a scalar tachyonic field''scalar'' meaning it does not transform under
Lorentz transformation In physics, the Lorentz transformations are a six-parameter family of Linear transformation, linear coordinate transformation, transformations from a Frame of Reference, coordinate frame in spacetime to another frame that moves at a constant vel ...
s, and ''tachyonic'' meaning the field (but not the particle) has imaginary mass, and in certain configurations must undergo
symmetry breaking In physics, symmetry breaking is a phenomenon where a disordered but Symmetry in quantum mechanics, symmetric state collapses into an ordered, but less symmetric state. This collapse is often one of many possible Bifurcation theory, bifurcatio ...
. It consists of four components: Two neutral ones and two charged component
fields Fields may refer to: Music *Fields (band), an indie rock band formed in 2006 * Fields (progressive rock band), a progressive rock band formed in 1971 * ''Fields'' (album), an LP by Swedish-based indie rock band Junip (2010) * "Fields", a song by ...
. Both of the charged components and one of the neutral fields are
Goldstone boson In physics, Goldstone bosons or Nambu–Goldstone bosons (NGBs) are bosons that appear necessarily in models exhibiting spontaneous breakdown of continuous symmetries. They were discovered by Yoichiro Nambu within the context of the BCS superco ...
s, which act as the longitudinal third-polarisation components of the massive W+, W, and Z bosons. The quantum of the remaining neutral component corresponds to (and is theoretically realised as) the massive Higgs boson. This component can interact with
fermions In particle physics, a fermion is a subatomic particle that follows Fermi–Dirac statistics. Fermions have a half-integer spin ( spin , spin , etc.) and obey the Pauli exclusion principle. These particles include all quarks and leptons and ...
via Yukawa coupling to give them mass as well. Mathematically, the Higgs field has imaginary mass and is therefore a ''tachyonic'' field. While
tachyon A tachyon () or tachyonic particle is a hypothetical particle that always travels Faster-than-light, faster than light. Physicists posit that faster-than-light particles cannot exist because they are inconsistent with the known Scientific law#L ...
s (
particle In the physical sciences, a particle (or corpuscle in older texts) is a small localized object which can be described by several physical or chemical properties, such as volume, density, or mass. They vary greatly in size or quantity, from s ...
s that move
faster than light Faster-than-light (superluminal or supercausal) travel and communication are the conjectural propagation of matter or information faster than the speed of light in vacuum (). The special theory of relativity implies that only particles with zero ...
) are a purely hypothetical concept, ''fields'' with imaginary mass have come to play an important role in modern physics. Under no circumstances do any excitations ever propagate faster than light in such theoriesthe presence or absence of a tachyonic mass has no effect whatsoever on the maximum velocity of signals (there is no violation of causality). Instead of faster-than-light particles, the imaginary mass creates an instability: Any configuration in which one or more field excitations are tachyonic must spontaneously decay, and the resulting configuration contains no physical tachyons. This process is known as
tachyon condensation Tachyon condensation is a process in particle physics in which a system can lower its potential energy by spontaneously producing particles. The end result is a "condensate" of particles that fills the volume of the system. Tachyon condensation is ...
, and is now believed to be the explanation for how the Higgs mechanism itself arises in nature, and therefore the reason behind electroweak symmetry breaking. Although the notion of imaginary mass might seem troubling, it is only the field, and not the mass itself, that is quantised. Therefore, the
field operator In physics, canonical quantization is a procedure for quantizing a classical theory, while attempting to preserve the formal structure, such as symmetries, of the classical theory to the greatest extent possible. Historically, this was not quit ...
s at
spacelike In mathematical physics, the causal structure of a Lorentzian manifold describes the possible causal relationships between points in the manifold. Lorentzian manifolds can be classified according to the types of causal structures they admit (''ca ...
separated points still commute (or anticommute), and information and particles still do not propagate faster than light. Tachyon condensation drives a physical system that has reached a local limitand might naively be expected to produce physical tachyonsto an alternate stable state where no physical tachyons exist. Once a tachyonic field such as the Higgs field reaches the minimum of the potential, its quanta are not tachyons any more but rather are ordinary particles such as the Higgs boson.


