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

The neutrinoless double-beta decay process nn 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_=300, 450, 510, and 806 MeV, the leading-order nn ppee transition matrix elements are predicted with a precision of 10\%-20\% and their volume dependence is investigated. This is possible thanks to the fact that the leading-order nn ppee transition matrix elements can be properly renormalized in the relativistic pionless EFT without the uncertain nn pp ee contact term, in contrast to the nonrelativistic case. The predictions for the nn ppee transition matrix elements can be directly matched to the LQCD calculations of the nn ppee process at the same pion masses. Therefore, the present results are expected to play a crucial role in the benchmark between the nuclear EFTs and the upcoming LQCD calculations of the nn pp ee process, which would provide a nontrivial test on the predictive power of nuclear EFTs on neutrinoless double-beta decay.