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

TL;DR

This paper develops a relativistic, model-free approach to predict the neutrinoless double beta decay transition amplitude, reducing uncertainties and providing a benchmark for nuclear matrix element calculations.

Contribution

It introduces a Lorentz-invariant chiral Lagrangian framework that allows renormalization of the decay amplitude at leading order without uncertain contact operators.

Findings

Provides a benchmark for $0 uetaeta$ transition amplitude estimates.

Reduces uncertainty in nuclear matrix element calculations.

Motivates relativistic ab initio calculations for light and medium-mass nuclei.

Abstract

Starting from a manifestly Lorentz-invariant chiral Lagrangian, we present a model-free prediction for the transition amplitude of the process $nn\rightarrow pp e^-e^-$ induced by light Majorana neutrinos, which is a key process of the neutrinoless double beta decay ($0\nu\beta\beta$) 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 $0\nu\beta\beta$ transition operator in the calculations of nuclear matrix elements. Generalizations of the present framework could also help to address the uncertainties in $0\nu\beta\beta$ decay induced by other mechanisms. In addition, the present work motivates a relativistic {\it ab initio} calculation of $0\nu\beta\beta$ decay in light and medium-mass nuclei.