Properties of the Higgs boson

Since the Higgs field is scalar, the Higgs boson has no spin. The Higgs boson is also its own
antiparticle In particle physics, every type of particle of "ordinary" matter (as opposed to antimatter) is associated with an antiparticle with the same mass but with opposite physical charges (such as electric charge). For example, the antiparticle of the ...
, is CP-even, and has zero
electric Electricity is the set of physical phenomena associated with the presence and motion of matter possessing an electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by Maxwel ...
and colour charge. The Standard Model does not predict the mass of the Higgs boson. If that mass is between (consistent with empirical observations of ), then the Standard Model can be valid at energy scales all the way up to the
Planck scale In particle physics and physical cosmology, Planck units are a system of units of measurement defined exclusively in terms of four universal physical constants: '' c'', '' G'', '' ħ'', and ''k''B (described further below). Expressing one of ...
(). It should be the only particle in the Standard Model that remains massive even at high energies. Many theorists expect new
physics beyond the Standard Model Physics beyond the Standard Model (BSM) refers to the theoretical developments needed to explain the deficiencies of the Standard Model, such as the inability to explain the fundamental parameters of the standard model, the strong CP problem, neut ...
to emerge at the TeV-scale, based on unsatisfactory properties of the Standard Model. The highest possible mass scale allowed for the Higgs boson (or some other electroweak symmetry breaking mechanism) is 1.4 TeV; beyond this point, the Standard Model becomes inconsistent without such a mechanism, because unitarity is violated in certain scattering processes. It is also possible, although experimentally difficult, to estimate the mass of the Higgs boson indirectly: In the Standard Model, the Higgs boson has a number of indirect effects; most notably, Higgs loops result in tiny corrections to masses of the W and Z bosons. Precision measurements of electroweak parameters, such as the Fermi constant and masses of the W and Z bosons, can be used to calculate constraints on the mass of the Higgs. As of July 2011, the precision electroweak measurements tell us that the mass of the Higgs boson is likely to be less than about at 95% confidence level. These indirect constraints rely on the assumption that the Standard Model is correct. It may still be possible to discover a Higgs boson above these masses, if it is accompanied by other particles beyond those accommodated by the Standard Model. The LHC cannot directly measure the Higgs boson's lifetime, due to its extreme brevity. It is predicted as based on the predicted decay width of . However it can be measured indirectly, based upon comparing masses measured from quantum phenomena occurring in the on shell production pathways and in the, much rarer, off shell production pathways, derived from Dalitz decay via a virtual photon . Using this technique, the lifetime of the Higgs boson was tentatively measured in 2021 as , at sigma 3.2 (1 in 1000) significance.


Production

If Higgs particle theories are valid, then a Higgs particle can be produced much like other particles that are studied, in a particle collider. This involves accelerating a large number of particles to extremely high energies and extremely close to the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...
, then allowing them to smash together.
Proton A proton is a stable subatomic particle, symbol , Hydron (chemistry), H+, or 1H+ with a positive electric charge of +1 ''e'' (elementary charge). Its mass is slightly less than the mass of a neutron and approximately times the mass of an e ...
s and lead
ion An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by convent ...
s (the bare nuclei of lead
atom Atoms are the basic particles of the chemical elements. An atom consists of a atomic nucleus, nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished fr ...
s) are used at the LHC. In the extreme energies of these collisions, the desired esoteric particles will occasionally be produced and this can be detected and studied; any absence or difference from theoretical expectations can also be used to improve the theory. The relevant particle theory (in this case the Standard Model) will determine the necessary kinds of collisions and detectors. The Standard Model predicts that Higgs bosons could be formed in a number of ways, although the probability of producing a Higgs boson in any collision is always expected to be very smallfor example, only one Higgs boson per 10 billion collisions in the Large Hadron Collider. The most common expected processes for Higgs boson production are: ; Gluon fusion : If the collided particles are
hadron In particle physics, a hadron is a composite subatomic particle made of two or more quarks held together by the strong nuclear force. Pronounced , the name is derived . They are analogous to molecules, which are held together by the electri ...
s such as the
proton A proton is a stable subatomic particle, symbol , Hydron (chemistry), H+, or 1H+ with a positive electric charge of +1 ''e'' (elementary charge). Its mass is slightly less than the mass of a neutron and approximately times the mass of an e ...
or
antiproton The antiproton, , (pronounced ''p-bar'') is the antiparticle of the proton. Antiprotons are stable, but they are typically short-lived, since any collision with a proton will cause both particles to be annihilated in a burst of energy. The exis ...
as is the case in the LHC and Tevatronthen it is most likely that two of the
gluon A gluon ( ) is a type of Massless particle, massless elementary particle that mediates the strong interaction between quarks, acting as the exchange particle for the interaction. Gluons are massless vector bosons, thereby having a Spin (physi ...
s binding the hadron together collide. The easiest way to produce a Higgs particle is if the two gluons combine to form a loop of virtual quarks. Since the coupling of particles to the Higgs boson is proportional to their mass, this process is more likely for heavy particles. In practice it is enough to consider the contributions of virtual
top Top most commonly refers to: * Top, a basic term of orientation, distinguished from bottom, front, back, and sides * Spinning top, a ubiquitous traditional toy * Top (clothing), clothing designed to be worn over the torso * Mountain top, a moun ...
and bottom quarks (the heaviest quarks). This process is the dominant contribution at the LHC and Tevatron being about ten times more likely than any of the other processes. ; Higgs Strahlung : If an elementary
fermion In particle physics, a fermion is a subatomic particle that follows Fermi–Dirac statistics. Fermions have a half-integer spin (spin 1/2, spin , Spin (physics)#Higher spins, spin , etc.) and obey the Pauli exclusion principle. These particles i ...
collides with an anti-fermione.g., a quark with an anti-quark or an
electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...
with a
positron The positron or antielectron is the particle with an electric charge of +1''elementary charge, e'', a Spin (physics), spin of 1/2 (the same as the electron), and the same Electron rest mass, mass as an electron. It is the antiparticle (antimatt ...
the two can merge to form a virtual W or Z boson which, if it carries sufficient energy, can then emit a Higgs boson. This process was the dominant production mode at the LEP, where an electron and a positron collided to form a virtual Z boson, and it was the second largest contribution for Higgs production at the Tevatron. At the LHC this process is only the third largest, because the LHC collides protons with protons, making a quark-antiquark collision less likely than at the Tevatron. Higgs Strahlung is also known as ''associated production''. ; Weak boson fusion : Another possibility when two (anti-)fermions collide is that the two exchange a virtual W or Z boson, which emits a Higgs boson. The colliding fermions do not need to be the same type. So, for example, an
up quark The up quark or u quark (symbol: u) is the lightest of all quarks, a type of elementary particle, and a significant constituent of matter. It, along with the down quark, forms the neutrons (one up quark, two down quarks) and protons (two up quark ...
may exchange a Z boson with an anti-down quark. This process is the second most important for the production of Higgs particle at the LHC and LEP. ; Top fusion : The final process that is commonly considered is by far the least likely (by two orders of magnitude). This process involves two colliding gluons, which each decay into a heavy quark–antiquark pair. A quark and antiquark from each pair can then combine to form a Higgs particle.


