Neutrinoless ββ decay nuclear matrix elements complete up to N2LO in heavy nuclei
Daniel Castillo, Lotta Jokiniemi, Pablo Soriano, J. Menéndez
Abstract
We evaluate all nuclear matrix elements (NMEs) up to next-to-next-to leading order (N 2 LO) in chiral effective field theory ( χ EFT) for the neutrinoless double-beta ( 0 ν β β ) decay of the nuclei most relevant for experiments, including 76 Ge, 100 Mo, and 136 Xe. We use the proton-neutron quasiparticle random-phase approximation (pnQRPA) and the nuclear shell model to calculate the N 2 LO NMEs from very low-momentum (ultrasoft) neutrinos and from loop diagrams usually neglected in 0 ν β β studies. Our results indicate that the overall N 2 LO contribution is centered around − ( 5 - 10 ) % for the shell model and + ( 10 - 15 ) % for the pnQRPA, with sizable uncertainties due to the scale dependence of the ultrasoft NMEs and the short-range nature of the loop NMEs. The sign discrepancy between many-body methods is common to all studied nuclei and points to the different behaviour of the intermediate states of the 0 ν β β decay. Within uncertainties, our results for the ultrasoft NME are of similar size as contributions usually referred to as “beyond the closure approximation”.