Renormalizability of the leading order operator for neutrinoless double beta decay with the effects of finite nucleon size

TL;DR

This paper investigates the impact of finite nucleon size on neutrinoless double beta decay within chiral effective field theory, demonstrating that a non-perturbative approach can effectively renormalize the transition amplitude.

Contribution

It introduces a non-perturbative method to incorporate finite nucleon size effects in neutrinoless double beta decay calculations, aligning with previous results and supporting the validity of this approach.

Findings

Finite nucleon size effects are comparable to leading contact terms.

The non-perturbative scheme successfully renormalizes the amplitude.

Results are consistent with previous perturbative studies.

Abstract

The fundamental process of neutrinoless double beta decay, $nn\to ppe^-e^-$, dominated by the exchange of light Majorana neutrinos, is studied in the framework of chiral effective field theory. Considering neutrinos as virtual states, we evaluate the contributions of finite nucleon size to the transition amplitude in a non-perturbative manner, as opposed to expanding these effects in powers of momentum. Based on the nucleon form factors expressed in terms of the dipole and Kelly parametrizations, we find that, at the leading order, the present scheme could renormalize the amplitude in the context of the standard mechanism and provide predictions consistent with the previous investigations. Consequently, we argue that the impact of the effects of finite nucleon size on the amplitude is comparable to that of the leading-order contact term introduced in [Phys. Rev. Lett.120, 202001(2018)] in a perturbative scheme. Our results provide not only a benchmark calculation for the transition amplitude between two schemes but also evidence for the reasonableness of non-perturbative treatment for the effects of finite nucleon size in conventional nuclear many-body methods.