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 toward the unification of electromagnetism and the weak force into the electroweak force, and led to the discovery of the W and Z bosons. The other kind of weak interactions are the charged currents, mediated by the W bosons.
In simple terms The weak force is best known for its role in nuclear decay. It has very short range but (apart from gravity) is the only force to interact with neutrinos. Like other subatomic forces, the weak force is mediated via exchange particles, the W and Z bosons. The W particles are involved in beta decay, and have electric charge – there are both positive and negative W particles. The Z boson does not have any electrical charge. Exchange of a Z boson transfers momentum, spin, and energy, but leaves the interacting particles' quantum numbers unaffected – charge, flavor, baryon number, lepton number, etc. Because there is no transfer of electrical charge involved, exchange of Z particles is referred to as "neutral" in the phrase "neutral current". However the word "current" here has nothing to do with electricity – it simply refers to the exchange of the Z particle. The Z boson's neutral current interaction is determined by a derived quantum number called weak charge, which acts similarly to weak isospin for interactions with the W bosons.
Definition The neutral current that gives the interaction its name is that of the interacting particles. For example, the neutral current contribution to the νee− → νee− elastic scattering amplitude is
M N C ∝ J μ ( N C ) ( ν e ) J ( N C ) μ ( e − ) , {\displaystyle {\mathfrak {M}}^{\mathsf {NC}}~\propto ~J_{\mu }^{\mathsf {(NC)}}(\nu _{\mathrm {e} })\;J^{{\mathsf {(NC)}}\ \mu }(\mathrm {e^{-}} )\ ,}
where the neutral currents describing the flow of the neutrino and of the electron are given by:
J ( N C ) μ ( f ) = u ¯ f γ μ 1 2 ( g V f − g A f γ 5 ) u f , {\displaystyle J^{{\mathsf {(NC)}}\ \mu }(f)={\bar {u}}_{f}\ \gamma ^{\mu }\ {\frac {1}{2}}\left(g_{\mathsf {V}}^{f}-g_{\mathsf {A}}^{f}\ \gamma ^{5}\right)\ u_{f}\ ,}
where:
g V f = T 3 ( f ) − 2 sin 2 θ W Q ( f ) = 1 2 Q W ( f ) {\displaystyle g_{\mathsf {V}}^{f}=T_{3}(f)-2\sin ^{2}\theta _{\mathsf {W}}\ Q(f)={\frac {1}{2}}\ Q_{\mathsf {W}}(f)}
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