Lattice calculation of short-range contributions to neutrinoless double-beta decay <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi>π</mml:mi> <mml:mo>−</mml:mo> </mml:msup> <mml:mo stretchy="false">→</mml

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> ) decays provide an excellent probe for determining whether neutrinos are Dirac or Majorana fermions. The short-range matrix elements associated with the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msup> <c:mi>π</c:mi> <c:mo>−</c:mo> </c:msup> <c:mo stretchy="false">→</c:mo> <c:msup> <c:mi>π</c:mi> <c:mo>+</c:mo> </c:msup> <c:mi>e</c:mi> <c:mi>e</c:mi> </c:math> process contribute at leading order in the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mn>0</f:mn> <f:mi>ν</f:mi> <f:mi>β</f:mi> <f:mi>β</f:mi> </f:math> decay channel <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:mi>n</h:mi> <h:mi>n</h:mi> <h:mo stretchy="false">→</h:mo> <h:mi>p</h:mi> <h:mi>p</h:mi> <h:mi>e</h:mi> <h:mi>e</h:mi> </h:math> through pion exchange between nucleons. However, current lattice calculations show notable discrepancies in predicting these short-range contributions. To address this issue, we perform a lattice QCD calculation of the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msup> <k:mi>π</k:mi> <k:mo>−</k:mo> </k:msup> <k:mo stretchy="false">→</k:mo> <k:msup> <k:mi>π</k:mi> <k:mo>+</k:mo> </k:msup> <k:mi>e</k:mi> <k:mi>e</k:mi> </k:math> matrix elements using domain wall fermion ensembles at the physical pion mass generated by the RBC/UKQCD Collaboration. To mitigate contamination from around-the-world effects, we develop a new method to reconstruct and subtract them directly from lattice data. We then perform nonperturbative renormalization in the regularization-independent symmetric momentum-subtraction scheme (RI/SMOM), using the <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:mo stretchy="false">(</n:mo> <n:msub> <n:mi>γ</n:mi> <n:mi>μ</n:mi> </n:msub> <n:mo>,</n:mo> <n:msub> <n:mi>γ</n:mi> <n:mi>μ</n:mi> </n:msub> <n:mo stretchy="false">)</n:mo> </n:math> and <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:mo stretchy="false">(</r:mo> <r:menclose notation="updiagonalstrike" other="updiag1"> <r:mi>q</r:mi> </r:menclose> <r:mo>,</r:mo> <r:menclose notation="updiagonalstrike" other="updiag1"> <r:mi>q</r:mi> </r:menclose> <r:mo stretchy="false">)</r:mo> </r:math> projectors. Compared with previous studies, this work reduces the uncertainties in the matrix elements and provides an independent cross-check that helps to reconcile the discrepancies among previous lattice calculations.