HOME

TheInfoList



OR:

In particle physics, flavour or flavor refers to the ''species'' of an elementary particle. The Standard Model counts six flavours 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 nuclei. All commonly o ...
s and six flavours of
lepton In particle physics, a lepton is an elementary particle of half-integer spin ( spin ) that does not undergo strong interactions. Two main classes of leptons exist: charged leptons (also known as the electron-like leptons or muons), and neut ...
s. They are conventionally parameterized with ''flavour
quantum number In quantum physics and chemistry, quantum numbers describe values of conserved quantities in the dynamics of a quantum system. Quantum numbers correspond to eigenvalues of operators that commute with the Hamiltonian—quantities that can be ...
s'' that are assigned to all
subatomic particle In physical sciences, a subatomic particle is a particle that composes an atom. According to the Standard Model of particle physics, a subatomic particle can be either a composite particle, which is composed of other particles (for example, a prot ...
s. They can also be described by some of the family symmetries proposed for the quark-lepton generations.


Quantum numbers

In classical mechanics, a force acting on a point-like particle can only alter the
particle In the physical sciences, a particle (or corpuscule 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 dynamical state, i.e., its momentum, angular momentum, etc. Quantum field theory, however, allows interactions that can alter other facets of a particle's nature described by non dynamical, discrete quantum numbers. In particular, the action of the
weak force Weak may refer to: Songs * "Weak" (AJR song), 2016 * "Weak" (Melanie C song), 2011 * "Weak" (SWV song), 1993 * "Weak" (Skunk Anansie song), 1995 * "Weak", a song by Seether from '' Seether: 2002-2013'' Television episodes * "Weak" (''Fear t ...
is such that it allows the conversion of quantum numbers describing mass and electric charge of both quarks and leptons from one discrete type to another. This is known as a flavour change, or flavour transmutation. Due to their quantum description, flavour states may also undergo quantum superposition. In
atomic physics Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. Atomic physics typically refers to the study of atomic structure and the interaction between atoms. It is primarily concerned w ...
the principal quantum number of an electron specifies the
electron shell In chemistry and atomic physics, an electron shell may be thought of as an orbit followed by electrons around an atom's nucleus. The closest shell to the nucleus is called the "1 shell" (also called the "K shell"), followed by the "2 shell" (or ...
in which it resides, which determines the energy level of the whole atom. Analogously, the five flavour quantum numbers ( isospin, strangeness,
charm Charm may refer to: Social science * Charisma, a person or thing's pronounced ability to attract others * Superficial charm, flattery, telling people what they want to hear Science and technology * Charm quark, a type of elementary particle * Ch ...
,
bottomness In physics, bottomness (symbol ''B''′ using a prime as plain ''B'' is used already for baryon number) or beauty is a flavour quantum number reflecting the difference between the number of bottom antiquarks (''n'') and the number of bottom ...
or
topness Topness (''T'', also called truth), a flavour quantum number, represents the difference between the number of top quarks (t) and number of top antiquarks () that are present in a particle: :T = n_\text - n_\bar By convention, top quarks have a ...
) can characterize the quantum state of quarks, by the degree to which it exhibits six distinct flavours (u, d, s, c, b, t). Composite particles can be created from multiple quarks, forming
hadron In particle physics, a hadron (; grc, ἁδρός, hadrós; "stout, thick") is a composite subatomic particle made of two or more quarks held together by the strong interaction. They are analogous to molecules that are held together by the e ...
s, such as mesons and
baryon In particle physics, a baryon is a type of composite subatomic particle which contains an odd number of valence quarks (at least 3). Baryons belong to the hadron family of particles; hadrons are composed of quarks. Baryons are also classified ...
s, each possessing unique aggregate characteristics, such as different masses, electric charges, and decay modes. A
hadron In particle physics, a hadron (; grc, ἁδρός, hadrós; "stout, thick") is a composite subatomic particle made of two or more quarks held together by the strong interaction. They are analogous to molecules that are held together by the e ...
's overall flavour quantum numbers depend on the numbers of
constituent quark A constituent quark is a current quark with a notional "covering" induced by the renormalization group. In the low-energy limit of QCD, a description by means of perturbation theory is not possible: Here, no asymptotic freedom exists, but collecti ...
s of each particular flavour.


