Lattice QCD calculation of the proton decay matrix element in the continuum limit

Abstract

We present a quenched lattice QCD calculation of the $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ parameters of the proton decay matrix element. The simulation is carried out using the Wilson quark action at three values of the lattice spacing in the range $a\ensuremath{\approx}0.1\ensuremath{-}0.064\text{ }\text{ }\mathrm{f}\mathrm{m}$ to study the scaling violation effect. We find only mild scaling violation when the lattice scale is determined by the nucleon mass. We obtain in the continuum limit, $|\ensuremath{\alpha}(\mathrm{N}\mathrm{D}\mathrm{R},2\text{ }\text{ }\mathrm{G}\mathrm{e}\mathrm{V})|=0.0090(09)(+5\ensuremath{-}19)\text{ }\text{ }{\mathrm{G}\mathrm{e}\mathrm{V}}^{3}$ and $|\ensuremath{\beta}(\mathrm{N}\mathrm{D}\mathrm{R},2\text{ }\text{ }\mathrm{G}\mathrm{e}\mathrm{V})|=0.0096(09)(+6\ensuremath{-}20)\text{ }\text{ }{\mathrm{G}\mathrm{e}\mathrm{V}}^{3}$ with $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ in a relatively opposite sign, where the first error is statistical and the second is due to the uncertainty in the determination of the physical scale.