Decay

Quantum mechanics predicts that if it is possible for a particle to decay into a set of lighter particles, then it will eventually do so. This is also true for the Higgs boson. The likelihood with which this happens depends on a variety of factors including: the difference in mass, the strength of the interactions, etc. Most of these factors are fixed by the Standard Model, except for the mass of the Higgs boson itself. For a Higgs boson with a mass of the SM predicts a mean life time of about . Since it interacts with all the massive elementary particles of the SM, the Higgs boson has many different processes through which it can decay. Each of these possible processes has its own probability, expressed as the ''branching ratio''; the fraction of the total number decays that follows that process. The SM predicts these branching ratios as a function of the Higgs mass (see plot). One way that the Higgs can decay is by splitting into a fermion–antifermion pair. As general rule, the Higgs is more likely to decay into heavy fermions than light fermions, because the mass of a fermion is proportional to the strength of its interaction with the Higgs. By this logic the most common decay should be into a
top Top most commonly refers to: * Top, a basic term of orientation, distinguished from bottom, front, back, and sides * Spinning top, a ubiquitous traditional toy * Top (clothing), clothing designed to be worn over the torso * Mountain top, a moun ...
–antitop quark pair. However, such a decay would only be possible if the Higgs were heavier than ~, twice the mass of the top quark. For a Higgs mass of the SM predicts that the most common decay is into a bottom–antibottom quark pair, which happens 57.7% of the time. The second most common fermion decay at that mass is a
tau Tau (; uppercase Τ, lowercase τ or \boldsymbol\tau; ) is the nineteenth letter of the Greek alphabet, representing the voiceless alveolar plosive, voiceless dental or alveolar plosive . In the system of Greek numerals, it has a value of 300 ...
–antitau pair, which happens only about 6.3% of the time. Another possibility is for the Higgs to split into a pair of massive gauge bosons. The most likely possibility is for the Higgs to decay into a pair of W bosons (the light blue line in the plot), which happens about 21.5% of the time for a Higgs boson with a mass of . The W bosons can subsequently decay either into a quark and an antiquark or into a charged lepton and a neutrino. The decays of W bosons into quarks are difficult to distinguish from the background, and the decays into leptons cannot be fully reconstructed (because neutrinos are impossible to detect in particle collision experiments). A cleaner signal is given by decay into a pair of Z-bosons (which happens about 2.6% of the time for a Higgs with a mass of ), if each of the bosons subsequently decays into a pair of easy-to-detect charged leptons (
electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...
s or
muon A muon ( ; from the Greek letter mu (μ) used to represent it) is an elementary particle similar to the electron, with an electric charge of −1 '' e'' and a spin of  ''ħ'', but with a much greater mass. It is classified as a ...
s). Decay into massless gauge bosons (i.e.,
gluon A gluon ( ) is a type of Massless particle, massless elementary particle that mediates the strong interaction between quarks, acting as the exchange particle for the interaction. Gluons are massless vector bosons, thereby having a Spin (physi ...
s or
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless particles that can ...
s) is also possible, but requires intermediate loop of virtual heavy quarks (top or bottom) or massive gauge bosons. The most common such process is the decay into a pair of gluons through a loop of virtual heavy quarks. This process, which is the reverse of the gluon fusion process mentioned above, happens approximately 8.6% of the time for a Higgs boson with a mass of . Much rarer is the decay into a pair of photons mediated by a loop of W bosons or heavy quarks, which happens only twice for every thousand decays. However, this process is very relevant for experimental searches for the Higgs boson, because the energy and momentum of the photons can be measured very precisely, giving an accurate reconstruction of the mass of the decaying particle. In 2021 the extremely rare Dalitz decay was tentatively observed, into two
lepton In particle physics, a lepton is an elementary particle of half-integer spin (Spin (physics), spin ) that does not undergo strong interactions. Two main classes of leptons exist: electric charge, charged leptons (also known as the electron-li ...
s (electrons or muons) and a photon (ℓℓγ), via
virtual photon Virtual photons are a fundamental concept in particle physics and quantum field theory that play a crucial role in describing the interactions between electrically charged particles. Virtual photons are referred to as " virtual" because they do no ...
decay. This can happen in three ways; Higgs to virtual photon to ℓℓγ in which the virtual photon (γ*) has very small but nonzero mass, Higgs to Z boson to ℓℓγ, or Higgs to two leptons, one of which emits a final-state photon leading to ℓℓγ. ATLAS searched for evidence of the first of these at low di-lepton mass , where this process should dominate. The observation is at sigma 3.2 (1 in 1000) significance. This decay path is important because it facilitates measuring the on- and off-shell mass of the Higgs boson (allowing indirect measurement of decay time), and the decay into two charged particles allows exploration of
charge conjugation In physics, charge conjugation is a transformation that switches all particles with their corresponding antiparticles, thus changing the sign of all charges: not only electric charge but also the charges relevant to other forces. The term C- ...
and charge parity (CP) violation.


