# Comparison between Variational Monte Carlo and Shell Model Calculations of Neutrinoless Double Beta Decay Matrix Elements in Light Nuclei

## TL;DR

This paper compares variational Monte Carlo and shell model methods for calculating neutrinoless double beta decay matrix elements in light nuclei, highlighting the importance of both long-range and short-range correlations for accuracy.

## Contribution

It provides a detailed benchmark comparison between VMC and shell model calculations, assessing uncertainties and the effects of model choices in light nuclei.

## Key findings

- VMC matrix elements show small variational uncertainties.
- Shell model results depend on model space and correlation treatments.
- Accurate decay matrix elements require proper inclusion of correlations.

## Abstract

Benchmark comparisons between many-body methods are performed to assess the ingredients necessary for an accurate calculation of neutrinoless double beta decay matrix elements. Shell model and variational Monte Carlo (VMC) calculations are carried out for $A=10$ and $12$ nuclei. Different variational wavefunctions are used to evaluate the uncertainties in the {\it ab initio} calculations, finding fairly small differences between the VMC double beta decay matrix elements. For shell model calculations, the role of model space truncation, radial wavefunction choices, and short-range correlation are investigated and all found to be important. Based on the detailed comparisons between the VMC and shell model approaches, we conclude that accurate descriptions of neutrinoless double beta decay matrix elements require a proper treatment of both long-range and short-range correlations.