Uncertainties in nuclear transition matrix elements for $\beta ^{+}\beta ^{+}$ and $\varepsilon \beta ^{+}$ modes of neutrinoless positron double-$\beta $ decay within PHFB model

TL;DR

This paper evaluates uncertainties in nuclear transition matrix elements for certain neutrinoless double-beta decay modes using the PHFB model, considering various interactions and correlations, and finds generally small uncertainties except for one isotope.

Contribution

It provides a detailed analysis of uncertainties in nuclear matrix elements for neutrinoless double-positron decay modes within the PHFB model, considering multiple interaction parameterizations.

Findings

Uncertainties are below 14% for light neutrino exchange in most isotopes.

Uncertainties are below 35% for heavy neutrino exchange in most isotopes.

Significant uncertainty for $^{130}$Ba in the studied modes.

Abstract

Uncertainties in the nuclear transition matrix elements $M^{(0\nu)}$ and $M^{(0N)}$ of the double-positron emission $(\beta ^{+}\beta ^{+})_{0\nu}$ and electron-positron conversion $(\varepsilon \beta ^{+})_{0\nu}$ modes due to the exchange of light and heavy Majorana neutrinos, respectively, are calculated for $^{96}$Ru, $^{102}$Pd, $^{106}$Cd, $^{124}$Xe, $^{130}$Ba and $^{156}$Dy isotopes by employing the PHFB model with four different parameterization of the pairing plus multipolar two-body interactions and three different parameterizations of the Jastrow short range correlations. In all cases but for $^{130}$Ba, the uncertainties are smaller than 14% for light Majorana neutrino exchange and 35% for the exchange of a heavy Majorana neutrino.