Nuclear matrix elements for $0\nu \beta \beta$ decays with light or heavy Majorana-neutrino exchange

We compute the nuclear matrix elements (NMEs) corresponding to the neutrinoless double beta ($0\nu \beta \beta$) decays of nuclei which attract current experimental interest. We concentrate on ground-state-to-ground-state decay transitions mediated by light (l-NMEs) or heavy (h-NMEs) Majorana neutrinos. The computations are done in realistic single-particle model spaces using the proton-neutron quasiparticle random-phase approximation (pnQRPA) with two-nucleon interactions based on the Bonn one-boson-exchange $G$ matrix. Both the l-NMEs and the h-NMEs include the appropriate short-range correlations, nucleon form factors, and higher-order nucleonic weak currents. In addition, both types of NMEs are corrected for the isospin symmetry by the recently proposed method in which the particle-particle proton-neutron interaction parameter ($g_{\mathrm{pp}}$) is decomposed into isoscalar ($g_{\mathrm{pp}}^{T=0}$) and isovector ($g_{\mathrm{pp}}^{T=1}$) parts. A detailed analysis of the l-NMEs and the h-NMEs is performed to benchmark our computer code and to compare with other recent calculations which produce h-NMEs that are in tension with each other.

Figure 1

Multipole decomposition of the l-NME $M^{\left(0\nu \right)}$ for ${}^{76}\text{Ge},{}^{82}\text{Se},{}^{96}\text{Zr},{}^{100}\text{Mo},{}^{110}\text{Pd},{}^{116}\text{Cd},{}^{124}\text{Sn}$, and ${}^{128}\text{Te}$.

Figure 2

Multipole decomposition of the h-NME $M^{\left(0\nu \right)}$ for ${}^{76}\text{Ge},{}^{82}\text{Se},{}^{96}\text{Zr},{}^{100}\text{Mo},{}^{110}\text{Pd},{}^{116}\text{Cd},{}^{124}\text{Sn}$, and ${}^{128}\text{Te}$.

Figure 3

Multipole decomposition of the l-NME $M^{\left(0\nu \right)}$ for ${}^{130}\mathrm{Te}$ and ${}^{136}\text{Xe}$.

Figure 4

Multipole decomposition of the h-NME $M^{\left(0\nu \right)}$ for ${}^{130}\text{Te}$ and ${}^{136}\text{Xe}$.

Figure 5

Radial dependence of the l-NMEs $M_{\mathrm{F}}^{\left(0\nu \right)},M_{\mathrm{GT}}^{\left(0\nu \right)},M_{\mathrm{T}}^{\left(0\nu \right)}$ and the full matrix element $M^{\left(0\nu \right)}$ in the case of ${}^{76}\mathrm{Ge}$.

Figure 6

Radial dependence of the h-NMEs $M_{\mathrm{F}}^{\left(0\nu \right)},M_{\mathrm{GT}}^{\left(0\nu \right)},M_{\mathrm{T}}^{\left(0\nu \right)}$ and the full matrix element $M^{\left(0\nu \right)}$ in the case of ${}^{76}\mathrm{Ge}$.