Relativistic model-free prediction for neutrinoless double beta decay at leading order

Starting from a manifestly Lorentz-invariant chiral Lagrangian, we present a model-free prediction for the transition amplitude of the process nn→ppe−e− induced by light Majorana neutrinos, which is a key process of the neutrinoless double beta decay (0νββ) in heavy nuclei employed in large-scale searches. Contrary to the nonrelativistic case, we show that the transition amplitude can be renormalized at leading order without any uncertain contact operators. The predicted amplitude defines a stringent benchmark for the previous estimation with model-dependent inputs, and greatly reduces the uncertainty of 0νββ transition operator in the calculations of nuclear matrix elements. Generalizations of the present framework could also help to address the uncertainties in 0νββ decay induced by other mechanisms. In addition, the present work motivates a relativistic ab initio calculation of 0νββ decay in light and medium-mass nuclei.