In
nuclear physics
Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter.
Nuclear physics should not be confused with atomic physics, which studies th ...
and
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 wit ...
, weak charge, or rarely neutral weak charge, refers to 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 ...
weak interaction
In nuclear physics and particle physics, the weak interaction, weak force or the weak nuclear force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interaction, and gravitation. It is th ...
coupling of a particle to the
Z boson
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 ...
. For example, for any given nuclear isotope, the total weak charge is approximately −0.99 per
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 ...
, and +0.07 per
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 ...
.
[ It also shows an effect of ]parity violation
In physics, a parity transformation (also called parity inversion) is the flip in the sign of ''one'' spatial coordinate. In three dimensions, it can also refer to the simultaneous flip in the sign of all three spatial coordinates (a point ref ...
during electron scattering.
This same term is sometimes also used to refer to other, different quantities, such as ''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 ...
''[ or '']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 ...
''; this article concerns the use of ''weak charge'' for a quantity that measures the degree of vector coupling of a 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 ...
to the Z boson
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 ...
(i.e. the coupling strength of weak neutral currents).[
]
Empirical formulas
Measurements in 2017 give the weak charge of the proton as .[
The weak charge may be summed in atomic nuclei, so that the predicted weak charge for Cs (55 protons, 78 neutrons) is 55×(+0.0719) + 78×(−0.989) −73.19, while the value determined experimentally, from measurements of parity violating electron scattering, was −72.58 .][
A recent study used four even-numbered isotopes of ]ytterbium
Ytterbium is a chemical element; it has symbol Yb and atomic number 70. It is a metal, the fourteenth and penultimate element in the lanthanide series, which is the basis of the relative stability of its +2 oxidation state. Like the other lanthani ...
to test the formula for weak charge, with corresponding to the number of neutrons and to the number of protons. The formula was found consistent to 0.1% accuracy using the Yb, Yb, Yb, and Yb isotopes of ytterbium.[
In the ]ytterbium
Ytterbium is a chemical element; it has symbol Yb and atomic number 70. It is a metal, the fourteenth and penultimate element in the lanthanide series, which is the basis of the relative stability of its +2 oxidation state. Like the other lanthani ...
test, atoms were excited by laser light in the presence of electric and magnetic fields, and the resulting parity violation was observed.[ The specific transition observed was the ]forbidden transition
In spectroscopy, a forbidden mechanism (forbidden transition or forbidden line) is a spectral line associated with absorption or emission of photons by atomic nuclei, atoms, or molecules which undergo a transition that is not allowed by a particu ...
from 6s S to 5d6s D (24489 cm). The latter state was mixed, due to weak interaction, with 6s6p P (25068 cm) to a degree proportional to the nuclear weak charge.[
]
Particle values
This table gives the values of the electric charge (the coupling to the photon, referred to in this article as Also listed are the approximate weak charge (the ''vector'' part of the Z boson coupling to fermions), ''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 ...
'' (the coupling to the W bosons), ''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 ...
'' (the coupling to the B boson) and the approximate Z boson coupling factors ( and in the "Theoretical" section, below).
If the variable correction terms shown for different values are not added in, then the table's constant values for weak charge are only approximate: They happen to be exact for particles whose energies make the weak mixing angle with This value is very close to the typical angle observed in particle accelerators. The embedded formulas give the (more) exact values for when the Weinberg angle, is known.
For brevity, the table omits antiparticles. Every particle listed (except for the uncharged bosons the 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 ...
, Z boson
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 ...
, 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 ...
, and Higgs boson
The Higgs boson, sometimes called the Higgs particle, is an elementary particle in the Standard Model of particle physics produced by the excited state, quantum excitation of the Higgs field,
one of the field (physics), fields in particl ...
which are their own antiparticles) has an antiparticle with identical mass and opposite charge. All non-zero signs in the table have to be reversed for antiparticles. The paired columns labeled and for fermions (top four rows), have to be swapped in addition to their signs being flipped.
All left-handed (regular) fermions and right-handed antifermions have and therefore interact with the W boson
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 ...
. They could be referred to as ''"proper"-handed'' (that is, they have the "proper" handedness for a W interaction). Right-handed fermions and left-handed antifermions, on the other hand, have zero weak isospin and therefore do not interact with the W boson
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 ...
(except for electrical interaction); they could therefore be referred to as ''"wrong"-handed'' (i.e. they are ''"wrong handed"'' for W interactions). "Proper"-handed fermions are organized into isospin doublets, while "wrong"-handed fermions are represented as isospin singlets. While "wrong"-handed particles do not interact with the W boson
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 ...
(no ''charged current interactions''), all "wrong"-handed fermions known to exist ''do'' interact with the Z boson
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 ...
(''neutral current interactions'').
"Wrong"-handed neutrinos ( sterile neutrinos) have never been observed, but may still exist since they would be invisible to existing detectors.[ Sterile neutrinos play a role in speculations about the way neutrinos have masses (see Seesaw mechanism). The above statement that the interacts with ''all'' fermions will need an exception for sterile neutrinos inserted, if they are ever detected experimentally.
