Effects of dispersion parity-violating interaction in electron scattering and atoms

Exchange of two neutrinos (as well as other fermions) generates a long-range parity-violating potential of the form ∼ G 2 / r 5 , with characteristic range ℏ / ( 2 m ν c ) . In atomic systems the corresponding matrix elements converge at distances r < 10 / M Z , so that the interaction between electron and quarks effectively reduces to a contact term ∼ G 2 M Z 2 δ 3 ( r → ) ∼ G α δ 3 ( r → ) . This interaction produces a − 0.8 % correction to the effective weak charge of cesium, resolving the 2 σ discrepancy between the Standard Model prediction and the measured Cs parity-violation amplitude. The corresponding value of the weak mixing angle is sin 2 θ W = 0.2375 ( 19 ) at q 2 ≈ 0 , in agreement with the Standard Model prediction sin 2 θ W = 0.23873 . The relative correction to the proton weak charge is about 3%. Using these results, we revisit the limits on an additional Z ′ boson and obtain a constraint on isospin-conserving oblique radiative corrections characterized by the Peskin–Takeuchi parameter S = − 0.32 ( 53 ) at q 2 ≈ 0 .