Long-range parity non-conserving electron-nucleon interaction

TL;DR

This paper investigates long-range parity non-conserving electron-nucleon interactions mediated by neutrino and electron vacuum polarization, showing they can significantly influence observed PNC effects and exceed experimental uncertainties.

Contribution

It introduces the calculation of long-range PNC potentials from neutrino and electron vacuum polarization, highlighting their substantial impact on atomic PNC measurements.

Findings

Long-range PNC potentials can account for a significant fraction of observed effects.

The contributions of these potentials exceed experimental error margins in Cs.

Long-range interactions extend the effective range of PNC effects by orders of magnitude.

Abstract

As known, electron vacuum polarization by nuclear Coulomb field produces Uehling potential with the range $\hbar/2m_e c$. Similarly, neutrino vacuum polarization by $Z$ boson field produces long range potential $\sim G^2/r^5$ with the large range $\hbar/2m_{\nu}c$. Attempts to measure parity-conserving part of this potential produced only limits on this potential which are several orders of magnitude higher than the standard model predictions. We show that parity non-conserving (PNC) part of the neutrino exchange potential $W_L(r)$ gives a significant fraction of the observed PNC effects. Mixed $Z-\gamma$ electron vacuum polarization produces PNC potential with range $\hbar/2m_e c$, which exceeds the range of the weak interaction by five orders of magnitude. We calculate contribution of the long-range PNC potentials to the nuclear spin independent and nuclear spin dependent PNC effects. The cases of the single-isotope PNC effects and the ratio of PNC effects in different isotopes are considered for Ca, Cs, Ba, Sm, Dy, Yb, Hg, Tl, Pb, Bi, Fr, Ra atoms and ions. Contributions of the long-range PNC potentials ($\sim$1\%) significantly exceed experimental error (0.35\%) for PNC effect in Cs.