Public discussion


Naming


Names used by physicists

The name most strongly associated with the particle and field is the Higgs boson and Higgs field. For some time the particle was known by a combination of its PRL author names (including at times Anderson), for example the Brout–Englert–Higgs particle, the Anderson–Higgs particle, or the Englert–Brout–Higgs–Guralnik–Hagen–Kibble mechanism, and these are still used at times. Fuelled in part by the issue of recognition and a potential shared Nobel Prize, the most appropriate name was still occasionally a topic of debate until 2013. Higgs himself preferred to call the particle either by an acronym of all those involved, or "the scalar boson", or "the so-called Higgs particle". A considerable amount has been written on how Higgs's name came to be exclusively used. Two main explanations are offered. The first is that Higgs undertook a step which was either unique, clearer or more explicit in his paper in formally predicting and examining the particle. Of the PRL papers' authors, only the paper by Higgs ''explicitly'' offered as a prediction that a massive particle would exist and calculated some of its properties; he was therefore "the first to postulate the existence of a massive particle" according to ''
Nature Nature is an inherent character or constitution, particularly of the Ecosphere (planetary), ecosphere or the universe as a whole. In this general sense nature refers to the Scientific law, laws, elements and phenomenon, phenomena of the physic ...
''. Physicist and author Frank Close and physicist-blogger
Peter Woit Peter Woit (; born September 11, 1957) is a Latvian-American mathematician who works in twistor theory. He works in the mathematics department at Columbia University. Woit, a critic of string theory, has published a book ''Not Even Wrong'' (2006 ...
both comment that the paper by GHK was also completed after Higgs and Brout–Englert were submitted to
Physical Review Letters ''Physical Review Letters'' (''PRL''), established in 1958, is a peer-reviewed, scientific journal that is published 52 times per year by the American Physical Society. The journal is considered one of the most prestigious in the field of physics ...
, and that Higgs alone had drawn attention to a predicted massive ''scalar'' boson, while all others had focused on the massive ''vector'' bosons. In this way, Higgs's contribution also provided experimentalists with a crucial "concrete target" needed to test the theory. However, in Higgs's view, Brout and Englert did not explicitly mention the boson since its existence is plainly obvious in their work, while according to Guralnik the GHK paper was a complete analysis of the entire symmetry breaking mechanism whose
mathematical rigour Rigour (British English) or rigor (American English; see spelling differences) describes a condition of stiffness or strictness. These constraints may be environmentally imposed, such as "the rigours of famine"; logically imposed, such as ma ...
is absent from the other two papers, and a massive particle may exist in some solutions. Higgs's paper also provided an "especially sharp" statement of the challenge and its solution according to science historian David Kaiser. The alternative explanation is that the name was popularised in the 1970s due to its use as a convenient shorthand or because of a mistake in citing. Many accounts including Higgs's own credit the "Higgs" name to physicist Benjamin Lee. Lee was a significant populariser of the theory in its early days, and habitually attached the name "Higgs" as a "convenient shorthand" for its components from 1972, and in at least one instance from as early as 1966. Although Lee clarified in his footnotes that "'Higgs' is an abbreviation for Higgs, Kibble, Guralnik, Hagen, Brout, Englert", his use of the term (and perhaps also Steven Weinberg's mistaken cite of Higgs's paper as the first in his seminal 1967 paper ) meant that by around 1975–1976 others had also begun to use the name "Higgs" exclusively as a shorthand. In 2012, physicist
Frank Wilczek Frank Anthony Wilczek ( or ; born May 15, 1951) is an American theoretical physicist, mathematician and Nobel laureate. He is the Herman Feshbach Professor of Physics at the Massachusetts Institute of Technology (MIT), Founding Director ...
, who was credited for naming the elementary particle, the
axion An axion () is a hypothetical elementary particle originally theorized in 1978 independently by Frank Wilczek and Steven Weinberg as the Goldstone boson of Peccei–Quinn theory, which had been proposed in 1977 to solve the strong CP problem ...
(over an alternative proposal "Higglet", by Weinberg), endorsed the "Higgs boson" name, stating "History is complicated, and wherever you draw the line, there will be somebody just below it."


