Lattice QCD calculation of light sterile neutrino contribution in $0\nu2\beta$ decay

TL;DR

This study uses lattice QCD to calculate the contribution of light sterile neutrinos to neutrinoless double beta decay, providing new low-energy constants across a range of neutrino masses and comparing results with previous methods.

Contribution

First lattice QCD calculation of light sterile neutrino effects in neutrinoless double beta decay at physical pion mass with detailed low-energy constants.

Findings

Lattice results are consistent with previous interpolation methods within 20% at small neutrino masses.

Discrepancy at zero neutrino mass is explained.

Results at large neutrino mass agree with previous lattice determinations.

Abstract

We present a lattice QCD study of the neutrinoless double beta decay involving light sterile neutrinos. The calculation is performed at physical pion mass using five gauge ensembles generated with the $2+1$-flavor domain wall fermions. We obtain the low-energy constants $g_{\text{LR}}^{\pi\pi}(m_\nu)$ with the neutrino mass $m_\nu$ from $0$ GeV to $3$ GeV. The lattice results are reasonably consistent with the previous interpolation method with a $\sim20\%$ deviation at small $m_\nu$. We provide an explanation on the discrepancy at vanishing neutrino mass. At large $m_\nu$, a good consistence between our results and the previous lattice determination of $g_{4}^{\pi\pi}(\mu)$ is found at $\mu=m_\nu=3$ GeV.