Ab initio calculation of the contact operator contribution in the standard mechanism for neutrinoless double beta decay

TL;DR

This paper calculates the impact of a contact operator on neutrinoless double beta decay NMEs using chiral interactions, demonstrating a significant enhancement in $^{48}$Ca with quantified uncertainties.

Contribution

It introduces a method to determine the contact operator's low-energy constant from synthetic data and assesses its effect on NMEs across different nuclei.

Findings

Contact term increases NME by 43% in $^{48}$Ca

Dependence on SRG scale and chiral order can be mitigated by LEC readjustment

First demonstration of contact term's quantitative impact on NMEs

Abstract

Starting from chiral nuclear interactions, we evaluate the contribution of the leading-order contact transition operator to the nuclear matrix element (NME) of neutrinoless double-beta decay, assuming a light Majorana neutrino-exchange mechanism. The corresponding low-energy constant (LEC) is determined by fitting the transition amplitude of the $nn\to ppe^-e^-$ process to a recently proposed synthetic datum. We examine the dependence of the amplitude on similarity renormalization group (SRG) scale and chiral expansion order of the nuclear interaction, finding that both dependences can be compensated to a large extent by readjusting the LEC. We evaluate the contribution of both the leading-order contact operator and standard long-range operator to the neutrinoless double-beta decays in the light nuclei $^{6,8}$He and the candidate nucleus $^{48}$Ca. Our results provide the first clear demonstration that the contact term enhances the NME by 43(7)% in $^{48}$Ca, where the uncertainty is propagated from the synthetic datum.