Nickname

The Higgs boson is often referred to as the "God particle" in popular media outside the scientific community. The nickname comes from the title of the 1993 book on the Higgs boson and particle physics, '' The God Particle: If the Universe Is the Answer, What Is the Question?'' by Physics Nobel Prize winner and
Fermilab Fermi National Accelerator Laboratory (Fermilab), located in Batavia, Illinois, near Chicago, is a United States Department of Energy United States Department of Energy National Labs, national laboratory specializing in high-energy particle phys ...
director
Leon Lederman Leon, Léon (French) or León (Spanish) may refer to: Places Europe * León, Spain, capital city of the Province of León * Province of León, Spain * Kingdom of León, an independent state in the Iberian Peninsula from 910 to 1230 and again fro ...
. Lederman wrote it in the context of failing US government support for the Superconducting Super Collider, a partially constructed titanic competitor to the
Large Hadron Collider The Large Hadron Collider (LHC) is the world's largest and highest-energy particle accelerator. It was built by the CERN, European Organization for Nuclear Research (CERN) between 1998 and 2008, in collaboration with over 10,000 scientists, ...
with planned collision energies of that was championed by Lederman since its 1983 inception and shut down in 1993. The book sought in part to promote awareness of the significance and need for such a project in the face of its possible loss of funding. Lederman, a leading researcher in the field, writes that he wanted to title his book ''The Goddamn Particle: If the Universe is the Answer, What is the Question?'' Lederman's editor decided that the title was too controversial and convinced him to change the title to ''The God Particle: If the Universe is the Answer, What is the Question?'' While media use of this term may have contributed to wider awareness and interest, many scientists feel the name is inappropriate since it is sensational
hyperbole Hyperbole (; adj. hyperbolic ) is the use of exaggeration as a rhetorical device or figure of speech. In rhetoric, it is also sometimes known as auxesis (literally 'growth'). In poetry and oratory, it emphasizes, evokes strong feelings, and cre ...
and misleads readers; the particle also has nothing to do with any God, leaves open numerous questions in fundamental physics, and does not explain the ultimate origin of the universe. Higgs, an
atheist Atheism, in the broadest sense, is an absence of belief in the existence of deities. Less broadly, atheism is a rejection of the belief that any deities exist. In an even narrower sense, atheism is specifically the position that there no ...
, was reported to be displeased and stated in a 2008 interview that he found it "embarrassing" because it was "the kind of misuse ..which I think might offend some people". ; original interview: The nickname has been satirised in mainstream media as well. Science writer Ian Sample stated in his 2010 book on the search that the nickname is "universally hate by physicists and perhaps the "worst derided" in the
history of physics Physics is a branch of science in which the primary objects of study are matter and energy. These topics were discussed across many cultures in ancient times by philosophers, but they had no means to distinguish causes of natural phenomena fro ...
, but that (according to Lederman) the publisher rejected all titles mentioning "Higgs" as unimaginative and too unknown. Lederman begins with a review of the long human search for knowledge, and explains that his tongue-in-cheek title draws an analogy between the impact of the Higgs field on the fundamental symmetries at the
Big Bang The Big Bang is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models based on the Big Bang concept explain a broad range of phenomena, including th ...
, and the apparent chaos of structures, particles, forces and interactions that resulted and shaped our present universe, with the biblical story of Babel in which the primordial single language of early Genesis was fragmented into many disparate languages and cultures. Lederman asks whether the Higgs boson was added just to perplex and confound those seeking knowledge of the universe, and whether physicists will be confounded by it as recounted in that story, or ultimately surmount the challenge and understand "how beautiful is the universe od hasmade".


Other proposals

A renaming competition by British newspaper ''
The Guardian ''The Guardian'' is a British daily newspaper. It was founded in Manchester in 1821 as ''The Manchester Guardian'' and changed its name in 1959, followed by a move to London. Along with its sister paper, ''The Guardian Weekly'', ''The Guardi ...
'' in 2009 resulted in their science correspondent choosing the name "the champagne bottle boson" as the best submission: "The bottom of a champagne bottle is in the shape of the Higgs potential and is often used as an illustration in physics lectures. So it's not an embarrassingly grandiose name, it is memorable, and thas some physics connection too." The name ''Higgson'' was suggested as well, in an opinion piece in the
Institute of Physics The Institute of Physics (IOP) is a UK-based not-for-profit learned society and professional body that works to advance physics education, physics research, research and applied physics, application. It was founded in 1874 and has a worldwide ...
' online publication ''physicsworld.com''.


