Threshold Corrections to Baryon Number Violating Operators in Supersymmetric $SU(5)$ GUTs

Abstract The nucleon decay is a significant phenomenon to verify grand unified theories (GUTs). For the precise prediction of the nucleon lifetime induced by the gauge bosons associated with the unified gauge group, it is important to include the renormalization effects on the Wilson coefficients of the dimension-six baryon number violating operators. In this study, we have derived the threshold corrections to these coefficients at the one-loop level in the minimal supersymmetric SU ( 5 ) GUT and the extended one with additional SU ( 5 ) vector-like pairs. As a result, it is found that the nucleon decay rate is suppressed about 5% in the minimal setup, and then the suppression could be O ( 10 ) % in the vector-like matter extensions.