Neutrinoless double-beta decay: combining quantum Monte Carlo and the nuclear shell model with the generalized contact formalism

TL;DR

This paper introduces a novel framework combining the nuclear shell model and quantum Monte Carlo methods via the generalized contact formalism to accurately compute neutrinoless double-beta decay nuclear matrix elements, revealing significant differences from previous models.

Contribution

It develops a new hybrid approach integrating quantum Monte Carlo and shell model techniques with the generalized contact formalism for improved decay matrix element calculations.

Findings

Long-range nuclear matrix elements are about 30% smaller than previous shell-model results.

Short-range nuclear matrix element is enhanced by around 30%.

Validation against variational Monte Carlo results in light nuclei.

Abstract

We devise a framework based on the generalized contact formalism that combines the nuclear shell model and quantum Monte Carlo methods and compute the neutrinoless double-beta decay of experimentally relevant nuclei, including $^{76}$Ge, $^{130}$Te, and $^{136}$Xe. In light nuclei, we validate our nuclear matrix element calculations by comparing against accurate variational Monte Carlo results. Due to additional correlations captured by quantum Monte Carlo and introduced within the generalized contact formalism, in heavier systems, we obtain long-range nuclear matrix elements that are about 30% smaller than previous shell-model results. We also evaluate the recently recognized short-range nuclear matrix element estimating its coupling by the charge-independence-breaking term of the Argonne $v_{18}$ potential used in the Monte Carlo calculations. Our results indicate an enhancement of the total nuclear matrix element by around 30%.