Long-distance nuclear matrix elements for neutrinoless double-beta decay from lattice QCD

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 a heretofore unobserved process which, if observed, would imply that neutrinos are Majorana particles. Interpretations of the stringent experimental constraints on <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 half-lives require calculations of nuclear matrix elements. This work presents the first lattice quantum chromodynamics (LQCD) calculation of the matrix element for <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mn>0</e:mn><e:mi>ν</e:mi><e:mi>β</e:mi><e:mi>β</e:mi></e:math> decay in a multinucleon system, specifically the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>n</g:mi><g:mi>n</g:mi><g:mo stretchy="false">→</g:mo><g:mi>p</g:mi><g:mi>p</g:mi><g:mi>e</g:mi><g:mi>e</g:mi></g:math> transition, mediated by a light left-handed Majorana neutrino propagating over nuclear-scale distances. This calculation is performed with quark masses corresponding to a pion mass of <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msub><j:mi>m</j:mi><j:mi>π</j:mi></j:msub><j:mo>=</j:mo><j:mn>806</j:mn><j:mtext> </j:mtext><j:mtext> </j:mtext><j:mi>MeV</j:mi></j:math> at a single lattice spacing and volume. The statistically cleaner <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:msup><l:mi mathvariant="normal">Σ</l:mi><l:mo>−</l:mo></l:msup><l:mo stretchy="false">→</l:mo><l:msup><l:mi mathvariant="normal">Σ</l:mi><l:mo>+</l:mo></l:msup><l:mi>e</l:mi><l:mi>e</l:mi></l:math> transition is also computed in order to investigate various systematic uncertainties. The prospects for matching the results of LQCD calculations onto a nuclear effective field theory to determine a leading-order low-energy constant relevant for <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>β</q:mi><q:mi>β</q:mi></q:math> decay with a light Majorana neutrino are investigated. This work, therefore, sets the stage for future calculations at physical values of the quark masses that, combined with effective field theory and nuclear many-body studies, will provide controlled theoretical inputs to experimental searches of <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mn>0</s:mn><s:mi>ν</s:mi><s:mi>β</s:mi><s:mi>β</s:mi></s:math> decay.