Proton decay matrix elements with domain-wall fermions

TL;DR

This paper presents the first lattice QCD calculations of nucleon decay matrix elements using domain-wall fermions, reducing systematic errors and comparing direct and indirect methods to improve proton decay lifetime estimates.

Contribution

It introduces the use of domain-wall fermions with non-perturbative renormalization for nucleon decay matrix elements in lattice QCD, including quenched and dynamical quark calculations.

Findings

Low energy constants |alpha| and |beta| are approximately 0.01 GeV^3.

Systematic errors from quenching are small compared to other uncertainties.

Direct calculation methods yield smaller form factors, implying longer proton lifetimes.

Abstract

Hadronic matrix elements of operators relevant to nucleon decay in grand unified theories are calculated numerically using lattice QCD. In this context, the domain-wall fermion formulation, combined with non-perturbative renormalization, is used for the first time. These techniques bring reduction of a large fraction of the systematic error from the finite lattice spacing. Our main effort is devoted to a calculation performed in the quenched approximation, where the direct calculation of the nucleon to pseudoscalar matrix elements, as well as the indirect estimate of them from the nucleon to vacuum matrix elements, are performed. First results, using two flavors of dynamical domain-wall quarks for the nucleon to vacuum matrix elements are also presented to address the systematic error of quenching, which appears to be small compared to the other errors. Our results suggest that the representative value for the low energy constants from the nucleon to vacuum matrix elements are given as |alpha| simeq |beta| simeq 0.01 GeV^3. For a more reliable estimate of the physical low energy matrix elements, it is better to use the relevant form factors calculated in the direct method. The direct method tends to give smaller value of the form factors, compared to the indirect one, thus enhancing the proton life-time; indeed for the pi^0 final state the difference between the two methods is quite appreciable.