$0^{+}$ to $2^{+}$ neutrinoless double-$\beta$ decay of ${}^{76}$Ge, ${}^{82}$Se, ${}^{130}$Te and ${}^{136}$Xe in the microscopic interacting boson model}

Abstract

Here, we study the neutrinoless double-$\beta$ ($0\nu \beta \beta$) decay between the ground state and the first $2^{+}$ state of ${}^{76}\text{mbox}Ge\to {}^{76}\text{mbox}Se$, ${}^{82}\text{mbox}Se\to {}^{82}\text{mbox}Kr$, ${}^{130}\text{mbox}Te\to {}^{130}\text{mbox}Xe$ and ${}^{136}\text{mbox}Xe\to {}^{136}\text{mbox}Ba$ systems. The relevant nuclear matrix elements (NMEs) involved in the process are calculated within the formalism of the microscopic interacting boson model (IBM-2). The IBM-2 has been widely used to obtain predictions for nuclear observables, such as the spectrum, but also to explore the possible emergence of beyond-the-Standard Model effects in the weak interactions of nuclei. Our calculations are carried out by considering the exchange of a Majorana neutrino between two nucleons ($2N$-mechanism). In addition to NMEs, we calculate the associated leptonic phase-space factors (PSFs) using electron radial wave functions, which are obtained by solving numerically the Dirac equation of a screened Coulomb potential that takes into account finite nuclear size. By combining our IBM-2 results for the NMEs with those for the PSFs along with experimental half-life limits, we can set limits on the $⟨\lambda ⟩$ and $⟨\eta ⟩$ couplings of left-right (L-R) models.

Comments: 9 pages, 1 figure