Nonextensive Quantum H-Theorem

A proof of the quantum $H$-theorem taking into account nonextensive effects on the quantum entropy $S^Q_q$ is shown. The positiveness of the time variation of $S^Q_q$ combined with a duality transformation implies that the nonextensive parameter $q$ lies in the interval [0,2]. It is also shown that the equilibrium states are described by quantum $q$-power law extensions of the Fermi-Dirac and Bose-Einstein distributions. Such results reduce to the standard ones in the extensive limit, thereby showing that the nonextensive entropic framework can be harmonized with the quantum distributions contained in the quantum statistics theory.Comment: 5 pages, LaTe

A Layman's guide to SUSY GUTs

The determination of the most straightforward evidence for the existence of the Superworld requires a guide for non-experts (especially experimental physicists) for them to make their own judgement on the value of such predictions. For this purpose we review the most basic results of Super-Grand unification in a simple and clear way. We focus the attention on two specific models and their predictions. These two models represent an example of a direct comparison between a traditional unified-theory and a string-inspired approach to the solution of the many open problems of the Standard Model. We emphasize that viable models must satisfy {\em all} available experimental constraints and be as simple as theoretically possible. The two well defined supergravity models, $SU(5)$ and $SU(5)\times U(1)$, can be described in terms of only a few parameters (five and three respectively) instead of the more than twenty needed in the MSSM model, \ie, the Minimal Supersymmetric extension of the Standard Model. A case of special interest is the strict no-scale $SU(5)\times U(1)$ supergravity where all predictions depend on only one parameter (plus the top-quark mass). A general consequence of these analyses is that supersymmetric particles can be at the verge of discovery, lurking around the corner at present and near future facilities. This review should help anyone distinguish between well motivated predictions and predictions based on arbitrary choices of parameters in undefined models.Comment: 25 pages, Latex, 11 figures (not included), CERN-TH.7077/93, CTP-TAMU-65/93. A complete ps file (1.31MB) with embedded figures is available by request from [email protected]

Hunting for the New Symmetries in Calabi-Yau Jungles

It was proposed that the Calabi-Yau geometry can be intrinsically connected with some new symmetries, some new algebras. In order to do this it has been analyzed the graphs constructed from K3-fibre CY_d (d \geq 3) reflexive polyhedra. The graphs can be naturally get in the frames of Universal Calabi-Yau algebra (UCYA) and may be decode by universal way with changing of some restrictions on the generalized Cartan matrices associated with the Dynkin diagrams that characterize affine Kac-Moody algebras. We propose that these new Berger graphs can be directly connected with the generalizations of Lie and Kac-Moody algebras.Comment: 29 pages, 15 figure

A new scenario for string unification

We present a new scenario for gauge coupling unification in flipped SU(5) string models, which identifies the $M_{32}$ scale of SU(3) and SU(2) unification with the empirical $M_{\rm LEP}\sim10^{15-16}$~GeV scale, and the $M_{51}$ scale of SU(5) and U(1) unification with the theoretical $M_{\rm string}\sim5\times10^{17}$~GeV string unification scale. The vacuum shift necessary for the cancellation of the anomalous $\rm U_A(1)$ and an SU(4) hidden sector with fractionally-charged particles, play a crucial role in the dynamical determination of all intermediate mass scales in this scenario.Comment: 8 pages, LaTeX, 2 figures (uuencoded

Precision Electroweak Tests of the Minimal and Flipped SU(5) Supergravity Models

We explore the one-loop electroweak radiative corrections in the minimal $SU(5)$ and the no-scale flipped $SU(5)$ supergravity models via explicit calculation of vacuum polarization contributions to the $\epsilon_{1,2,3}$ parameters. Experimentally, $\epsilon_{1,2,3}$ are obtained from a global fit to the LEP observables, and $M_W/M_Z$ measurements. We include $q^2$-dependent effects which have been neglected in most previous ``model-independent" analyses of this type. These effects induce a large systematic negative shift on $\epsilon_{1,2,3}$ for light chargino masses (m_{\chi^\pm_1}\lsim70\GeV). In agreement with previous general arguments, we find that for increasingly large sparticle masses, the heavy sector of both models rapidly decouples, \ie, the values for $\epsilon_{1,2,3}$ quickly asymptote to the Standard Model values with a {\it light} Higgs (m_{H_{SM}}\sim100\GeV). Specifically, at present the $90\%$ CL upper limit on the top-quark mass is m_t\lsim175\GeV in the no-scale flipped $SU(5)$ supergravity model. These bounds can be strengthened for increasing chargino masses in the 50-100\GeV interval. In particular, for m_t\gsim160\GeV, the Tevatron may be able to probe through gluino($\tilde g$) and squark($\tilde q$) production up to m_{\tilde g}\approx m_{\tilde q}\approx250\GeV, exploring at least half of the parameter space in this model.Comment: 15 pages,(6 ps figures available upon request), TeX(harvmac), CTP-TAMU-19/93, ACT-07/9

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

Planck Scale Physics and the Testability of SU(5) Supergravity GUT

GUT scale threshold corrections in minimal SU(5) supergravity grand unification are discussed. It is shown that predictions may be made despite uncertainties associated with the high energy scale. A bound relating the strong coupling constant to the mass scales associated with proton decay and supersymmetry is derived, and a sensitive probe of the underlying theory is outlined. In particular, low energy measurements can in principle determine the presence of Planck scale ($1 / {{\rm M}_{\rm Pl}}$) terms.Comment: 12 pages, REVTeX, 2 figures included in an uuencoded Z-compressed PostScript file. Ready to print PostScript version (with figures) may be picked up at ftp://phys.tamu.edu/urano/planck/paper_prep.p

Proton Decay and Cosmology Strongly Constrain the Minimal SU(5) Supergravity Model

We present the results of an extensive exploration of the five-dimensional parameter space of the minimal $SU(5)$ supergravity model, including the constraints of a long enough proton lifetime (\tau_p>1\times10^{32}\y) and a small enough neutralino cosmological relic density ($\Omega_\chi h^2_0\le1$). We find that the combined effect of these two constraints is quite severe, although still leaving a small region of parameter space with m_{\tilde g,\tilde q}<1\TeV. The allowed values of the proton lifetime extend up to \tau_p\approx1\times10^{33}\y and should be fully explored by the SuperKamiokande experiment. The proton lifetime cut also entails the following mass correlations and bounds: m_h\lsim100\GeV, m_\chi\approx{1\over2}m_{\chi^0_2}\approx0.15\gluino, $m_{\chi^0_2}\approx m_{\chi^+_1}$, and m_\chi<85\,(115)\GeV, m_{\chi^0_2,\chi^+_1}<165\,(225)\GeV for $\alpha_3=0.113\,(0.120)$. Finally, the {\it combined} proton decay and cosmology constraints predict that if m_h\gsim75\,(80)\GeV then m_{\chi^+_1}\lsim90\,(110)\GeV for $\alpha_3=0.113\,(0.120)$. Thus, if this model is correct, at least one of these particles will likely be observed at LEPII.Comment: 11 pages plus 5 figures (not included). CERN-TH.6628/92, CTP-TAMU-61/92. A condensed version of this paper will appear in the Proceedings of the XXVI International Conference on High Energy Physics, Dallas--Texas, August 5--12, 199