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

Abstract

Exchange of two neutrinos (as well as other fermions) generates a long-range parity-violating potential of the form $\sim G^2/r^5$, with characteristic range $\hslash /(2m_{\nu }c)$. 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 $\sim G^2{M}_Z^2{\delta }^3(\vec{r})\sim G\alpha {\delta }^3(\vec{r})$. This interaction produces a $-0.8\%$ correction to the effective weak charge of cesium, resolving the $2\sigma$ discrepancy between the Standard Model prediction and the measured Cs parity-violation amplitude. The corresponding value of the weak mixing angle is ${\sin }^2{\theta }_W=0.2375(19)$ at $q^2\approx 0$, in agreement with the Standard Model prediction ${\sin }^2{\theta }_W=0.23873$. The relative correction to the proton weak charge is about $3\%$. Using these results, we revisit the limits on an additional $Z^{\prime }$ boson and obtain a constraint on isospin-conserving oblique radiative corrections characterized by the Peskin--Takeuchi parameter $S=-0.32(53)$ at $q^2\approx 0$.

Comments: 9 pages, journal version