Uncertainties in nuclear transition matrix elements for neutrinoless $\beta \beta $ decay within the PHFB model

TL;DR

This paper calculates nuclear transition matrix elements for neutrinoless double beta decay in various isotopes using the PHFB model, assessing uncertainties with different parameterizations and short-range correlations.

Contribution

It introduces a comprehensive method to estimate uncertainties in nuclear matrix elements by employing multiple parameterizations and correlation models within the PHFB framework.

Findings

Calculated $M^{(0 u)}$ for multiple isotopes.

Provided uncertainty estimates for the matrix elements.

Compared effects of different parameterizations on results.

Abstract

The nuclear transition matrix elements $M^{(0\nu)}$ for the neutrinoless double beta decay of $^{94,96}$Zr, $^{98,100}$Mo, $^{104}$Ru, $^{110}$Pd, $^{128,130}$Te and $^{150}$Nd isotopes in the case of $0^{+}\rightarrow 0^{+}$ transition are calculated using the PHFB wave functions, which are eigenvectors of four different parameterizations of a Hamiltonian with pairing plus multipolar effective two-body interaction. \QCOM{35}{In addition, the consideration of} Employing two (three) different parameterizations of Jastrow-type short range correlations, \QCOM{19}{provides us with} a set of eight (twelve) different nuclear transition matrix elements $M^{(0\nu)}$ is built for each decay, whose averages in conjunction with their standard deviations provide an estimate of the model uncertainties.