Benchmarking nuclear matrix elements of $0\nu\beta\beta$ decay with high-energy nuclear collisions

Reducing uncertainties in the nuclear matrix elements (NMEs) remains a critical challenge in designing and interpreting experiments aimed at discovering neutrinoless double beta ($0\nu\beta\beta$) decay. Here, we identify a class of observables, distinct from those employed in low-energy nuclear structure applications, that are strongly correlated with the NMEs: momentum correlations among hadrons produced in high-energy nuclear collisions. Focusing on the $^{150}$Nd$\rightarrow$$^{150}$Sm transition, we combine a Bayesian analysis of the structure of $^{150}$Nd with simulations of high-energy $^{150}$Nd+$^{150}$Nd collisions. We reveal prominent correlations between the NMEs and features of the quark-gluon plasma (QGP) formed in these processes, such as spatial gradients and anisotropies, which are accessible via collective flow measurements. Our findings demonstrate collider experiments involving $0\nu\beta\beta$ decay candidates as a platform for benchmarking theoretical predictions of the NMEs.