Lattice Calculation of Short-Range Contributions to Neutrinoless Double-Beta Decay $\ddot{I}{€}^{-}\to \ddot{I}{€}^{+}ee$ at Physical Pion Mass

Abstract

Neutrinoless double-beta ($0\hat{I}½{\hat{I}}^2{\hat{I}}^2$) decays provide an excellent probe for determining whether neutrinos are Dirac or Majorana fermions. The short-range matrix elements associated with the $\ddot{I}{€}^{-}\to \ddot{I}{€}^{+}ee$ process contribute at leading order in the $0\hat{I}½{\hat{I}}^2{\hat{I}}^2$ decay channel $nn\to ppee$ 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 $\ddot{I}{€}^{-}\to \ddot{I}{€}^{+}ee$ matrix elements using domain wall fermion ensembles at the physical pion mass generated by the RBC and UKQCD Collaborations. 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 a nonperturbative renormalization using the RI/SMOM scheme. 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.

26 pages, 13 figures