Conservation laws

All of the various charges discussed above are conserved by the fact that the corresponding charge operators can be understood as ''generators of symmetries'' that commute with the Hamiltonian. Thus, the eigenvalues of the various charge operators are conserved. Absolutely conserved flavour quantum numbers in the Standard Model are: * electric charge () *
weak isospin In particle physics, weak isospin is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol or , with the third component written as or . It can ...
() *
baryon number In particle physics, the baryon number is a strictly conserved additive quantum number of a system. It is defined as ::B = \frac\left(n_\text - n_\bar\right), where ''n''q is the number of quarks, and ''n'' is the number of antiquarks. Baryon ...
() *
lepton number In particle physics, lepton number (historically also called lepton charge) is a conserved quantum number representing the difference between the number of leptons and the number of antileptons in an elementary particle reaction. Lepton number ...
() In some theories, such as the grand unified theory, the individual baryon and lepton number conservation can be violated, if the difference between them () is conserved (see ''
Chiral anomaly In theoretical physics, a chiral anomaly is the anomalous nonconservation of a chiral current. In everyday terms, it is equivalent to a sealed box that contained equal numbers of left and right-handed bolts, but when opened was found to have mor ...
'').
Strong interaction The strong interaction or strong force is a fundamental interaction that confines quarks into proton, neutron, and other hadron particles. The strong interaction also binds neutrons and protons to create atomic nuclei, where it is called the ...
s conserve all flavours, but all flavour quantum numbers (other than and ) are violated (changed, non-conserved) by
electroweak interaction In particle physics, the electroweak interaction or electroweak force is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very differe ...
s.


Flavour symmetry

If there are two or more particles which have identical interactions, then they may be interchanged without affecting the physics. Any (complex) linear combination of these two particles give the same physics, as long as the combinations are
orthogonal In mathematics, orthogonality is the generalization of the geometric notion of ''perpendicularity''. By extension, orthogonality is also used to refer to the separation of specific features of a system. The term also has specialized meanings in ...
, or perpendicular, to each other. In other words, the theory possesses symmetry transformations such as M\left(\right), where and are the two fields (representing the various ''
generations A generation is "all of the people born and living at about the same time, regarded collectively." Generation or generations may also refer to: Science and technology * Generation (particle physics), a division of the elementary particles * Gen ...
'' of leptons and quarks, see below), and is any
unitary matrix In linear algebra, a complex square matrix is unitary if its conjugate transpose is also its inverse, that is, if U^* U = UU^* = UU^ = I, where is the identity matrix. In physics, especially in quantum mechanics, the conjugate transpose ...
with a unit determinant. Such matrices form a
Lie group In mathematics, a Lie group (pronounced ) is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the ad ...
called SU(2) (see
special unitary group In mathematics, the special unitary group of degree , denoted , is the Lie group of unitary matrices with determinant 1. The more general unitary matrices may have complex determinants with absolute value 1, rather than real 1 in the special ...
). This is an example of flavour symmetry. In
quantum chromodynamics In theoretical physics, quantum chromodynamics (QCD) is the theory 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 o ...
, flavour is a conserved
global symmetry In physics, a symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is preserved or remains unchanged under some transformation. A family of particular transformations may be ''continuou ...
. In the
electroweak theory In particle physics, the electroweak interaction or electroweak force is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very differe ...
, on the other hand, this symmetry is broken, and flavour changing processes exist, such as quark decay or neutrino oscillations.


