Neutrinoless Double Beta Decay from Lattice QCD: The Short-Distance $\pi^-\rightarrow\pi^+ e^- e^-$ Amplitude

TL;DR

This paper uses lattice QCD to calculate short-distance contributions to a hypothetical pion decay process, providing key inputs for neutrinoless double beta decay studies.

Contribution

It presents the first lattice QCD determination of pion matrix elements for five EFT operators relevant to neutrinoless double beta decay.

Findings

Computed matrix elements for five EFT operators.

Extrapolated results to physical quark masses and continuum limit.

Provided low-energy constants for $ ext{EFT}$ calculations.

Abstract

This work presents a determination of potential short-distance contributions to the unphysical $\pi^-\rightarrow\pi^+ e^- e^-$ decay through lattice QCD calculations. The hadronic contributions to the transition amplitude are described by the pion matrix elements of five Standard Model Effective Field Theory operators, which are computed on five ensembles of domain-wall fermions with $N_f = 2 + 1$ quark flavors with a range of heavier-than-physical values of the light quark masses. The matrix elements are extrapolated to the continuum, physical light-quark mass, and infinite volume limit using a functional form derived in chiral Effective Field Theory ($\chi\mathrm{EFT}$). This extrapolation also yields the relevant low-energy constants of $\chi\mathrm{EFT}$, which are necessary input for $\chi\mathrm{EFT}$ calculations of neutrinoless double beta decay of nuclei.