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

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