An Improved Precision Calculation of the $0\nu\beta\beta$ Contact Term within Chiral Effective Field Theory

TL;DR

This paper refines the calculation of the contact term in neutrinoless double-beta decay within chiral effective field theory, reducing uncertainties and improving the reliability of decay rate predictions.

Contribution

It provides an updated, more precise estimate of the contact term coefficient by including inelastic intermediate states, advancing theoretical understanding of $0 uetaeta$ decay.

Findings

Contact term coefficient estimated as 1.4(3) at $m=m_$

Uncertainty in the contact term reduced by half

Enhanced precision aids in resolving theoretical discrepancies

Abstract

Neutrinoless double-beta ($0\nu\beta\beta$) decay is an as-yet unobserved nuclear process, which stands to provide crucial insights for model-building beyond the Standard Model of particle physics. Its detection would simultaneously confirm the hypothesis that neutrinos are Majorana fermions, thus violating lepton-number conservation, and provide the first measurement of the absolute neutrino mass scale. This work aims to improve the estimation within chiral effective field theory of the so-called ''contact term'' for $0\nu\beta\beta$-decay, a short-range two-nucleon effect which is unaccounted for in traditional nuclear approaches to the process. We conduct a thorough review of the justifications for this contact term and the most precise computation of its size to date ($g_\nu^{NN}$ = 1.3(6) at renormalisation point $\mu=m_\pi$), whose precision is limited by a truncation to elastic intermediate hadronic states. We then perform an extension of this analysis to a subleading class of inelastic intermediate states which we characterise, delivering an updated figure for the contact coefficient ($g_\nu^{NN}$ = 1.4(3) at $\mu=m_\pi$) with uncertainty reduced by half. Such ab initio nuclear results, especially with enhanced precision, show promise for the resolution of disagreements between estimates of $0\nu\beta\beta$ from different many-body methods.