Infrared quasifixed solutions in a nonminimal supersymmetric standard model

The constraints from LEPII on the mass of the lightest Higgs boson are such that, in the parameter space of the minimal supersymmetric standard model (MSSM), a considerable part of the region that corresponds to the scenario of an infrared fixed point is virtually ruled out by available experimental data. In a nonminimal supersymmetric standard model (NMSSM), the mass of the lightest Higgs boson takes its maximum value in the regime of strong Yukawa coupling, in which case the Yukawa coupling constants are much greater than the gauge coupling constants at the Grand Unification scale \((Y_i (0) \gg \tilde \alpha _i (0))\). In this limiting case, solutions to the renormalization-group equations are attracted to Hill and infrared fixed lines or surfaces in the space of Yukawa coupling constants; for Y_i(0) → ∞, they are concentrated in the vicinities of quasifixed points. However, this attraction is quite weak. For this reason, solutions to the renormalization-group equations are grouped near some line on the Hill surface when all Y_i(0) are close to unity. Approximate solutions for the Yukawa coupling constants within the NMSSM are presented. In addition, the possibility of unifying the Yukawa coupling constants for the b quark and the τ lepton at the scale M_X is discussed.