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

TL;DR

This paper investigates the impact of parity-violating neutrino exchange interactions in atomic systems, revealing a correction to weak charges that aligns experimental results with the Standard Model and constrains new physics models.

Contribution

It introduces a long-range parity-violating potential from neutrino exchange, showing its effects on atomic weak charges and providing updated limits on new physics parameters.

Findings

A 0.8% correction to cesium's weak charge resolves a discrepancy.

The weak mixing angle at low momentum transfer agrees with Standard Model.

Constraints on additional Z' bosons and oblique corrections are improved.

Abstract

Exchange of two neutrinos (as well as other fermions) generates a long-range parity-violating (PV) potential of the form $\sim G^2/r^5$, with characteristic range $\hbar/(2m_\nu c)$. 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 $3\%$, with a similar correction for the electron weak charge. 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 $q^2 \approx 0$.