Radiative Electroweak Breaking with Pseudogoldstone Higgs Doublets

We consider a realistic example of supersymmetric grand unification based on $SU(3)_c \times SU(3)_L \times SU(3)_R$ in which the electroweak (EW) higgs doublets are `light' as a consequence of the `pseudogoldstone' mechanism. We discuss radiative EW breaking in this model, exploring in particular the `small' (order unity) and `large' $(\approx m_t/m_b)$ $\tan \beta$ regions by studying the variations of $r (\equiv \sqrt{\mu^2_{1,2}/\mu^2_3})$, where $\mu^2_{1,2,3}$ are the well known MSSM parameters evaluated at the GUT scale. For $r$ sufficiently close to unity the quantity $\tan \beta$ can be of order unity, but the converse is not always true.Comment: 18 pages plain LaTeX (to be run twice) and 11 figures available separately from uuencoded file

Supersymmetric Models With Tan(beta) Close to Unity

Within the framework of supersymmetric grand unification, estimates of the $b$ quark mass based on the asymptotic relation $m_b \simeq m_\tau$ single out the region with $\tan\beta$ close to unity, particularly if $m_t(m_t) \stackrel{_<}{_\sim} 170\ GeV$. We explore the radiative breaking of the electroweak symmetry and the associated sparticle and higgs spectroscopy in models with $1 < \tan\beta \stackrel{_<}{_\sim} 1.6$. The lightest scalar higgs is expected to have a mass below $100\ GeV$, while the remaining four higgs masses exceed $300\ GeV$. The lower bounds on some of the sparticle masses are within the range of LEP 200.Comment: 13 pages in plain LaTeX, BA-94-02, 15 figures (available on request

Zeroing In On the Top Quark, LSP and Scalar Higgs Masses

We estimate the top quark, lightest sparticle (LSP) and scalar higgs masses within a supersymmetric grand unified framework in which $\tan\beta \simeq m_t/m_b$ and the electroweak symmetry is radiatively broken. The requirement that the calculated $b$ quark mass lie close to its measured value, together with the cosmological constraint $\Omega_{LSP} \approx 1$, fixes the top quark mass to be $m_t(m_t) \approx 170 \pm 15\ GeV$. The LSP (of bino purity $\stackrel{_>}{_\sim} 98\%)$ has mass $\sim 200 - 350\ GeV$. In the scalar higgs sector the CP-odd scalar mass $m_A \stackrel{_<}{_\sim} 220\ GeV$. With $m_A \stackrel{_>}{_\sim} M_Z$, as suggested by the decay $b \rightarrow s\gamma$, we find $M_Z \stackrel{_<}{_\sim} m_{h^0} (m_{H^0}) \stackrel{_<}{_\sim} 140 (220)\ GeV$ and $120\ GeV \stackrel{_<}{_\sim} m_{H^\pm} \stackrel{_<}{_\sim} 240\ GeV$.Comment: 14 pages in plain LaTeX, BA-93-25, PRL-TH-93/

Yukawa coupling unification and non-universal gaugino mediation of supersymmetry breaking

The requirement of Yukawa coupling unification highly constrains the SUSY parameter space. In several SUSY breaking scenarios it is hard to reconcile Yukawa coupling unification with experimental constraints from B(b->s gamma) and the muon anomalous magnetic moment a_mu. We show that b-tau or even t-b-tau Yukawa unification can be satisfied simultaneously with b->s gamma and a_mu in the non-universal gaugino mediation scenario. Non-universal gaugino masses naturally appear in higher dimensional grand unified models in which gauge symmetry is broken by orbifold compactification. Relations between SUSY contributions to fermion masses, b->s gamma and a_mu which are typical for models with universal gaugino masses are relaxed. Consequently, these phenomenological constraints can be satisfied simultaneously with a relatively light SUSY spectrum, compared to models with universal gaugino masses.Comment: 20 pages, 8 figures. References added. A copy of the paper with better resolution figures can be found at http://www.hep.fsu.edu/~balazs/Physics/Papers/2003

Predictions for Higgs and SUSY spectra from SO(10) Yukawa Unification with mu > 0

