Upper bound of the proton lifetime in product-group unification

Models of supersymmetric grand unied theories based on the SU(5)GUTU(N)H gauge group (N =2 ; 3) have a symmetry that guarantees light Higgs doublets and the absence of dimension-ve proton-decay operators. We analysed the proton decay induced by the gauge-boson exchange in these models. Upper bounds of proton lifetime are obtained; (p ! 0 e + ) < 6:0 10 33 yrs in the SU(5)GUTU(2)H model and (p ! 0 e + ) < 5:3 10 35 yrs in the SU(5)GUTU(3)H model. Various uncertainties in the predictions are also discussed.