Unified minimal supersymmetric model with large Yukawa couplings

Abstract

The consequences of assuming the third-generation Yukawa couplings are all large and comparable are studied in the context of the minimal supersymmetric extension of the standard model. General aspects of the RG evolution of the parameters, theoretical constraints needed to ensure proper electroweak symmetry breaking, and experimental and cosmological bounds on low-energy parameters are presented. We also present complete and exact semi-analytic solutions to the 1-loop RG equations. Focusing on SU(5) or SO(10) unification, we analyze the relationship between the top and bottom masses and the superspectrum, and the phenomenological implications of the GUT conditions on scalar masses. Future experimental measurements of the superspectrum and of the strong coupling will distinguish between various GUT-scale scenarios. And if present experimental knowledge is to be accounted for most naturally, a particular set of predictions is singled out.

The soft supersymmetry-breaking Lagrangian: theory and applications

“…the U(1) P Q and U(1) R symmetries of the MSSM) result in a light chargino with mass ≪ m Z , which is ruled out experimentally [159,52]. For example, µ is typically much lighter than m Z in the U(1) P Q scenario, while the soft parameters B ≡ b/µ ∼ M 2 ∼ A are typically much lighter than m Z for U(1) R [52]. Either scenario predicts a chargino lighter than the current LEP limits.…”

“…Second, if the parameters of the Higgs potential are comparable in size, it is natural for the Higgs fields to have VEVs of similar magnitudes. One argument in the opposite direction is that the attractive idea that the t, b, and τ Yukawa couplings unify at a high scale requires large tan β [150,151,152,153,154,155,156,52,157,158]. Precisely how large is subtle, since one must include running effects on masses and higher order effects.…”

“…It was noticed quite some time ago that radiative electroweak symmetry breaking without fine tuning can be more difficult to achieve in the very large tan β limit [159,52]. To see this, rewrite the minimization conditions as follows: 15) in which m 2 A is the mass of the CP-odd Higgs boson.…”

“…Radiative electroweak symmetry breaking with large tan β is also complicated by the similar running of the soft mass-squared parameters of the two Higgs doublets when the t and b quark Yukawa couplings are comparable [52] However, this problem can be alleviated via the well-known mechanism of splitting the scalar masses using additional D term contributions [162,163,164,165,137]. Whenever a gauged U(1) symmetry is broken, contributions to soft scalar mass squareds can result via the D terms, which can change the superpartner spectrum in a significant way.…”

“…and R was done for the MSSM in [52,53]. For completeness, the the spurion charge assignments for the MSSM parameters under U(1) P Q and U(1) R are given in Table 3.…”