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

Abstract

The neutrinoless double-beta decay process $nn\to ppee$ 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 $nn\to ppee$ transition matrix elements are predicted and their volume dependence is investigated. The predictions for the $nn\to ppee$ transition matrix elements can be directly compared to the lattice QCD calculations of the $nn\to ppee$ 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 $nn\to ppee$ process, which would provide a nontrivial test on the predictive power of nuclear EFTs on neutrinoless double-beta decay.

35 pages, 7 figures

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