Flavour quantum numbers


Leptons

All
lepton In particle physics, a lepton is an elementary particle of half-integer spin ( spin ) that does not undergo strong interactions. Two main classes of leptons exist: charged leptons (also known as the electron-like leptons or muons), and neut ...
s carry a
lepton number In particle physics, lepton number (historically also called lepton charge) is a conserved quantum number representing the difference between the number of leptons and the number of antileptons in an elementary particle reaction. Lepton number ...
. In addition, leptons carry
weak isospin In particle physics, weak isospin is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol or , with the third component written as or . It can ...
, , which is − for the three charged leptons (i.e. electron, muon and tau) and + for the three associated neutrinos. Each doublet of a charged lepton and a neutrino consisting of opposite are said to constitute one generation of leptons. In addition, one defines a quantum number called
weak hypercharge In the 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 denoted Y_\mathsf and corresponds to the gauge ...
, , which is −1 for all left-handed leptons. Weak isospin and weak hypercharge are gauged in the Standard Model. Leptons may be assigned the six flavour quantum numbers: electron number, muon number, tau number, and corresponding numbers for the neutrinos. These are conserved in strong and electromagnetic interactions, but violated by weak interactions. Therefore, such flavour quantum numbers are not of great use. A separate quantum number for each generation is more useful: electronic lepton number (+1 for electrons and electron neutrinos), muonic lepton number (+1 for muons and muon neutrinos), and tauonic lepton number (+1 for tau leptons and tau neutrinos). However, even these numbers are not absolutely conserved, as neutrinos of different generations can
mix Mix, mixes or mixing may refer to: Persons & places * Mix (surname) ** Tom Mix (1880-1940), American film star * nickname of Mix Diskerud (born Mikkel, 1990), Norwegian-American soccer player * Mix camp, an informal settlement in Namibia * ...
; that is, a neutrino of one flavour can transform into another flavour. The strength of such mixings is specified by a matrix called the
Pontecorvo–Maki–Nakagawa–Sakata matrix In particle physics, the Pontecorvo–Maki–Nakagawa–Sakata matrix (PMNS matrix), Maki–Nakagawa–Sakata matrix (MNS matrix), lepton mixing matrix, or neutrino mixing matrix is a unitary mixing matrix which contains information on the mismat ...
(PMNS matrix).