Educational explanations and analogies

There has been considerable public discussion of analogies and explanations for the Higgs particle and how the field creates mass, including coverage of explanatory attempts in their own right and a competition in 1993 for the best popular explanation by then-UK Minister for Science Sir William Waldegrave and articles in newspapers worldwide. An educational collaboration involving an LHC physicist and
High School Teachers at CERN
educator suggests that dispersion of lightresponsible for the
rainbow A rainbow is an optical phenomenon caused by refraction, internal reflection and dispersion of light in water droplets resulting in a continuous spectrum of light appearing in the sky. The rainbow takes the form of a multicoloured circular ...
and dispersive prismis a useful analogy for the Higgs field's symmetry breaking and mass-causing effect. Matt Strassler uses electric fields as an analogy: A similar explanation was offered by ''
The Guardian ''The Guardian'' is a British daily newspaper. It was founded in Manchester in 1821 as ''The Manchester Guardian'' and changed its name in 1959, followed by a move to London. Along with its sister paper, ''The Guardian Weekly'', ''The Guardi ...
'': The Higgs field's effect on particles was famously described by physicist David Miller as akin to a room full of political party workers spread evenly throughout a room: The crowd gravitates to and slows down famous people but does not slow down others. He also drew attention to well-known effects in
solid state physics Solid-state physics is the study of rigid matter, or solids, through methods such as solid-state chemistry, quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state p ...
where an electron's effective mass can be much greater than usual in the presence of a crystal lattice. Analogies based on drag effects, including analogies of "
syrup In cooking, syrup (less commonly sirup; from ; , beverage, wine and ) is a condiment that is a thick, viscous liquid consisting primarily of a Solution (chemistry), solution of sugar in water, containing a large amount of dissolved sugars but ...
" or "
molasses Molasses () is a viscous byproduct, principally obtained from the refining of sugarcane or sugar beet juice into sugar. Molasses varies in the amount of sugar, the method of extraction, and the age of the plant. Sugarcane molasses is usuall ...
" are also well known, but can be somewhat misleading since they may be understood (incorrectly) as saying that the Higgs field simply resists some particles' motion but not others'a simple resistive effect could also conflict with Newton's third law. The Higgs boson is commonly misunderstood as responsible for mass, rather than the Higgs field, and as relating to most mass in the universe.


Recognition and awards

There was considerable discussion prior to late 2013 of how to allocate the credit if the Higgs boson is proven, made more pointed as a
Nobel prize The Nobel Prizes ( ; ; ) are awards administered by the Nobel Foundation and granted in accordance with the principle of "for the greatest benefit to humankind". The prizes were first awarded in 1901, marking the fifth anniversary of Alfred N ...
had been expected, and the very wide basis of people entitled to consideration. These include a range of theoreticians who made the Higgs mechanism theory possible, the theoreticians of the 1964 PRL papers (including Higgs himself), the theoreticians who derived from these a working electroweak theory and the Standard Model itself, and also the experimentalists at CERN and other institutions who made possible the proof of the Higgs field and boson in reality. The Nobel prize has a limit of three persons to share an award, and some possible winners are already prize holders for other work, or are deceased (the prize is only awarded to persons in their lifetime). Existing prizes for works relating to the Higgs field, boson, or mechanism include: * Nobel Prize in Physics (1979) – Glashow, Salam, and Weinberg, ''for contributions to the theory of the unified weak and electromagnetic interaction between elementary particles'' * Nobel Prize in Physics (1999) – 't Hooft and Veltman, ''for elucidating the quantum structure of electroweak interactions in physics'' * J. J. Sakurai Prize for Theoretical Particle Physics (2010)Hagen, Englert, Guralnik, Higgs, Brout, and Kibble, ''for elucidation of the properties of spontaneous symmetry breaking in four-dimensional relativistic gauge theory and of the mechanism for the consistent generation of vector boson masses'' (for the 1964 papers described above) *
Wolf Prize The Wolf Prize is an international award granted in Israel, that has been presented most years since 1978 to living scientists and artists for "achievements in the interest of mankind and friendly relations among people ... irrespective of natio ...
(2004)Englert, Brout, and Higgs * Special Breakthrough Prize in Fundamental Physics (2013)
Fabiola Gianotti Fabiola Gianotti (; born 29 October 1960) is an Italian experimental particle physicist who is the current and first woman Director general, Director-General at CERN (European Organization for Nuclear Research) in Switzerland. Her first mandate ...
and Peter Jenni, spokespersons of the ATLAS Collaboration and Michel Della Negra, Tejinder Singh Virdee, Guido Tonelli, and Joseph Incandela spokespersons, past and present, of the CMS collaboration, "For
heir Inheritance is the practice of receiving private property, titles, debts, entitlements, privileges, rights, and obligations upon the death of an individual. The rules of inheritance differ among societies and have changed over time. Offi ...
leadership role in the scientific endeavour that led to the discovery of the new Higgs-like particle by the ATLAS and CMS collaborations at CERN's Large Hadron Collider". * Nobel Prize in Physics (2013) –
Peter Higgs Peter Ware Higgs (29 May 1929 – 8 April 2024) was a British theoretical physicist, professor at the University of Edinburgh,Griggs, Jessica (Summer 2008The Missing Piece ''Edit'' the University of Edinburgh Alumni Magazine, p. 17 and Nobel ...
and
François Englert François, Baron Englert (; born 6 November 1932) is a Belgian theoretical physicist and 2013 Nobel Prize laureate. Englert is professor emeritus at the Université libre de Bruxelles (ULB), where he is a member of the Service de Physique Thé ...
, ''for the theoretical discovery of a mechanism that contributes to our understanding of the origin of mass of subatomic particles, and which recently was confirmed through the discovery of the predicted fundamental particle, by the ATLAS and CMS experiments at CERN's Large Hadron Collider'' Englert's co-researcher Robert Brout had died in 2011 and the Nobel Prize is not ordinarily given posthumously. Additionally
Physical Review Letters ''Physical Review Letters'' (''PRL''), established in 1958, is a peer-reviewed, scientific journal that is published 52 times per year by the American Physical Society. The journal is considered one of the most prestigious in the field of physics ...
' 50-year review (2008) recognised the 1964 PRL symmetry breaking papers and Weinberg's 1967 paper ''A model of Leptons'' (the most cited paper in particle physics, as of 2012) "milestone Letters". Following reported observation of the Higgs-like particle in July 2012, several
Indian media Mass media in India consists of several different means of communication: television, radio, internet, cinema, newspapers and magazines. Indian media was active since the late 18th century; the print media started in India as early as 1780. R ...
outlets reported on the supposed neglect of credit to Indian physicist
Satyendra Nath Bose Satyendra Nath Bose (; 1 January 1894 – 4 February 1974) was an Indian theoretical physicist and mathematician. He is best known for his work on quantum mechanics in the early 1920s, in developing the foundation for Bose–Einstein statist ...
after whose work in the 1920s the class of particles "
bosons In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value (0, 1, 2, ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have half odd-integer ...
" is named (although physicists have described Bose's connection to the discovery as tenuous).


