Correlations Between Neutrinoless Double-Beta, Double Gamow-Teller and Double-Magnetic Decays in the pnQRPA Framework

We explore the relation between the nuclear matrix elements of neutrinoless double-beta ($0\nu \beta \beta$) 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 $0\nu \beta \beta$ and both DGT and M1M1 matrix elements. Together with future measurements of DGT and M1M1 transitions, these correlations could help constrain the values of the $0\nu \beta \beta$-decay nuclear matrix elements.