Quarks

All
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 nuclei. All commonly o ...
s carry a
baryon number In particle physics, the baryon number is a strictly conserved additive quantum number of a system. It is defined as ::B = \frac\left(n_\text - n_\bar\right), where ''n''q is the number of quarks, and ''n'' is the number of antiquarks. Baryon ...
and all anti-quarks have They also all carry
weak isospin In particle physics, weak isospin is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol or , with the third component written as or . It can ...
, The positively charged quarks (up, charm, and top quarks) are called ''up-type quarks'' and have the negatively charged quarks (down, strange, and bottom quarks) are called ''down-type quarks'' and have Each doublet of up and down type quarks constitutes one generation of quarks. For all the quark flavour quantum numbers listed below, the convention is that the flavour charge and the electric charge of a quark have the same sign. Thus any flavour carried by a charged meson has the same sign as its charge. Quarks have the following flavour quantum numbers: * The third component of isospin (usually just "isospin") (), which has value for the up quark and for the down quark. * Strangeness (): Defined as where represents the number of strange quarks () and represents the number of strange antiquarks (). This quantum number was introduced by Murray Gell-Mann. This definition gives the strange quark a strangeness of −1 for the above-mentioned reason. *
Charm Charm may refer to: Social science * Charisma, a person or thing's pronounced ability to attract others * Superficial charm, flattery, telling people what they want to hear Science and technology * Charm quark, a type of elementary particle * Ch ...
(): Defined as where represents the number of
charm quark The charm quark, charmed quark or c quark (from its symbol, c) is the third-most massive of all quarks, a type of elementary particle. Charm quarks are found in hadrons, which are subatomic particles made of quarks. Examples of hadrons containin ...
s () and represents the number of charm antiquarks. The charm quark's value is +1. *
Bottomness In physics, bottomness (symbol ''B''′ using a prime as plain ''B'' is used already for baryon number) or beauty is a flavour quantum number reflecting the difference between the number of bottom antiquarks (''n'') and the number of bottom ...
(or ''beauty'') (): Defined as where represents the number of
bottom quark The bottom quark or b quark, also known as the beauty quark, is a third-generation heavy quark with a charge of −  ''e''. All quarks are described in a similar way by electroweak and quantum chromodynamics, but the bottom quark has excep ...
s () and represents the number of bottom antiquarks. *
Topness Topness (''T'', also called truth), a flavour quantum number, represents the difference between the number of top quarks (t) and number of top antiquarks () that are present in a particle: :T = n_\text - n_\bar By convention, top quarks have a ...
(or ''truth'') (): Defined as where represents the number 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 Boson. This coupling y_ is very close to unity; in the Standard ...
s () and represents the number of top antiquarks. However, because of the extremely short half-life of the top quark (predicted lifetime of only ), by the time it can interact strongly it has already decayed to another flavour of quark (usually to a
bottom quark The bottom quark or b quark, also known as the beauty quark, is a third-generation heavy quark with a charge of −  ''e''. All quarks are described in a similar way by electroweak and quantum chromodynamics, but the bottom quark has excep ...
). For that reason the top quark doesn't hadronize, that is it never forms any meson or
baryon In particle physics, a baryon is a type of composite subatomic particle which contains an odd number of valence quarks (at least 3). Baryons belong to the hadron family of particles; hadrons are composed of quarks. Baryons are also classified ...
. These five quantum numbers, together with baryon number (which is not a flavour quantum number), completely specify numbers of all 6 quark flavours separately (as i.e. an antiquark is counted with the minus sign). They are conserved by both the electromagnetic and strong interactions (but not the weak interaction). From them can be built the derived quantum numbers: *
Hypercharge In particle physics, the hypercharge (a portmanteau of hyperonic and charge) ''Y'' of a particle is a quantum number conserved under the strong interaction. The concept of hypercharge provides a single charge operator that accounts for propert ...
(): * Electric charge (): (see
Gell-Mann–Nishijima formula The Gell-Mann–Nishijima formula (sometimes known as the NNG formula) relates the baryon number ''B'', the strangeness ''S'', the isospin ''I3'' of quarks and hadrons to the electric charge ''Q''. It was originally given by Kazuhiko Nishijima an ...
) The terms "strange" and "strangeness" predate the discovery of the quark, but continued to be used after its discovery for the sake of continuity (i.e. the strangeness of each type of hadron remained the same); strangeness of anti-particles being referred to as +1, and particles as −1 as per the original definition. Strangeness was introduced to explain the rate of decay of newly discovered particles, such as the kaon, and was used in the Eightfold Way classification of hadrons and in subsequent
quark model In particle physics, the quark model is a classification scheme for hadrons in terms of their valence quarks—the quarks and antiquarks which give rise to the quantum numbers of the hadrons. The quark model underlies "flavor SU(3)", or the Ei ...
s. These quantum numbers are preserved under strong and
electromagnetic interaction In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...
s, but not under
weak interaction In nuclear physics and particle physics, the weak interaction, which is also often called the weak force or weak nuclear force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interaction ...
s. For first-order weak decays, that is processes involving only one quark decay, these quantum numbers (e.g. charm) can only vary by 1, that is, for a decay involving a charmed quark or antiquark either as the incident particle or as a decay byproduct, likewise, for a decay involving a bottom quark or antiquark Since first-order processes are more common than second-order processes (involving two quark decays), this can be used as an approximate " selection rule" for weak decays. A special mixture of quark flavours is an
eigenstate In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution in t ...
of the
weak interaction In nuclear physics and particle physics, the weak interaction, which is also often called the weak force or weak nuclear force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interaction ...
part of the
Hamiltonian Hamiltonian may refer to: * Hamiltonian mechanics, a function that represents the total energy of a system * Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system ** Dyall Hamiltonian, a modified Hamiltonian ...
, so will interact in a particularly simple way with the
W 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 , , and ...
(charged weak interactions violate flavour). On the other hand, a
fermion In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks and ...
of a fixed mass (an eigenstate of the kinetic and strong interaction parts of the Hamiltonian) is an eigenstate of flavour. The transformation from the former basis to the flavour-eigenstate/mass-eigenstate basis for quarks underlies the Cabibbo–Kobayashi–Maskawa matrix (CKM matrix). This matrix is analogous to the PMNS matrix for neutrinos, and quantifies flavour changes under charged weak interactions of quarks. The CKM matrix allows for CP violation if there are at least three generations.


