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

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 $0^{+}\to 0^{+}$ 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.