Majorana neutrino mass constraints in the landscape of nuclear matrix elements

TL;DR

This paper reviews current constraints on Majorana neutrino mass from neutrinoless double beta decay experiments across different isotopes, analyzing the impact of nuclear matrix elements and combining data to refine bounds and potential signals.

Contribution

It introduces a simplified quadratic likelihood approach for combining multi-isotope data and explores how nuclear matrix element uncertainties affect neutrino mass constraints.

Findings

Combined isotope data tighten bounds on $m_{\beta\beta}$.

Certain NME values allow for nonzero $m_{\beta\beta}$ at best fit.

The method clarifies the influence of different experiments on neutrino mass limits.

Abstract

We discuss up-to-date constraints on the Majorana neutrino mass $m_{\beta\beta}$ from neutrinoless double beta decay ($0\nu\beta\beta$) searches in experiments using different isotopes: KamLAND-Zen and EXO ($^{136}$Xe), GERDA and MAJORANA ($^{76}$Ge) and CUORE ($^{130}$Te). Best fits and upper bounds on $m_{\beta\beta}$ are explored in the general landscape of nuclear matrix elements (NME), as well as for specific NME values obtained in representative nuclear models. By approximating the likelihood of $0\nu\beta\beta$ signals through quadratic forms, the analysis of separate and combined isotope data becomes exceedingly simple, and allows to clarify various aspects of multi-isotope data combinations. In particular, we analyze the relative impact of different data in setting upper bounds on $m_{\beta\beta}$, as well as the conditions leading to nonzero $m_{\beta\beta}$ at best fit, for variable values of the NMEs. Detailed results on $m_{\beta\beta}$ from various combinations of data are reported in graphical and numerical form. Implications for future $0\nu\beta\beta$ data analyses and NME calculations are briefly discussed.