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

TL;DR

This paper reports a lattice QCD calculation of proton decay matrix elements, demonstrating mild scaling violations and providing continuum limit estimates for the lpha and eta parameters with quantified uncertainties.

Contribution

The study introduces a quenched lattice QCD approach with multiple lattice spacings to accurately determine proton decay matrix elements in the continuum limit.

Findings

Mild scaling violation observed across lattice spacings.

Continuum limit values for lpha and eta parameters obtained.

Quantified uncertainties include statistical and scale determination errors.

Abstract

We present a quenched lattice QCD calculation of the \alpha and \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\approx 0.1-0.064 fm 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, |\alpha(NDR,2GeV)|=0.0090(09)(^{+5}_{-19})GeV^3 and |\beta(NDR,2GeV)|=0.0096(09)(^{+6}_{-20})GeV^3 with \alpha and \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.