Abstract:
We evaluate the branching ratio BR($b\rightarrow s,\gamma$) in the minimal supersymmetric standard model (MSSM), determining the corresponding phenomenological restrictions on two attractive supergravity scenarios, namely minimal supergravity and a class of models with a natural solution to the $\mu$ problem. We have included in the calculation some one--loop refinements that have a substantial impact on the results. The numerical results show some disagreements with part of the previous results in the literature, while they are in agreement with others. For minimal supergravity the CLEO upper and lower bounds put important restrictions on the scalar and gaugino masses in both cases $\mu<0$ and $\mu>0$. For the other supergravity scenarios the relevant CLEO bound is the upper one. It is stressed the fact that an eventual improvement of the experimental bounds of order $10^{-4}$ would strengthen the restrictions on the MSSM dramatically. This would be enough to discard these supergravity scenarios with $\mu<0$ if no discrepancy is found with the standard model prediction, while for $\mu>0$ there will remain low-energy windows.

Abstract:
We evaluate the branching ratio BR($b\rightarrow s,\gamma$) in the minimal supersymmetric standard model (MSSM), determining the corresponding phenomenological restrictions on two attractive supergravity scenarios, namely minimal supergravity and a class of models with a natural solution to the $\mu$ problem. We have included in the calculation some one--loop refinements that have a substantial impact on the results. It is stressed the fact that an eventual improvement of the experimental bounds of order $10^{-4}$ would strengthen the restrictions on the MSSM dramatically. This would be enough to discard these supergravity scenarios with $\mu<0$ if no discrepancy is found with the standard model prediction, while for $\mu>0$ there will remain low-energy windows.

Abstract:
We discuss inflaton decay in supergravity, taking account of the gravitational effects. It is shown that, if the inflaton has a nonzero vacuum expectation value, it generically couples to any matter fields that appear in the superpotential at the tree level, and to any gauge sectors through anomalies in the supergravity. Through these processes, the inflaton generically decays into the supersymmetry breaking sector, producing many gravitinos. The inflaton also directly decays into a pair of the gravitinos. We derive constraints on both inflation models and supersymmetry breaking scenarios for avoiding overproduction of the gravitinos. Furthermore, the inflaton naturally decays into the visible sector via the top Yukawa coupling and SU(3)_C gauge interactions.

Abstract:
The $b\rightarrow s+ \gamma$ decay is a powerful tool for testing models of new physics because the new physics diagrams enter in the same loop order as the Standard Model ones. The current experimental and theoretical status of this decay is reviewed. Predictions based on the minimal supergravity model (MSGM) in the leading order (LO) are discussed. It is shown that results are sensitive to the value of $m_{t}$ and $\alpha_{G}$. The current experimental value for the $b\rightarrow s + \gamma$ rate already very likely eliminates part of the SUSY parameter space when both $m_{o}$ and $m_{\tilde{g}}$ are small and when $A_{t}$ and $\mu$ have the same sign. Dark matter detection rates for $\tilde{Z}_{1}$ cold dark matter for $\mu <0$ are only minimally affected by the current data, as are proton decay predictions for models consistent with current proton lifetime and $\tilde{Z}_{1}$ relic density bounds. [\dag Invited talk at ``Physics From Planck Scale to Electroweak Scale'', Warsaw, Sept. 21-24, 1994].

Abstract:
Production and decay of gaugino-like charginos are crucially determined by sneutrino exchange. Therefore we study the pair production of charginos e^+ e^- -> chi^+_1 chi^-_1 with polarized beams and the subsequent decay chi^-_1 -> chi^0_1 e^- nu_e, including the complete spin correlations between production and decay. The spin correlations have strong influence on the decay angular distribution and on the corresponding forward-backward asymmetry. We show for two representative scenarios for sqrt{s}=270 GeV and for sqrt{s}=500 GeV that forward-backward asymmetries for polarized beams are an important tool for constraining the sneutrino mass m_{tilde{nu}_e}.

