Improved precision calculation of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>0</mml:mn><mml:mi>ν</mml:mi><mml:mi>β</mml:mi><mml:mi>β</mml:mi></mml:mrow></mml:math> contact term within chiral effect

Neutrinoless double-beta (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mn>0</a:mn><a:mi>ν</a:mi><a:mi>β</a:mi><a:mi>β</a:mi></a:math>) 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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mn>0</c:mn><c:mi>ν</c:mi><c:mi>β</c:mi><c:mi>β</c:mi></c:math> decay, a short-range two-nucleon effect that 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 [<e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:msubsup><e:mrow><e:mi>g</e:mi></e:mrow><e:mrow><e:mi>ν</e:mi></e:mrow><e:mrow><e:mi>N</e:mi><e:mi>N</e:mi></e:mrow></e:msubsup><e:mo>=</e:mo><e:mn>1.3</e:mn><e:mo stretchy="false">(</e:mo><e:mn>6</e:mn><e:mo stretchy="false">)</e:mo></e:mrow></e:math> at renormalization point <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>μ</i:mi><i:mo>=</i:mo><i:msub><i:mi>m</i:mi><i:mi>π</i:mi></i:msub></i:math>], 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 that we characterize, delivering an updated figure for the contact coefficient [<k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msubsup><k:mi>g</k:mi><k:mi>ν</k:mi><k:mrow><k:mi>N</k:mi><k:mi>N</k:mi></k:mrow></k:msubsup><k:mo>=</k:mo><k:mn>1.4</k:mn><k:mo stretchy="false">(</k:mo><k:mn>3</k:mn><k:mo stretchy="false">)</k:mo></k:math> at <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>μ</o:mi><o:mo>=</o:mo><o:msub><o:mi>m</o:mi><o:mi>π</o:mi></o:msub></o:math>] with uncertainty reduced by half. Such nuclear results, especially with enhanced precision, show promise for the resolution of disagreements between estimates of <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mn>0</q:mn><q:mi>ν</q:mi><q:mi>ν</q:mi><q:mi>β</q:mi><q:mi>β</q:mi></q:math> from different many-body methods.