Proton decay matrix elements with domain-wall fermions

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 nonperturbative 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 values for the low-energy constants from the nucleon to vacuum matrix elements are given as vertical bar {alpha} vertical bar {approx_equal} vertical bar {beta} vertical bar {approx_equal}0.01 GeV{sup 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 a smaller value ofmore » the form factors, compared to the indirect one, thus enhancing the proton lifetime; indeed, for the {pi}{sup 0} final state the difference between the two methods is quite appreciable.« less