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 \(0\nu\nu\beta\beta\) from different many-body methods.