Antiparticles and hadrons

Flavour quantum numbers are additive. Hence
antiparticle In particle physics, every type of particle is associated with an antiparticle with the same mass but with opposite physical charges (such as electric charge). For example, the antiparticle of the electron is the positron (also known as an antie ...
s have flavour equal in magnitude to the particle but opposite in sign.
Hadron In particle physics, a hadron (; grc, ἁδρός, hadrós; "stout, thick") is a composite subatomic particle made of two or more quarks held together by the strong interaction. They are analogous to molecules that are held together by the e ...
s inherit their flavour quantum number from their valence quarks: this is the basis of the classification in the
quark model In particle physics, the quark model is a classification scheme for hadrons in terms of their valence quarks—the quarks and antiquarks which give rise to the quantum numbers of the hadrons. The quark model underlies "flavor SU(3)", or the Ei ...
. The relations between the hypercharge, electric charge and other flavour quantum numbers hold for hadrons as well as quarks.


Flavour problem

The Flavour problem (also known as the Flavour puzzle) is the inability of current Standard Model flavour physics to explain why the free parameters of particles in the Standard Model have the values they have, and why there are specified values for mixing angles in the PMNS and CKM matrices. These free parameters - the
fermion In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks and ...
masses and their mixing angles - appear to be specifically tuned. Understanding the reason for such tuning would be the solution to the flavor puzzle. There are very fundamental questions involved in this puzzle such as why are there three generations 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 nuclei. All commonly o ...
s (up-down, charm-strange, and top-bottom quarks) and
lepton In particle physics, a lepton is an elementary particle of half-integer spin ( spin ) that does not undergo strong interactions. Two main classes of leptons exist: charged leptons (also known as the electron-like leptons or muons), and neut ...
s (electron, muon and tau neutrino), and how and why does the mass and mixing hierarchy arise among different flavours of these fermions.


Quantum chromodynamics

Quantum chromodynamics In theoretical physics, quantum chromodynamics (QCD) is the theory 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 o ...
(QCD) contains six flavours 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 nuclei. All commonly o ...
s. However, their masses differ and as a result they are not strictly interchangeable with each other. The up and down flavours are close to having equal masses, and the theory of these two quarks possesses an approximate SU(2) symmetry ( isospin symmetry).


Chiral symmetry description

Under some circumstances (for instance when the quark masses are much smaller than the
chiral symmetry breaking In particle physics, chiral symmetry breaking is the spontaneous symmetry breaking of a chiral symmetry – usually by a gauge theory such as quantum chromodynamics, the quantum field theory of the strong interaction. Yoichiro Nambu was award ...
scale of 250 MeV), the masses of quarks do not substantially contribute to the system's behavior, and to zeroth approximation the masses of the lightest quarks can be ignored for most purposes, as if they had zero mass. The simplified behavior of flavour transformations can then be successfully modeled as acting independently on the left- and right-handed parts of each quark field. This approximate description of the flavour symmetry is described by a chiral group .


Vector symmetry description

If all quarks had non-zero but equal masses, then this chiral symmetry is broken to the ''vector symmetry'' of the "diagonal flavour group" , which applies the same transformation to both helicities of the quarks. This reduction of symmetry is a form of '' explicit symmetry breaking''. The strength of explicit symmetry breaking is controlled by the current quark masses in QCD. Even if quarks are massless, chiral flavour symmetry can be spontaneously broken if the vacuum of the theory contains a
chiral condensate A fermionic condensate or Fermi–Dirac condensate is a superfluid phase formed by fermionic particles at low temperatures. It is closely related to the Bose–Einstein condensate, a superfluid phase formed by bosonic atoms under similar condi ...
(as it does in low-energy QCD). This gives rise to an effective mass for the quarks, often identified with the valence quark mass in QCD.


