Probing the desert using gauge coupling unification

Abstract

Abstract We present analytic one-loop expressions for sin 2 θ w , the unification scale M x , and the coupling at the unification scale α ( M x ), in supersymmetric grand-unified models with arbitrary intermediate scales. We correct these expressions to agree with a two-loop calculation for central values of the inputs. Our general results quickly determine whether a particular model has hope of compatibility with the low energy couplings. We then apply these results to traditional supersymmetric SU (5) and to supersymmetric flipped SU (5) × U (1). These results translate into a narrow bound on a function of the extra intermediate scales. In particular, we conclude that even allowing for the experimental uncertainties in low-energy couplings and effects of supersymmetric and Higgs thresholds, traditional supersymmetric SU (5) grand unification without extra thresholds is about one standard deviation away from the measured value of sin 2 θ w . We also calculate the range of proton decay in minimal flipped SU (5) × U (1) allowing for uncertainties in the low-energy couplings and the effects of supersymmetric and Higgs thresholds. Non-observation of proton decay gives a bound on another function of additional intermediate scales beyond the minimal model.