Model-independent determination of nuclear weak form factors and implications for Standard Model precision tests

TL;DR

This paper proposes a model-independent method to determine nuclear weak form factors using charge radii data, which could improve the precision of Standard Model tests and address the CKM unitarity issue.

Contribution

It introduces a new strategy to fix nuclear weak form factors model-independently, challenging existing theoretical uncertainties in beta decay analyses.

Findings

Existing theory uncertainties in the statistical rate function may be underestimated.

The proposed method could impact Standard Model precision tests and CKM unitarity.

Motivates new experiments for charge radii measurements.

Abstract

We analyze the recoil corrections in superallowed beta decays of $T=1$, $J^P=0^+$ nuclei by fixing the mean square charge weak radius model-independently using the data of multiple charge radii across the nuclear isotriplet. By comparing to model estimations, we argue that the existing theory uncertainty in the statistical rate function $f$ might have been substantially underestimated. We discuss the implications of our proposed strategy for precision tests of Standard Model, including a potential alleviation of the first-row CKM unitarity deficit, and motivate new experiments for charge radii measurements.