Symmetries of QCD

Analysis of experiments indicate that the current quark masses of the lighter flavours of quarks are much smaller than the QCD scale, ΛQCD, hence chiral flavour symmetry is a good approximation to
QCD In theoretical physics, quantum chromodynamics (QCD) is the theory 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 o ...
for the up, down and strange quarks. The success of
chiral perturbation theory Chiral perturbation theory (ChPT) is an effective field theory constructed with a Lagrangian consistent with the (approximate) chiral symmetry of quantum chromodynamics (QCD), as well as the other symmetries of parity and charge conjugation.
and the even more naive
chiral model In nuclear physics, the chiral model, introduced by Feza Gürsey in 1960, is a phenomenological model describing effective interactions of mesons in the chiral limit (where the masses of the quarks go to zero), but without necessarily mentioning ...
s spring from this fact. The valence quark masses extracted from the
quark model In particle physics, the quark model is a classification scheme for hadrons in terms of their valence quarks—the quarks and antiquarks which give rise to the quantum numbers of the hadrons. The quark model underlies "flavor SU(3)", or the Ei ...
are much larger than the current quark mass. This indicates that QCD has spontaneous chiral symmetry breaking with the formation of a
chiral condensate A fermionic condensate or Fermi–Dirac condensate is a superfluid phase formed by fermionic particles at low temperatures. It is closely related to the Bose–Einstein condensate, a superfluid phase formed by bosonic atoms under similar condi ...
. Other phases of QCD may break the chiral flavour symmetries in other ways.


History


Isospin

Isospin, strangeness and hypercharge predate the quark model. The first of those quantum numbers, Isospin, was introduced as a concept in 1932 by
Werner Heisenberg Werner Karl Heisenberg () (5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the main pioneers of the theory of quantum mechanics. He published his work in 1925 in a Über quantentheoretische Umdeutung kinematis ...
, to explain symmetries of the then newly discovered neutron (symbol n): * The mass of the neutron and the proton (symbol ) are almost identical: They are nearly degenerate, and both are thus often referred to as “
nucleon In physics and chemistry, a nucleon is either a proton or a neutron, considered in its role as a component of an atomic nucleus. The number of nucleons in a nucleus defines the atom's mass number (nucleon number). Until the 1960s, nucleons were ...
s”, a term that ignores their differences. Although the proton has a positive electric charge, and the neutron is neutral, they are almost identical in all other aspects, and their nuclear binding-force interactions (old name for the residual color force) are so strong compared to the electrical force between some, that there is very little point in paying much attention to their differences. * The strength of the strong interaction between any pair of nucleons is the same, independent of whether they are interacting as protons or as neutrons. Protons and neutrons were grouped together as
nucleon In physics and chemistry, a nucleon is either a proton or a neutron, considered in its role as a component of an atomic nucleus. The number of nucleons in a nucleus defines the atom's mass number (nucleon number). Until the 1960s, nucleons were ...
s and treated as different states of the same particle, because they both have nearly the same mass and interact in nearly the same way, if the (much weaker) electromagnetic interaction is neglected. Heisenberg noted that the mathematical formulation of this symmetry was in certain respects similar to the mathematical formulation of non-relativistic
spin Spin or spinning most often refers to: * Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning * Spin, the rotation of an object around a central axis * Spin (propaganda), an intentionally b ...
, whence the name "isospin" derives. The neutron and the proton are assigned to the doublet (the spin-, 2, or fundamental representation) of SU(2), with the proton and neutron being then associated with different isospin projections and respectively. The pions are assigned to the triplet (the spin-1, 3, or
adjoint representation In mathematics, the adjoint representation (or adjoint action) of a Lie group ''G'' is a way of representing the elements of the group as linear transformations of the group's Lie algebra, considered as a vector space. For example, if ''G'' is ...
) of SU(2). Though there is a difference from the theory of spin: The group action does not preserve flavor (in fact, the group action is specifically an exchange of flavour). When constructing a physical theory of nuclear forces, one could simply assume that it does not depend on isospin, although the total isospin should be conserved. The concept of isospin proved useful in classifying hadrons discovered in the 1950s and 1960s (see
particle zoo In particle physics, the term particle zoo is used colloquially to describe the relatively extensive list of known subatomic particles by comparison to the variety of species in a zoo. In the history of particle physics, the topic of particles was ...
), where particles with similar mass are assigned an SU(2) isospin
multiplet In physics and particularly in particle physics, a multiplet is the state space for 'internal' degrees of freedom of a particle, that is, degrees of freedom associated to a particle itself, as opposed to 'external' degrees of freedom such as the ...
.