Technical aspects and mathematical formulation

In the Standard Model, the Higgs field is a four-component scalar field that forms a complex doublet of the
weak isospin In particle physics, weak isospin is a quantum number relating to the electrically charged part of the weak interaction: Particles with half-integer weak isospin can interact with the bosons; particles with zero weak isospin do not. Weak isospin ...
SU(2) symmetry: : \phi = \frac \left( \begin \phi^1 + i\phi^2 \\ \phi^0 + i \phi^3 \end \right)\, while the field has charge + under the
weak hypercharge In the Standard Model (mathematical formulation), Standard Model of electroweak interactions of particle physics, the weak hypercharge is a quantum number relating the electric charge and the third component of weak isospin. It is frequently deno ...
U(1) symmetry. The Higgs part of the Lagrangian is : \mathcal_\text = \left, \left(\partial_\mu - i g W_ \tfrac\sigma^a - i\tfrac g' B_\mu\right)\phi\^2 + \mu_\text^2 \phi^\dagger\phi - \lambda \left(\phi^\dagger\phi\right)^2\ , where W_ and B_\mu are the
gauge boson In particle physics, a gauge boson is a bosonic elementary particle that acts as the force carrier for elementary fermions. Elementary particles whose interactions are described by a gauge theory interact with each other by the exchange of gauge ...
s of the SU(2) and U(1) symmetries, g and g' their respective
coupling constant In physics, a coupling constant or gauge coupling parameter (or, more simply, a coupling), is a number that determines the strength of the force exerted in an interaction. Originally, the coupling constant related the force acting between tw ...
s, \sigma^a are the
Pauli matrices In mathematical physics and mathematics, the Pauli matrices are a set of three complex matrices that are traceless, Hermitian, involutory and unitary. Usually indicated by the Greek letter sigma (), they are occasionally denoted by tau () ...
(a complete set of generators of the SU(2) symmetry), and \lambda > 0 and \mu^_\text > 0, so that the
ground state The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state ...
breaks the SU(2) symmetry (see figure). The ground state of the Higgs field (the bottom of the potential) is degenerate with different ground states related to each other by a SU(2) gauge transformation. It is always possible to pick a gauge such that in the ground state \phi^1 = \phi^2 = \phi^3 = 0. The expectation value of \phi^0 in the ground state (the
vacuum expectation value In quantum field theory, the vacuum expectation value (VEV) of an operator is its average or expectation value in the vacuum. The vacuum expectation value of an operator O is usually denoted by \langle O\rangle. One of the most widely used exa ...
or VEV) is then \left\langle\phi^0\right\rangle = \tfrac v, where v = \tfrac \left, \mu_\text\. The measured value of this parameter is ~. It has units of mass, and is the only free parameter of the Standard Model that is not a dimensionless number. Quadratic terms in W_ and B_ arise, which give masses to the W and Z bosons: : \begin m_\text &= \tfrac v \left, \,g\,\\ , \\ m_\text &= \tfrac v \sqrt\ , \end with their ratio determining the Weinberg angle, \cos \theta_\text = \frac = \frac, and leave a massless U(1)
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless particles that can ...
, \gamma. The mass of the Higgs boson itself is given by : m_\text = \sqrt \equiv \sqrt. The quarks and the leptons interact with the Higgs field through
Yukawa interaction In particle physics, Yukawa's interaction or Yukawa coupling, named after Hideki Yukawa, is an interaction between particles according to the Yukawa potential. Specifically, it is between a scalar field (or pseudoscalar field) \ \phi\ and a Dira ...
terms: : \begin\mathcal_\text = &- \lambda_u^\frac\overline u^i_\text u^j_\text + \lambda_u^\frac\overline d^i_\text u^j_\text\\ &-\lambda_d^\frac\overline d^i_\text d^j_\text - \lambda_d^\frac\overline u^i_\text d^j_\text\\ &- \lambda_e^\frac\overline e^i_\text e^j_\text - \lambda_e^\frac\overline \nu^i_\text e^j_\text + \textrm\ ,\end where (d,u,e,\nu)_\text^i are left-handed and right-handed quarks and leptons of the th
generation A generation is all of the people born and living at about the same time, regarded collectively. It also is "the average period, generally considered to be about 20–⁠30 years, during which children are born and grow up, become adults, and b ...
, \lambda_\text^ are matrices of Yukawa couplings where h.c. denotes the hermitian conjugate of all the preceding terms. In the symmetry breaking ground state, only the terms containing \phi^0 remain, giving rise to mass terms for the fermions. Rotating the quark and lepton fields to the basis where the matrices of Yukawa couplings are diagonal, one gets : \mathcal_\text = -m_\text^i \overline u^i_\text u^i_\text - m_\text^i\overline d^i_\text d^i_\text - m_\text^i\overline e^i_\text e^i_\text + \textrm, where the masses of the fermions are m_\text^i = \tfrac\lambda_\text^i v, and \lambda_\text^i denote the eigenvalues of the Yukawa matrices.


