Nucleon Decay Matrix Elements for Domain-Wall Fermions

Nucleon decay is one of the most important aspect that any (SUSY) GUT model has. In low-energy effective theories it is represented by dimension six operators made of one lepton field and three quark fields. In the decay of p → π + e, for example, we need to calculate hadronic matrix element of the three quark operator O R/L;L = ǫ(uCPR/Ld)PLu with initial proton and final pion states, where C is the charge conjugation matrix. PR/L represents the right or left projection matrix, respectively. Lattice calculation of the nucleon decay matrix elements historically started with the indirect calculation [1]. First, one estimates the overlap of the operator to the proton state, α and β,