Correlations between neutrinoless double-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi></mml:math>, double Gamow-Teller, and double-magnetic decays in the proton-neutron quasiparticle random-phase approximation framework

Abstract

We explore the relation between the nuclear matrix elements of neutrinoless double-beta ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) 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 ($pn$QRPA) framework. We explore a wide span of isoscalar proton-neutron pairing strengths covering the typical range of values that describe well $\ensuremath{\beta}$- and two-neutrino $\ensuremath{\beta}\ensuremath{\beta}$-decay data. Our results indicate good linear correlations between $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ 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 $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-decay nuclear matrix elements.