See also


Standard Model

* * * * * * ** Standard Model fields overview ** mass terms and the Higgs mechanism * *


Other

* * Composite Higgs models, an extension of the SM where the Higgs boson is made of smaller constituents * * '' Particle Fever'', a 2013 American documentary film following various LHC experiments and concluding with the identification of the Higgs boson * * * * *


Explanatory notes


References


Sources

* * * *


Further reading

* * * * * * * *


External links


Popular science, mass media, and general coverage


Higgs Boson observation at CERN

Hunting the Higgs Boson at C.M.S. Experiment, at CERN


by the CERN exploratorium.

* ttp://theatomsmashers.com/ ''The Atom Smashers'', documentary film about the search for the Higgs Boson at Fermilab.
Collected Articles at the ''Guardian''

Video (04:38)
nbsp;–
CERN The European Organization for Nuclear Research, known as CERN (; ; ), is an intergovernmental organization that operates the largest particle physics laboratory in the world. Established in 1954, it is based in Meyrin, western suburb of Gene ...
Announcement on 4 July 2012, of the discovery of a particle which is suspected will be a Higgs Boson.
Video1 (07:44)

Video2 (07:44)
nbsp;– Higgs Boson Explained by CERN Physicist
Dr. Daniel Whiteson
(16 June 2011).

* * ''New York Times'' "behind the scenes" style article on the Higgs search at ATLAS and CMS * The story of the Higgs theory by the authors of the PRL papers and others closely associated: ** (also: ) ** (also: ) ** , , and Guralnik, Gerald (2013)
"Heretical Ideas that Provided the Cornerstone for the Standard Model of Particle Physics".
SPG Mitteilungen March 2013, No. 39, (p. 14), an
Talk at Brown University about the 1964 PRL papers
*
Philip Anderson (not one of the PRL authors) on symmetry breaking in superconductivity and its migration into particle physics and the PRL papers

Cartoon about the search
*
Higgs Boson
BBC Radio 4 discussion with Jim Al-Khalili, David Wark & Roger Cashmore (''In Our Time'', 18 November 2004)


Significant papers and other

* *
Particle Data Group: Review of searches for Higgs Bosons.

2001, a spacetime odyssey: proceedings of the Inaugural Conference of the Michigan Center for Theoretical Physics
: Michigan, 21–25 May 2001, (pp. 86–88), ed. Michael J. Duff, James T. Liu, , containing Higgs's story of the Higgs Boson. * example of a 1966 Russian paper on the subject.
The Department of Energy Explains ... the Higgs Boson


Introductions to the field


Electroweak Symmetry Breaking
– A pedagogic introduction to electroweak symmetry breaking with step by step derivations of many key relations, by Robert D. Klauber, 15 January 2018 (archived at Wayback Machine)
Spontaneous symmetry breaking, gauge theories, the Higgs mechanism and all that (Bernstein, ''Reviews of Modern Physics'' Jan 1974)
an introduction of 47 pages covering the development, history and mathematics of Higgs theories from around 1950 to 1974. {{Authority control 2012 in science Bosons Electroweak theory Elementary particles Mass Phase transitions Standard Model Quantum field theory Subatomic particles with spin 0 Force carriers