Infrared quasifixed solutions in a nonminimal supersymmetric standard model

Abstract

The considerable part of the parameter space in the MSSM corresponding to the infrared quasi fixed point scenario is almost excluded by LEP II bounds on the lightest Higgs boson mass. In the NMSSM the mass of the lightest Higgs boson reaches its maximum value in the strong Yukawa coupling limit when Yukawa couplings are essentially larger than gauge ones at the Grand Unification scale. In this limit the solutions of the renormalisation group equations are attracted to the infrared and Hill type effective fixed lines or surfaces in the Yukawa coupling parameter space. They are concentrated in the vicinity of quasi fixed points for Y i (0) → ∞. However the solutions are attracted to such points rather weakly. For this reason when all Y i (0) ∼ 1 the solutions of the renormalisation group equations are gathered near a line in the Hill type effective surface. In the paper the approximate solutions for the NMSSM Yukawa couplings are given. The possibility of b-quark and τ -lepton Yukawa coupling unification at the scale M X is also discussed.

The Higgs sector of the next-to-minimal supersymmetric standard model

“…(36) A similar analysis of the renormalization group equations for the other parameters shows that a low value of tan β is favoured [26]. Note that the bounds on tan β derived from the LEP experiments cannot be applied here since these experiments assume MSSM couplings.…”

“…(23)(24)(25)(26)(27)(28) does not lend itself easily to obtaining analytic expressions for the physical Higgs masses. However, reasonably simple expressions can be found by making an approximation, providing expressions which may be used to shed some light on the behaviour of the Higgs masses as the other parameters are varied.…”

“…The above pseudoscalar and scalar mass matrices, Eqns. (20)(21)(22)(23)(24)(25)(26)(27)(28), do not lend themselves easily to obtaining analytic expressions for the physical Higgs masses. However, reasonably simple expressions can be found by performing a systematic expansion for large tan β and large M A [on the generic electroweak scale].…”

On the Origin of Approximate Custodial Symmetry in the Two-Higgs Doublet Model

“…, which coincides with the intersection point of the invariant and Hill type effective lines [72]- [74].…”

“…Thus, at the electroweak scale, the solutions of the RG equations for the Yukawa couplings are concentrated near the quasi-fixed point, which is located at the intersection of the invariant line with the Hill type effective surface [72]- [74].…”