Calculating fermion masses in superstring derived standard-like models

Abstract

One of the intriguing achievements of the superstring derived standard-like models in the free fermionic formulation is the possible explanation of the top quark mass hierarchy and the successful prediction of the top quark mass. An important property of the superstring derived standard-like models, which enhances their predictive power, is the existence of three and only three generations in the massless spectrum. Up to some motivated assumptions with regard to the light Higgs spectrum, it is then possible to calculate the fermion masses in terms of string tree-level amplitudes and some VEVs that parameterize the string vacuum. I discuss the calculation of the heavy generation masses in the superstring derived standard-like models. The top quark Yukawa coupling is obtained from a cubic-level mass term while the bottom quark and tau lepton mass terms are obtained from non-renormalizable terms. The calculation of the heavy fermion Yukawa couplings is outlined in detail in a specific toy model. The dependence of the effective bottom quark and tau lepton Yukawa couplings on the flat directions at the string scale is examined. The gauge and Yukawa couplings are extrapolated from the string unification scale to low energies. Agreement with α strong, sin 2 θ w and α em at M z is imposed, which necessitates the existence of intermediate matter thresholds. The needed intermediate matter thresholds exist in the specific toy model. The effect of the intermediate matter thresholds on the extrapolated Yukawa couplings in studied. It is observed that the intermediate matter thresholds also help to maintain the correct b τ mass relation. It is found that for a large portion of the parameter space, the LEP precision data for α strong, sin 2 θ w and α em, as well the top quark mass and the b τ mass relation can all simultaneously be consistent with the superstring derived standard-like models. Possible corrections due to the supersymmetric mass spectrum are studied as well as the minimization of the supersymmetric Higgs potential. It is demonstrated that the calculated values of the Higgs VEV ratio, tan β = η 1 η 2 , can be compatible with the minimization of the one-loop effective Higgs potential.