Neutrinoless double-beta decay in a finite volume from relativistic effective field theory

TL;DR

This paper uses relativistic pionless effective field theory to predict neutrinoless double-beta decay matrix elements in finite volume, comparing with lattice QCD results at various pion masses to test nuclear EFTs' predictive power.

Contribution

It provides the first predictions of the $nn\rightarrow ppee$ transition matrix elements in finite volume using relativistic EFT, directly comparing with lattice QCD data at multiple pion masses.

Findings

Predicted matrix elements at different pion masses match lattice QCD results.

Volume dependence of the transition matrix elements is characterized.

Benchmarking of nuclear EFTs against lattice QCD is facilitated.

Abstract

The neutrinoless double-beta decay process $nn\rightarrow ppee$ within the light Majorana-exchange scenario is studied using the relativistic pionless effective field theory (EFT) in finite-volume cubic boxes with the periodic boundary conditions. Using the low-energy two-nucleon scattering observables from lattice QCD available at $m_\pi=300$, 450, 510, and 806 MeV, the leading-order $nn\rightarrow ppee$ transition matrix elements are predicted and their volume dependence is investigated. The predictions for the $nn\rightarrow ppee$ transition matrix elements can be directly compared to the lattice QCD calculations of the $nn\rightarrow ppee$ process at the same pion masses. In particular for the matrix element at $m_\pi=806$ MeV, the predictions with relativistic pionless EFT are confronted to the recent first lattice QCD evaluation. Therefore, the present results are expected to play a crucial role in the benchmark between the nuclear EFTs and the upcoming lattice QCD calculations of the $nn\rightarrow pp ee$ process, which would provide a nontrivial test on the predictive power of nuclear EFTs on neutrinoless double-beta decay.