We present an ab initio study of the correlation between nuclear matrix elements (NMEs) of $0\nu \beta \beta$ decay and nucleon-nucleon scattering phase shifts in the ${}^{1}S_0$ channel. Starting from 34 statistically weighted interactions derived from chiral effective field theory, we apply the valence-space in-medium similarity renormalization group to calculate NMEs in the four experimentally relevant isotopes. Comparing with the ${}^{1}S_0$-channel phase shifts given from each interaction, in all cases we observe a strong correlation for scattering energies above approximately 75 MeV. From a global sensitivity analysis, enabled by newly developed machine-learning emulators, we find that $0\nu \beta \beta$ NMEs indeed depend primarily on the $C_{1S0}$ low-energy constant, which is associated with phase shifts in that partial wave. These results provide the first clear correlation between $0\nu \beta \beta$ decay NMEs and a measured observable, and have already been shown to reduce the total uncertainty of the NME in ${}^{76}\mathrm{Ge}$ by $\approx 25\%$. This correlation will serve as a crucial component in ongoing and future refinements of ab initio uncertainty estimates for $0\nu \beta \beta$ decay.

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• Effective field theory
• Neutrinoless double beta decay
• Nucleon-nucleon interactions
• 59 ≤ A ≤ 89
• 90 ≤ A ≤ 149
• Ab initio calculations