Uncertainties in nuclear transition matrix elements for neutrinoless $\beta \beta $ decay II: the heavy Majorana neutrino mass mechanism

TL;DR

This paper estimates the uncertainties in nuclear transition matrix elements for neutrinoless double beta decay involving heavy Majorana neutrinos across multiple isotopes, highlighting a 25% uncertainty range.

Contribution

It provides a comprehensive analysis of uncertainties in nuclear matrix elements using various interaction parametrizations and short range correlation models.

Findings

Uncertainties in matrix elements are around 25%.

Excluding Miller-Spenser parametrization reduces uncertainties by 10-15%.

Multiple isotopes analyzed for neutrinoless double beta decay.

Abstract

Employing four different parametrization of the pairing plus multipolar type of effective two-body interaction and three different parametrizations of Jastrow-type of short range correlations, the uncertainties in the nuclear transition matrix elements $M_{N}^{(0\nu)}$ due to the exchange of heavy Majorana neutrino for the $0^{+}\rightarrow 0^{+}$ transition of neutrinoless double beta decay of $^{94}$Zr, $^{96}$Zr, $^{98}$Mo, $^{100}$Mo, $^{104}$Ru, $^{110}$Pd, $^{128,130}$Te and $^{150}$Nd isotopes in the PHFB model are estimated to be around 25%. Excluding the nuclear transition matrix elements calculated with Miller-Spenser parametrization of Jastrow short range correlations, the uncertainties are found to be 10%-15% smaller.