Long-distance contributions to neutrinoless double beta decay π- → π+ ee

Neutrinoless double beta decay, if detected, would prove that neutrinos are Majorana fermions and provide the direct evidence for lepton number violation. If such decay exists in nature, then pi(-)pi(-) -> ee and pi(-) -> pi(+)ee (or equivalently pi(-)e(+) -> pi(+)e(-)) are the two simplest processes accessible via first-principle lattice QCD calculations. In this work, we calculate the long-distance contributions to the pi(-) -> pi(+)ee transition amplitude using four ensembles at the physical pion mass with various volumes and lattice spacings. We adopt the infinite-volume reconstruction method [1] to control the finite-volume effects arising from the (almost) massless neutrino. Providing the lattice QCD inputs for chiral perturbation theory, we obtain the low energy constant g(nu)(pi pi) (m(rho)) = -10.89(28)(stat)(74)(sys), which is close to g(nu)(pi pi) (m(rho)) = -11.96(31)(stat) determined from the crossed-channel pi(-)pi(-) -> ee decay [2].