Majorana neutrino mass constraints in the landscape of nuclear matrix elements

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.

Comments: Minor clarifications and additions in the text. Matches published version, Phys. Rev. D 106 (2022) 1, 013009