Correlations between neutrinoless double-β, double Gamow-Teller, and double-magnetic decays in the proton-neutron quasiparticle random-phase approximation framework

We explore the relation between the nuclear matrix elements of neutrinoless double-beta (0v beta beta) decay and two other processes: double Gamow-Teller (DGT) and double-magnetic-dipole (M1M1) transitions, with focus on medium-mass to heavy nuclei studied with the proton-neutron quasiparticle random-phase approximation (pnQRPA) framework. We explore a wide span of isoscalar proton-neutron pairing strengths covering the typical range of values that describe well beta- and two-neutrino beta beta-decay data. Our results indicate good linear correlations between 0v beta beta and both DGT and M1M1 matrix elements. Together with future measurements of DGT and M 1M 1 transitions, these correlations could help constrain the values of the 0v beta beta-decay nuclear matrix elements.