Long-distance nuclear matrix elements for neutrinoless double-beta decay from lattice QCD

Neutrinoless double-beta (0) decay is a heretofore unobserved process which, if observed, would imply that neutrinos are Majorana particles. Interpretations of the stringent experimental constraints on 0-decay half-lives require calculations of nuclear matrix elements. This work presents the first lattice quantum-chromodynamics (LQCD) calculation of the matrix element for 0 decay in a multi-nucleon system, specifically the nn pp ee transition, mediated by a light left-handed Majorana neutrino propagating over nuclear-scale distances. This calculation is performed with quark masses corresponding to a pion mass of m_ = 806 MeV at a single lattice spacing and volume. The statistically cleaner ^- ^+ ee transition is also computed in order to investigate various systematic uncertainties. The prospects for matching the results of LQCD calculations onto a nuclear effective field theory to determine a leading-order low-energy constant relevant for 0 decay with a light Majorana neutrino are investigated. This work, therefore, sets the stage for future calculations at physical values of the quark masses that, combined with effective field theory and nuclear many-body studies, will provide controlled theoretical inputs to experimental searches of 0 decay.