# Computation of products of phase space factors and nuclear matrix elements for the Double Beta Decay

## TL;DR

This paper introduces a novel method for calculating the product of phase space factors and nuclear matrix elements in double-beta decay, improving consistency and reducing uncertainties in theoretical predictions and experimental interpretations.

## Contribution

It proposes a direct computation of the product of PSF and NME, enhancing coherence and comparability across different studies and isotopes in double-beta decay research.

## Key findings

- New constraints on light neutrino mass from recent half-life limits.
- Method applicable to both two-neutrino and neutrinoless decay modes.
- Suggestions to reduce uncertainties related to the axial-vector constant.

## Abstract

The nuclear matrix elements (NME) and phase space factors (PSF) entering the half-life formulas of the double-beta decay (DBD) process are two key quantities whose accurate computation still represents a challenge. In this paper we propose a new approach of calculating them, namely to compute directly their product as an unique formula. This procedure allows a more coherent treatment of the nuclear approximations and input parameters appearing in both quantities and avoids possible confusion in interpreting the DBD data due to different individual expressions adopted for PSF and NME (and consequently their reporting in different units) by different authors. Our calculations are performed for both two neutrino ($2\nu\beta\beta$) and neutrinoless ($0\nu\beta\beta$) decay modes, and for five nuclei of most experimental interest. Further, using the most recent experimental limits for $0\nu\beta\beta$ decay half-lives, we provide new constraints on the light mass neutrino parameter. Finally, by separating in the half-lives formulas the factor representing the axial-vector constant to the forth, we advance suggestions on how to reduce the errors introduced in calculation by the uncertain value of this constant by exploiting the DBD data from different isotopes and/or decay modes.