In nuclear physics and atomic physics, weak charge, or rarely neutral weak charge, refers to the Standard Model weak interaction coupling of a particle to the Z boson.
For example, for any given nuclear isotope, the total weak charge is approximately −0.99 per neutron, and +0.07 per proton.
[1] It also shows an effect of parity violation during electron scattering.
[3] Measurements in 2017 give the weak charge of the proton as 0.0719±0.0045 .
[4] The weak charge may be summed in atomic nuclei, so that the predicted weak charge for 133Cs (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 .
[5] A recent study used four even-numbered isotopes of ytterbium to test the formula Qw = −0.989 N + 0.071 Z , for weak charge, with N corresponding to the number of neutrons and Z to the number of protons.
The formula was found consistent to 0.1% accuracy using the 170Yb, 172Yb, 174Yb, and 176Yb isotopes of ytterbium.
[6] In the ytterbium test, atoms were excited by laser light in the presence of electric and magnetic fields, and the resulting parity violation was observed.
[6] This table gives the values of the electric charge (the coupling to the photon, referred to in this article as
(the vector part of the Z boson coupling to fermions), weak isospin
The table's values are approximate: They happen to be exact for particles whose energies make the weak mixing angle
This value is very close to the typical approximately 29° angle observed in particle accelerators.
All non-zero signs in the table have to be reversed for antiparticles.
The paired columns labeled LEFT and RIGHT 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
The above statement that the Z0 interacts with all fermions will need an exception for sterile neutrinos inserted, if they are ever detected experimentally.
Massive fermions – except (perhaps) neutrinos[c] – always exist in a superposition of left-handed and right-handed states, and never in pure chiral states.
This mixing is caused by interaction with the Higgs field, which acts as an infinite source and sink of weak isospin and / or hypercharge, due to its non-zero vacuum expectation value (for further information see Higgs mechanism).
The formula for the weak charge is derived from the Standard Model, and is given by[9][10]
This relation only directly applies to quarks and leptons (fundamental particles), since weak isospin is not clearly defined for composite particles, such as protons and neutrons, partly due to weak isospin not being conserved.
One can set the weak isospin of the proton to ++1/2 and of the neutron to −+1/2,[11][12] 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.
Corrections arise when doing the full theoretical calculation for nucleons, however.
Specifically, when evaluating Feynman diagrams beyond the tree level (i.e. diagrams containing loops), the weak mixing angle becomes dependent on the momentum scale due to the running of coupling constants,[10] and due to the fact that nucleons are composite particles.
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°.
The Standard Model coupling of fermions to the Z boson and photon is given by:[13]
where and the expansion uses for its basis vectors the (mostly implicit) Pauli matrices from the Weyl equation:[clarification needed]
term that is present for both left- and right-handed fermions represents the familiar electromagnetic interaction.
The terms involving the Z boson depend on the chirality of the fermion, thus there are two different coupling strengths: