Suppression of Higgsino mediated proton decay by cancellations in grand unified theories and strings

A mechanism for the enhancement for proton lifetime in supersymmetric/supergravity (SUSY/SUGRA) grand unified theories (GUTs) and in string theory models is discussed where Higgsino mediated proton decay arising from color triplets (anti-triplets) with charges $Q=-1/3(1/3)$ and $Q=-4/3(4/3)$ is suppressed by an internal cancellation due to contributions from different sources. We exhibit the mechanism for an SU(5) model with $45_H+\bar{45}_H$ Higgs multiplets in addition to the usual Higgs structure of the minimal model. This model contains both $Q=-1/3(1/3)$ and $Q=-4/3(4/3)$ Higgs color triplets (anti-triplets) and simple constraints allow for a complete suppression of Higgsino mediated proton decay. Suppression of proton decay in an SU(5) model with Planck scale contributions is also considered. The suppression mechanism is then exhibited for an SO(10) model with a unified Higgs structure involving $144_H+\bar{144}_H$ representations.The SU(5) decomposition of $144_H+\bar{144}_H$ contains $5_H+\bar 5_H$ and $45_H+\bar{45}_H$ and the cancellation mechanism arises among these contributions which mirrror the SU(5) case. The cancellation mechanism appears to be more generally valid for a larger class of unification models. Specifically the cancellation mechanism may play a role in string model constructions to suppress proton decay from dimension five operators. The mechanism allows for the suppression of proton decay consistent with current data allowing for the possibility that proton decay may be visible in the next round of nucleon stability experiment.Comment: 26 pages, no figures. Revtex 4. To appear in Physical Review