Lattice QCD calculation of light sterile neutrino contribution in $0\nu 2\beta$ decay

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 $\sim 20\%$ 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.

Comments: 19 pages, 5 figures