Lattice calculation of short-range contributions to neutrinoless double-beta decay 𝜋 − → 𝜋 + 𝑒𝑒 at physical pion mass
Neutrinoless double-beta (0𝜈𝛽𝛽) decays provide an excellent probe for determining whether neutrinos are Dirac or Majorana fermions. The short-range matrix elements associated with the 𝜋 − → 𝜋 + 𝑒𝑒 process contribute at leading order in the 0𝜈𝛽𝛽 decay channel 𝑛𝑛 → 𝑝𝑝𝑒𝑒 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 𝜋 − → 𝜋 + 𝑒𝑒 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 (𝛾 𝜇 , 𝛾 𝜇 ) and ($\not{𝑞}$, $\not{𝑞}$) 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.