Strangeness and hypercharge

The discovery of strange particles like the kaon led to a new quantum number that was conserved by the strong interaction: strangeness (or equivalently hypercharge). The
Gell-Mann–Nishijima formula The Gell-Mann–Nishijima formula (sometimes known as the NNG formula) relates the baryon number ''B'', the strangeness ''S'', the isospin ''I3'' of quarks and hadrons to the electric charge ''Q''. It was originally given by Kazuhiko Nishijima an ...
was identified in 1953, which relates strangeness and hypercharge with isospin and electric charge.


The eightfold way and quark model

Once the kaons and their property of strangeness became better understood, it started to become clear that these, too, seemed to be a part of an enlarged symmetry that contained isospin as a subgroup. The larger symmetry was named the Eightfold Way by Murray Gell-Mann, and was promptly recognized to correspond to the adjoint representation of SU(3). To better understand the origin of this symmetry, Gell-Mann proposed the existence of up, down and strange
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 nuclei. All commonly o ...
s which would belong to the fundamental representation of the SU(3) flavor symmetry.


GIM-Mechanism and charm

To explain the observed absence of
flavor-changing neutral current In particle physics, flavor-changing neutral currents or flavour-changing neutral currents (FCNCs) are hypothetical interactions that change the flavor of a fermion without altering its electric charge. Details If they occur in nature (as refl ...
s, the
GIM mechanism In particle physics, the GIM mechanism (or Glashow–Iliopoulos–Maiani mechanism) is the mechanism through which flavour-changing neutral currents (FCNCs) are suppressed in loop diagrams. It also explains why weak interactions that change strang ...
was proposed in 1970, which introduced the charm quark and predicted the J/psi meson. The J/psi meson was indeed found in 1974, which confirmed the existence of charm quarks. This discovery is known as the ''November Revolution''. The flavor quantum number associated with the charm quark became known as ''charm''.


Bottomness and topness

The bottom and top quarks were predicted in 1973 in order to explain CP violation, {{cite journal , first1=M. , last1=Kobayashi , first2=T. , last2=Maskawa , title=CP-Violation in the Renormalizable Theory of Weak Interaction , url=http://ptp.ipap.jp/link?PTP/49/652/pdf , journal= Progress of Theoretical Physics , volume=49 , issue=2 , pages=652–657 , year=1973 , doi=10.1143/PTP.49.652 , bibcode = 1973PThPh..49..652K , doi-access=free which also implied two new flavor quantum numbers: ''bottomness'' and ''topness''.


See also

*
Standard Model (mathematical formulation) This article describes the mathematics of the Standard Model of particle physics, a gauge quantum field theory containing the internal symmetries of the unitary product group . The theory is commonly viewed as describing the fundamental set ...
* Cabibbo–Kobayashi–Maskawa matrix * Strong CP problem and
chirality (physics) A chiral phenomenon is one that is not identical to its mirror image (see the article on mathematical chirality). The spin of a particle may be used to define a handedness, or helicity, for that particle, which, in the case of a massless particle ...
*
Chiral symmetry breaking In particle physics, chiral symmetry breaking is the spontaneous symmetry breaking of a chiral symmetry – usually by a gauge theory such as quantum chromodynamics, the quantum field theory of the strong interaction. Yoichiro Nambu was award ...
and
quark matter Quark matter or QCD matter ( quantum chromodynamic) refers to any of a number of hypothetical phases of matter whose degrees of freedom include quarks and gluons, of which the prominent example is quark-gluon plasma. Several series of conferences ...
*Quark flavour tagging, such as B-tagging, is an example of particle identification in experimental particle physics.


References


Further reading


Lessons in Particle Physics
Luis Anchordoqui and Francis Halzen, University of Wisconsin, 18th Dec. 2009


External links


The particle data group.
Physical quantities Standard Model Quantum chromodynamics Quark matter Conservation laws