Neutrinoless $\beta \beta$ decay transition matrix elements within mechanisms involving light Majorana neutrinos, classical Majorons, and sterile neutrinos

In the projected-Hartree-Fock-Bogoliubov (PHFB) model, uncertainties in the nuclear transition matrix elements for the neutrinoless double-$\beta$ decay of ${}^{94,96}$Zr, ${}^{98,100}$Mo, ${}^{104}$Ru, ${}^{110}$Pd, ${}^{128,130}$Te, and ${}^{150}$Nd isotopes within mechanisms involving light Majorana neutrinos, classical Majorons, and sterile neutrinos are statistically estimated by considering sets of 16 (24) matrix elements calculated with four different parametrizations of the pairing plus multipolar type of effective two-body interaction, two sets of form factors, and two (three) different parametrizations of Jastrow type of short-range correlations. In the mechanisms involving the light Majorana neutrinos and classical Majorons, the maximum uncertainty is about 15% and in the scenario of sterile neutrinos, it varies in between approximately 4 (9)%–20 (36)% without(with) Jastrow short range correlations with the Miller-Spencer parametrization, depending on the considered mass of the sterile neutrinos.

Figure 1

Distribution of $g_V\left(q^2\right)$ and $g_M\left(q^2\right)$ for FNS1 and FNS2.

Figure 2

Radial dependence of $C^{\left(0\nu \right)}\left(r\right)$ for the ${\left({\beta }^{-}{\beta }^{-}\right)}_{0\nu }$ mode of ${}^{100}$Mo isotope.

Figure 3

Radial dependence of $C^{\left(0\nu \right)}\left(r\right)$ for the ${\left({\beta }^{-}{\beta }^{-}\right)}_{0\nu }$ mode of ${}^{96}$Zr, ${}^{100}$Mo, ${}^{110}$Pd, ${}^{128,130}$Te, and ${}^{150}$Nd isotopes. (a), (b), (c), and (d) correspond to HOC1, HOC1+SRC1, HOC1+SRC2, and HOC1+SRC3, respectively.

Figure 4

Variation in extracted limits on the ${\nu }_h-{\nu }_e$ mixing matrix element $|U_{eh}{|}^2$ with the mass $m_h$.