γγ decay as a probe of neutrinoless ββ decay nuclear matrix elements

We study double gamma ($\gamma\gamma$) decay nuclear matrix elements (NMEs) for a wide range of nuclei from titanium to xenon, and explore their relation neutrinoless double-beta ($0\nu\beta\beta$) NMEs. To favor the comparison, we focus on double-magnetic dipole transitions in final $\beta\beta$ nuclei, particular $\gamma\gamma$ isobaric analog initial state into ground state. For with equal-energy photons, our large-scale shell model results show good linear correlation between $0\nu\beta\beta$ Our analysis reveals that holds driven by spin or orbital angular momentum due dominance zero-coupled nucleon pairs, feature common decay. shell-model findings point out potential future measurements constrain NMEs, which are key answer fundamental physics questions based experiments.