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

TL;DR

This study reveals a strong correlation between neutrinoless double-beta decay nuclear matrix elements and nucleon-nucleon phase shifts, linking nuclear decay properties to measurable scattering data, and highlighting the importance of the $C_{1S0}$ low-energy constant.

Contribution

It demonstrates a clear correlation between decay matrix elements and phase shifts using ab initio methods and machine learning, advancing uncertainty quantification in nuclear physics.

Findings

Strong correlation above 75 MeV scattering energy.

Decay matrix elements depend mainly on the $C_{1S0}$ low-energy constant.

First clear link between decay matrix elements and measurable observable.

Abstract

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.