A pathway to unveiling neutrinoless ββ decay nuclear matrix elements via γγ decay

We investigate the experimental feasibility of detecting second-order double-magnetic dipole ( γγ - M 1 M 1 ) decays from double isobaric analog states (DIAS), which have recently been found to be strongly correlated with the nuclear matrix elements of neutrinoless ββ decay. Using the nuclear shell model, we compute theoretical branching ratios for γγ - M 1 M 1 decays and compare them with other competing processes, such as single- γ decay and proton emission, which represent the dominant decay channels. We also estimate the potential competition from internal conversion and internal pair creation, which can influence the decay dynamics. Additionally, we propose an experimental strategy based on using LaBr 3 scintillators to identify γγ - M 1 M 1 transitions from the DIAS amidst the background of the competing processes. Our approach emphasizes the challenges of isolating the rare γγ - M 1 M 1 decay and suggests ways to enhance the experimental detection sensitivity. Our simulations suggest that it may be possible to access experimentally γγ - M 1 M 1 decays from DIAS, shedding light on the neutrinoless ββ decay nuclear matrix elements.