Massive fermions – except (perhaps) neutrinos – always exist in a ]superposition
In mathematics, a linear combination or superposition is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of ''x'' and ''y'' would be any expression of the form ...
of left-handed and right-handed states, and never in pure chiral states. This mixing is caused by interaction with the Higgs field
The Higgs boson, sometimes called the Higgs particle, is an elementary particle in the Standard Model of particle physics produced by the excited state, quantum excitation of the Higgs field,
one of the field (physics), fields in particl ...
, which acts as an infinite source and sink of 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 ...
and / or hypercharge, due to its 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 ...
(for further information see 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 ...
).
Theoretical basis
The formula for the weak charge is derived from the Standard Model, and is given by[
where is the weak charge,
is the weak isospin,
is the weak mixing angle, and is the ]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 ...
.
The approximation for the weak charge is usually valid, since the weak mixing angle typically is and and a discrepancy of only a little more than
Extension to larger, composite protons and neutrons
This relation only directly applies to 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 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 ( fundamental particles), since 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 ...
is not clearly defined for composite particles
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, ...
, such as protons and neutrons, partly due to weak isospin not being conserved. One can set the weak isospin of the proton to and of the neutron to ,[ in order to obtain approximate value for the weak charge. Equivalently, one can sum up the weak charges of the constituent quarks to get the same result.
Thus the calculated weak charge for the neutron is
The weak charge for the proton calculated using the above formula and a weak mixing angle of 29° is
a very small value, similar to the nearly zero total weak charge of charged leptons (see the table above).
Corrections arise when doing the full theoretical calculation for nucleons, however. Specifically, when evaluating ]Feynman diagrams
In theoretical physics, a Feynman diagram is a pictorial representation of the mathematical expressions describing the behavior and interaction of subatomic particles. The scheme is named after American physicist Richard Feynman, who introduced ...
beyond the tree level (i.e. diagrams containing loops), the weak mixing angle becomes dependent on the momentum scale due to the running
Running is a method of terrestrial locomotion by which humans and other animals move quickly on foot. Running is a gait with an aerial phase in which all feet are above the ground (though there are exceptions). This is in contrast to walkin ...
of coupling constants,[ and due to the fact that nucleons are composite particles.
]
Relation to weak hypercharge
Because 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 ...
is given by
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 ...
, weak charge , and electric charge are related by
or equivalently
where is the weak hypercharge for ''left-handed'' fermions and ''right-handed'' antifermions, hence
in the typical case, when the weak mixing angle is approximately 30°.
Derivation
The Standard Model coupling of 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 ...
to the Z boson and 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 ...
is given by:[
where
* and are a left-handed and right-handed fermion field respectively,
* is the B boson field, is the W boson field, and
* is the ]elementary charge
The elementary charge, usually denoted by , is a fundamental physical constant, defined as the electric charge carried by a single proton (+1 ''e'') or, equivalently, the magnitude of the negative electric charge carried by a single electron, ...
expressed as rationalized Planck units,
and the expansion uses for its basis vectors
In mathematics, a set of elements of a vector space is called a basis (: bases) if every element of can be written in a unique way as a finite linear combination of elements of . The coefficients of this linear combination are referred to as ...
the (mostly implicit) 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 () ...
from the Weyl equation
In physics, particularly in quantum field theory, the Weyl equation is a relativistic wave equation for describing massless spin-1/2 particles called Weyl fermions. The equation is named after Hermann Weyl. The Weyl fermions are one of the three ...
:
and
The fields for B and W boson are related to the Z boson field and 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 ...
(photons) by
and
By combining these relations with the above equation and separating by and one obtains:
The term that is present for both left- and right-handed fermions represents the familiar electromagnetic interaction
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 ...
. The terms involving the Z boson
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 ...
depend on the chirality
Chirality () is a property of asymmetry important in several branches of science. The word ''chirality'' is derived from the Greek (''kheir''), "hand", a familiar chiral object.
An object or a system is ''chiral'' if it is distinguishable fro ...
of the fermion, thus there are two different coupling strengths:
and
It is however more convenient to treat fermions as a single particle instead of treating left- and right-handed fermions separately. The Weyl basis
In mathematical physics, the gamma matrices, \ \left\\ , also called the Dirac matrices, are a set of conventional matrices with specific commutation relation, anticommutation relations that ensure they generating set, generate a matrix representat ...
is chosen for this derivation:[
Thus the above expression can be written fairly compactly as:
where
]
See also
* 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 ...
* 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 ...
* Z boson
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 ...
* Weak interaction
In nuclear physics and particle physics, the weak interaction, weak force or the weak nuclear force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interaction, and gravitation. It is th ...
* Neutral current
Weak neutral current interactions are one of the ways in which subatomic particles can interact by means of the weak force. These interactions are mediated by the Z boson. The discovery of weak neutral currents was a significant step towa ...
Notes
References
{{Standard model of physics
Nuclear physics