Abstract:
Selectrons may be produced in pairs at LEPII if their mass is less than about 100 GeV. Preferably, they decay into the lightest neutralino plus an electron. In a scenario where selectrons are observed at LEPII, we show that: (i) in a first stage where experimental errors are large, the measurement of the total cross section of selectron pair production, the selectron mass, and the lightest neutralino mass, allow us to validate or rule out the Minimal Supergravity Model in its simplest form, and that (ii) in a second stage where precision measurements are available, the value of $\tan\beta$ can be determined together with the rest of the parameters that specify the Minimal Supergravity Model and, with them, the entire supersymmetric spectrum can be calculated. We include experimental constraints from sparticle searches, $Z$--pole physics, stability of the lightest supersymmetric particle (LSP) and the decay $b\rightarrow s\gamma$. In these scenarios, small values of $\tan\beta$ and negative values of $\mu$ are preferred, and the lightest Higgs mass satisfies $m_h<110$ GeV, which makes it likely to be detected at LEPII.

Abstract:
We have recently shown that, if the inflaton has a nonzero vacuum expectation value, it generically couples to any matter fields that appear in the superpotential at the tree level, and to any gauge sectors through anomalies in the supergravity. Through these processes, the inflaton decays into the supersymmetry breaking sector, producing many gravitinos. The inflaton also directly decays into a pair of the gravitinos. Taking account of these processes, we derive constraints on both inflation models and supersymmetry breaking scenarios for avoiding overproduction of the gravitinos.

Abstract:
The effect of loops involving charginos with up-type squarks, and gluinos with down-type squarks, on the inclusive decay mode $b\rightarrow s\gamma$ is studied in the context of minimal $N=1$ Supergravity models with a radiatively broken electroweak symmetry group. It is confirmed that the strong constraints imposed by the CLEO upper bound $B(b\rightarrow s\gamma)<5.4\times 10^{-4}$ on two-Higgs doublets models are much weaker in supersymmetric theories due to partial cancelations from loops involving charginos and up-type squarks. The dependence of the branching ratio and the supersymmetry masses on the top quark mass is explored.

Abstract:
We study the predictions of the simplest SU(5) grand unified model within the framework of minimal supergravity, including constraints from the radiative breaking of electroweak symmetry. As a consequence of the unification of the $b$-quark and $\tau$-lepton Yukawa couplings, the top quark mass is predicted to be close to its fixed point value. We delineate the regions of the supergravity parameter space allowed by constraints from the non-observation of proton decay and from the requirement that the LSP does not overclose the universe. These constraints lead to a definite pattern of sparticle masses: the feature unique to Yukawa unified models is that some of the third generation squarks are much lighter than those of the first two generations. Despite the fact that all sparticle masses and mixings are determined by just four SUSY parameters at the GUT scale (in addition to $m_t$), we find that the signals for sparticle production can vary substantially over the allowed parameter space. We identify six representative scenarios and study the signals from sparticle production at the LHC. We find that by studying the signal in various channels, these scenarios may be distinguished from one another, and also from usually studied ``minimal models'' where squarks and sleptons are taken to be degenerate. In particular, our studies allow us to infer that some third generation squarks are lighter than other squarks---a feature that could provide the first direct evidence of supergravity grand unification.

Abstract:
The Tevatron collaborations have searched for associated production of charginos and neutralinos via trilepton final states. No events above the Standard Model prediction were observed. We employ these results to put stringent bounds on R-parity violating models with a right-handed scalar electron as the lightest supersymmetric particle. We work in the framework of lepton number violating minimal supergravity. We find that within these models the complete parameter space consistent with the anomalous magnetic moment of the muon can be excluded at 90% confidence level. We also give prospects for Tevatron trilepton searches assuming an integrated luminosity of 10 fb^{-1}. We find that Tevatron will be able to test selectron LSP masses up to 170 GeV.