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

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.