Narrow Results

Employing projected–Hartree–Fock–Bogoliubov (PHFB) model, nuclear transition matrix elements (NTMEs) $M^{(K)}$ for the neutrinoless double-${\beta }^{-}$ decay of ${}^{76}$Ge isotope are calculated within mechanisms involving light as well as heavy Majorana neutrinos, and classical Majorons. By considering the spin-tensor decomposition of realistic KUO and empirical JUN45 effective two-body interactions, it is noticed that the effect due to SRC on NTMEs $M^{(0\nu )}$ and $M^{(0N)}$ involving the exchange of light and heavy Majorana neutrinos, respectively, is maximally incorporated by the central part of the effective two-body interaction, which varies by a small amount with the inclusion of spin-orbit and tensor components. Presently, the model-dependent uncertainties in the average NTMEs ${\overline{M}}^{(0\nu )}$ and ${\overline{M}}^{(0N)}$ turn out to be about 10% and 37%, respectively.

Within the squark-neutrino mechanism of $R_p$-violating SUSY, sets of 12 nuclear transition matrix elements (NTMEs) are calculated for the neutrinoless double-$\beta$ decay $(0^{+}\to 0^{+}\mathrm{\text{transition}})$ of ${}^{94,96}$Zr, ${}^{100}$Mo, ${}^{110}$Pd, ${}^{128,130}$Te and ${}^{150}$Nd isotopes. Specifically, four sets of HFB wave functions generated with four different parametrizations of the pairing plus multipolar two-body interactions, dipole form factor and three different parametrizations of the Jastrow short-range correlations are employed in the calculation of NTMEs with two possible prescriptions for the hadronization, namely the two-nucleon mode and the pionic mode. Without (with) Miller–Spencer parametrization of short-range correlation, uncertainties in average NTMEs ${\overline{M}}_{2N}^{(\tilde{q}\nu )}$ (QBM), ${\overline{M}}_{2N}^{(\tilde{q}\nu )}$ (NRQM), ${\overline{M}}_{2N}^{(\tilde{q}\nu )}$ (FF3) and ${\overline{M}}_{\pi }^{(\tilde{q}\nu )}$ turn out be 11–18% (29–37%), 11–16% (27–31%), 5–12% (13–17%) and 3–13% (9–15%), respectively.

Using HFB wave functions generated with a realistic KUO and an empirical JUNE45 effective two-body interactions, nuclear transition matrix elements (NTMEs) $M^{(K)}$ for the $0^{+}\to 0^{+}$ transition of neutrinoless double-$\beta$ decay of ${}^{76}$Ge isotope are calculated within mechanisms involving sterile neutrinos, Majorons and compositeness scenario. Uncertainties in nuclear transition matrix elements are estimated by calculating sets of 12 NTMEs with these two sets of wave functions, two alternative forms of finite size effects (FNS) and three different parametrizations of short range correlations (SRC). Uncertainties in NTMEs within mechanisms involving sterile neutrinos, Majorons and composite neutrinos turn out to be about 10%–36% depending on the mass of sterile neutrinos, 10% and 37%, respectively.