Kinematic sensitivity to the Fierz term of $\beta$-decay differential spectra

TL;DR

This paper investigates how the Fierz term affects the energy spectra in beta decay, highlighting that certain differential observables are more sensitive than previously thought, and corrects past errors in analyzing angular correlation data.

Contribution

It reveals that differential spectra can provide enhanced sensitivity to the Fierz term and corrects earlier misinterpretations in experimental analyses.

Findings

Differential observables like beta and recoil energy spectra are more sensitive to the Fierz term.

Previous analyses of beta-nu angular correlations contained errors affecting constraints on exotic couplings.

Implications for selecting decay transitions in searches for new physics.

Abstract

The current most stringent constraints on exotic scalar or tensor couplings in neutron and nuclear $\beta$ decay, involving left-handed neutrinos, are obtained from the Fierz interference term. The sensitivity to this term in a correlation coefficient is usually driven by an energy-averaged kinematic factor that increases monotonically toward smaller values of the $\beta$ endpoint energies. We first point out here that this property does not hold for certain differential observables that are directly sensitive to the Fierz term, such as the $\beta$ or the recoil energy spectrum. This observation is relevant for the selection of sensitive transitions in searches for exotic couplings through spectrum shape measurements. We then point out previous errors in the exploitation of measurements of the $\beta-\nu$ angular correlation coefficient and discuss their impact on the extraction of constraints on exotic couplings.