Implications of the Partial Width Z->bb for Supersymmetry Searches and Model-Building

Assuming that the actual values of the top quark mass at FNAL and of the ratio of partial widths Z->bb/Z->hadrons at LEP are within their current one-sigma reported ranges, we present a No-Lose Theorem for superpartner searches at LEP II and an upgraded Tevatron. We impose only two theoretical assumptions: the Lagrangian is that of the Minimal Supersymmetric Standard Model with arbitrary soft-breaking terms, and all couplings remain perturbative up to scales of order 10^16 GeV; there are no assumptions about the soft SUSY breaking parameters, proton decay, cosmology, etc. In particular, if the LEP and FNAL values hold up and supersymmetry is responsible for the discrepancy with the SM prediction of the partial width of Z->bb, then we must have charginos and/or top squarks observable at the upgraded machines. Furthermore, little deviation from the SM is predicted within "super-unified" SUSY. Finally, it appears to be extremely difficult to find any unified MSSM model, regardless of the form of soft SUSY breaking, that can explain the partial width for large tan(beta); in particular, no model with top-bottom-tau Yukawa coupling unification appears to be consistent with the experiments.Comment: 15 pages, University of Michigan preprint UM-TH-94-23. LaTeX file with 4 uuencoded figures sent separately. Compressed PS file (114Kb) available by anonymous FTP from 141.211.96.66 in /pub/preprints/UM-TH-94-23.ps.

Predictions for Constrained Minimal Supersymmetry with Bottom-Tau Mass Unification

We examine the Constrained Minimal Supersymmetric Standard Model (CMSSM) with an additional requirement of strict b - tau unification in the region of small tan(beta). We find that the parameter space becomes completely limited below about 1 TeV by physical constraints alone, without a fine-tuning constraint. We study the resulting phenomenological consequences, and point out several ways of falsifying the adopted b - tau unification assumption. We also comment on the effect of a constraint from the non-observation of proton decay.Comment: Michigan preprint UM-TH-94-03, LaTeX, 18 pages with inline figures (figures included in uuencoded file). Complete PS file also available by anonymous FTP to williams.physics.lsa.umich.edu in /pub/preprints/UM-TH-94-03.ps.Z or by e-mailing reques

Quasi-Fixed Points and Charge and Colour Breaking in Low Scale Models

We show that the current LEP2 lower bound upon the minimal supersymmetric standard model (MSSM) lightest Higgs mass rules out quasi-fixed scenarios for string scales between 10^6 and 10^{11} GeV unless the heaviest stop mass is more than 2 TeV. We consider the implications of the low string scale for charge and colour breaking (CCB) bounds in the MSSM, and demonstrate that CCB bounds from F and D-flat directions are significantly weakened. For scales less than 10^{10} GeV these bounds become merely that degenerate scalar mass squared values are positive at the string scale.Comment: 17 pages, 4 figures. Replacement has added discussion on errors due to alpha_s(MZ) errors, as well as deviations from the quasi-fixed point. Text has been clarifie

The Higgs Boson Mass as a Probe of the Minimal Supersymmetric Standard Model

Recently, the LEP collaborations have reported a lower bound on a Standard Model-like Higgs boson of order 89 GeV. We discuss the implications of this bound for the minimal supersymmetric extension of the Standard Model (MSSM). In particular, we show that the lower bound on $\tan\beta$, which can be obtained from the presently allowed Higgs boson mass value, becomes stronger than the one set by the requirement of perturbative consistency of the theory up to scales of order $M_{GUT}$ (associated with the infrared fixed-point solution of the top quark Yukawa coupling) in a large fraction of the allowed parameter space. The potentiality of future LEP2 searches to further probe the MSSM parameter space is also discussed.Comment: 15 pages, 5 figures, LateX, psfi

The Higgs Mass as the Discriminator of Electroweak Models

In the Minimal Supersymmetric Model (MSSM) and the Next to Minimal Supersymmetric Model [(M+1)SSM], an upper bound on the lightest higgs mass can be calculated. On the other hand, vacuum stability implies a lower limit on the mass of the higgs boson in the Standard Model (SM). We find that a gap exists for $m_t \stackrel{>}{\sim} 165$ GeV between the SM and both the MSSM and the (M+1)SSM bounds. Thus, if the new top quark mass measurement by CDF remains valid, a first measurement of the higgs mass will serve to exclude either the SM or the MSSM/(M+1)SSM higgs sectors. In addition, we discuss Supersymmetric Grand Unified Theories, other extentions of the SM, the discovery potential of the lightest higgs, and the assumptions on which our conclusions are based.Comment: 9 pages, 2 figures, VAND-TH-94-1

Information-theoretic lower bounds on the oracle complexity of stochastic convex optimization

Relative to the large literature on upper bounds on complexity of convex optimization, lesser attention has been paid to the fundamental hardness of these problems. Given the extensive use of convex optimization in machine learning and statistics, gaining an understanding of these complexity-theoretic issues is important. In this paper, we study the complexity of stochastic convex optimization in an oracle model of computation. We improve upon known results and obtain tight minimax complexity estimates for various function classes