A path from lattice QCD to the short-distance contribution to 0νββ with a light Majorana neutrino

Neutrinoless double beta (0νββ) decay is a lepton number violating nuclear transition whose observation will have profound consequences on elementary particle physics. To draw reliable conclusions from the current experimental limits and potential future discoveries, the uncertainties in the theoretical predictions of its decay rate are needed to be reduced. A major contribution to these uncertainties comes from the effective field theories (EFT) matched ab initio nuclear many-body calculation of its nuclear matrix element. A recently identified short-distance contribution at leading order in the effective field theory amplitude of the subprocess nn→ pp(ee) remains undetermined, and only lattice quantum chromodynamics (QCD) can directly and reliably determine the associated low-energy constant. We provide here a framework to obtain the physical decay amplitude, and hence the missing contribution, from the lattice QCD calculation of the correlation function for this process. The complications arising from the Euclidean and finite-volume nature of the corresponding correlation functions are fully resolved. This work fills the gap between first-principles studies of the nn→ pp(ee) amplitude from lattice QCD and those from effective field theory and can be readily employed in the ongoing lattice QCD studies of this process.