Lattice Calculation of Short-Range Contributions to Neutrinoless Double-Beta Decay $\pi^-\to\pi^+ ee$ at Physical Pion Mass

TL;DR

This study uses lattice QCD with physical pion mass to accurately compute short-range contributions to neutrinoless double-beta decay, addressing previous discrepancies and improving theoretical understanding.

Contribution

It introduces a new method to subtract contamination effects and performs nonperturbative renormalization, reducing uncertainties in lattice calculations of decay matrix elements.

Findings

Reduced uncertainties in short-range matrix elements.

Developed a method to subtract around-the-world effects.

Provides an independent cross-check for previous lattice results.

Abstract

Neutrinoless double-beta ($0\nu\beta\beta$) decays provide an excellent probe for determining whether neutrinos are Dirac or Majorana fermions. The short-range matrix elements associated with the $\pi^- \to \pi^+ ee$ process contribute at leading order in the $0\nu\beta\beta$ 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 $\pi^- \to \pi^+ ee$ 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.