We use $t, b, \tau$ Yukawa unification to constrain SUSY parameter space. We find a narrow region survives for $\mu > 0$ (suggested by \bsgam and the anomalous magnetic moment of the muon) with $A_0 \sim - 1.9 m_{16}$, $m_{10} \sim 1.4 m_{16}$, $m_{16} \sim 1200 -3000$ \gev and $\mu, M_{1/2} \sim 100 - 500$ \gev. Demanding Yukawa unification thus makes definite predictions for Higgs and sparticle masses.Comment: 10 pages, 3 figures, revised version to be published in PR

Sparticle mass spectra from SU(5) SUSY GUT models with b−τb-\tau Yukawa coupling unification

Supersymmetric grand unified models based on the gauge group SU(5) often require in addition to gauge coupling unification, the unification of b-quark and $\tau$-lepton Yukawa couplings. We examine SU(5) SUSY GUT parameter space under the condition of $b-\tau$ Yukawa coupling unification using 2-loop MSSM RGEs including full 1-loop threshold effects. The Yukawa-unified solutions break down into two classes. Solutions with low tan\beta ~3-11 are characterized by gluino mass ~1-4 TeV and squark mass ~1-5 TeV. Many of these solutions would be beyond LHC reach, although they contain a light Higgs scalar with mass <123 GeV and so may be excluded should the LHC Higgs hint persist. The second class of solutions occurs at large tan\beta ~35-60, and are a subset of $t-b-\tau$ unified solutions. Constraining only $b-\tau$ unification to ~5% favors a rather light gluino with mass ~0.5-2 TeV, which should ultimately be accessible to LHC searches. While our $b-\tau$ unified solutions can be consistent with a picture of neutralino-only cold dark matter, invoking additional moduli or Peccei-Quinn superfields can allow for all of our Yukawa-unified solutions to be consistent with the measured dark matter abundance.Comment: 19 pages, 5 figures, 1 table, PDFLate

SUSY GUT Model Building

I discuss an evolution of SUSY GUT model building, starting with the construction of 4d GUTs, to orbifold GUTs and finally to orbifold GUTs within the heterotic string. This evolution is an attempt to obtain realistic string models, perhaps relevant for the LHC. This review is in memory of the sudden loss of Julius Wess, a leader in the field, who will be sorely missed.Comment: 24 pages, 14 figures, lectures given at PiTP 2008, Institute for Advanced Study, Princeton, to be published in the European Physical Journal

The Bottom Mass Prediction in Supersymmetric Grand Unification; Uncertainties and Constraints

Grand unified theories often predict unification of Yukawa couplings (e.g., $h_{b} = h_{\tau}$), and thus certain relations among fermion masses. The latter can distinguish these from models that predict only coupling constant unification. The implications of Yukawa couplings of the heavy-family in the supersymmetric extension of the standard model (when embedded in a GUT) are discussed. In particular, uncertainties associated with $m_{t}$ and $m_{b}$, threshold corrections at the low-scale, and threshold and nonrenormalizable-operator corrections associated with a grand-unified sector at the high-scale are parametrized and estimated. The implication of these and of the correlation between $m_{t}$ and the prediction for $\alpha_{s}$ are discussed. Constraints on the $\tan\beta$ range in such models and an upper bound on the $t$-quark pole mass are given and are shown to be affected by the $\alpha_{s}-m_{t}$ correlation. Constraints on the low-scale thresholds are found to be weakened by uncertainties associated with the high-scale.Comment: 23 pages + 7 figures (figures are available upon request), LaTex + RevTex 3.0, UPR-0556

On Supersymmetric b-tau Unification, Gauge Unification, and Fixed Points

The equality assumption of the b and tau Yukawa couplings at the grand-unification scale can strongly constrain the allowed parameter space of supersymmetric models. We examine the constraints in the case that there is a discrepancy > 10% in the gauge coupling unification assumption (which necessarily implies large perturbations at the grand scale). The constraints are shown to diminish in that case [most significantly so if alpha_{s}(M_{Z}) \approx 0.11]. In particular, the requirement that the t Yukawa coupling, h_{t}, is near its quasi-fixed point may not be necessary. We discuss the colored-triplet threshold as a simple example of a source for the discrepancies, and comment on its possible implications. In addition, we point out that supersymmetric (as well as unification-scale) threshold corrections to h_{t} shift the fixed-point curve in the m_{t} - \tan\beta plane. The implications for the prediction of the Higgs boson mass are briefly discussed.Comment: 17 pages + 7 postscript figures (packaged as a .uu file), LaTex + RevTex