Nucleon Decay with Domain-Wall Fermions

There are two methods to calculate nucleon decay matrix elements using lattice QCD. One is the direct calculation of the matrix elements dealing with threeand various two-point functions [1,2,3]. The other is the indirect method where one relies on chiral perturbation theory whose low energy constants are calculated on the lattice [4,5,1,2,3]. The former method is preferable but requires huge computation, typically 10 times larger than the latter to achieve similar statistical accuracy. In a previous work [3], we made use of good chiral symmetry of the domain-wall fermion with the DBW2 gauge action [6]. The proton decay matrix element of the pion final state was calculated with both methods. The results are consistent with each other within the relatively large error. There we assumed the mixing of operators arising from the explicit chiral symmetry breaking is negligible. Here we reconsider this issue by calculating the mixing with a non-perturbative renormalization (NPR). Also the matrix elements of the proton decay in case of the non-degenerate quark mass in the pseudoscalar state are calculated allowing further discussion on the effectiveness of the chiral perturbation theory. All of our calculations are done on the