Correlation of neutrinoless double-beta decay nuclear matrix elements with nucleon-nucleon phase shifts

We present an ab initio study of the correlation between nuclear matrix elements of neutrinoless double-beta ($0\nu\beta\beta$) decay and nucleon-nucleon scattering phase shifts in the $^1S_0$ channel. Starting from thirty-four statistically weighted interactions derived from chiral effective field theory, we apply the valence-space in-medium similarity renormalization group to calculate nuclear matrix elements in four key experimental isotopes. Comparing with the $^1S_0$-channel phase shifts given from each interaction, in all cases we observe a strong correlation for scattering energies above 75 MeV. Furthermore, a global sensitivity analysis, enabled by newly developed machine-learning emulators, confirms that the nuclear matrix elements of the decay depend primarily on the $C_{1S0}$ low-energy constant, which is associated with the phase shifts in that partial wave. These results provide the first clear correlation between $0\nu\beta\beta$ decay nuclear matrix elements and a measured observable and will therefore serve as a crucial component in ongoing and future refinements of ab initio uncertainty estimates.