Coupling Constant Unification and LEP Data

The recent LEP data for gauge coupling constants constrain many grand unified models. In this paper, we study several possibilities for unification of gauge coupling constants. Without an intermediate scale, the minimal supersymmetric standard model with two Higgs doublets is the only possibility. For one intermediate scale, we present a few unification schemes without supersymmetry. One of the best theoretical ideas in the last few decades has been to understand the strengths of gauge coupling constants. The first great advance in this direction has been the invention of grand unified theories[1]. The second advance has been four dimensional superstring models[2]. The string theory requires that the coupling must be the same at the string scale[4]. Among the predictions of GUT, the value sin θW , proton decay and fermion mass ratios have attracted most attention. Proton decay experiment constrained the unification scale[5]. In this regard, LEP data[6] of three coupling constants have played the crucial role in testing this idea. Until recently, the strong coupling has not been measured accurately, and the value of sin θw was the prime constraint for the unification models. Thus the accurate measurement of αc at LEP[7] triggered an interest for the study of unification condition. For example, Giveon, Hall and Sarid [8] studied the criteria for unification of coupling constants recently. Our philosophy here is the same as their’s: in search of greater number of possible unification models. With a more accurate determination of αc available now[7], it is timely to study this problem again. Furthermore, in this paper we go beyond the minimal unification models by introducing an intermediate mass scale. The success of coupling constant unification originates from the observation that the apparent difference of coupling constants at low energy is attributed to the running of coupling constants[9]. If the coupling constants are unified to αX at some high energy scale, say MX , then it evolves to α i (μ) = α −1 X − bi 2π ln ( μ MX )