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.
Highlights
The supersymmetric grand unified theories (SUSY GUTs) are attractive extensions of the Standard Model (SM)
We find that the threshold correction makes the proton decay rate enhanced about 5% in the minimal SUSY SU (5) GUT
We find that the threshold corrections give tiny effects in spite of the large unified gauge coupling
Summary
The supersymmetric grand unified theories (SUSY GUTs) are attractive extensions of the Standard Model (SM). In the minimal SUSY SU (5) GUT, the color-triplet Higgs exchange induces dangerous dimension-five operators to cause baryon number violation [18, 19]. In this paper we derive the threshold corrections to the Wilson coefficients of the baryonnumber violating dimension-six operators induced by the X boson in the minimal setup of the SU (5) GUT and the extended one with extra SU (5) vector-like pairs. In the minimal SUSY SU (5) GUT, the Kahler potential and the superpotential in the flavor basis of matter superfields are written as KMSGUT = Φ†iA(e−2g5V5 )B AΦiB + Ψ†iAB (e2g5V5 )AC (e2g5V5 )B DΨCi D. y denotes the cubic coupling constant of the adjoint Higgs multiplet and vΣ is the VEV of the adjoint Higgs multiplet. The gauge interactions in the minimal SUSY SU(5) GUT, which are relevant to the evaluation of the threshold correction to the baryon-number violating operators, are summarized in Appendix A. We omit the generation indices (i, j · · · ) below
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