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_π=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.