This thesis describes the research I did during my Master's study. I investigated the stau-neutralino coannihilation region of the Mirage Mediation Model at the Large Hadron Collider (LHC). By constructing five kinematic observables at the LHC, the masses of supersymmetric particles (sparticles) were determined. The Mirage Mediation Model parameters were determined from the sparticles' masses. This is the first time to establish the Mirage Mediation Model at the LHC. All these techniques can be applied to other coannihilation regions of the Mirage Mediation Model and other supersymmetry (SUSY) models.

This dissertation presents the results of a search for supersymmetry in protonantiproton collisions with a center of mass energy of 1.96 TeV studied with the Collider Detector at Fermilab. Our strategy is to select collisions with two photons in the nal state that have the properties of being the decays of very massive supersymmetric particles. This includes looking for large total energy from the decayed particles as well as for the presence of particles that leave the detector without interacting. We nd no events using 2.6 fb-1 of data collected during the 2004-2008 collider run of the Fermilab Tevatron which is consistent with the background estimate of 1.4 +/- 0.4 events. Since there is no evidence of new particles we set cross section limits in a gaugemediated supersymmetry model with e 01 ! eG, where the e 01 and eG are the lightest neutralino and the gravitino (the lightest supersymmetric particle), respectively. We set limits on models as a function of the e 01 mass and lifetime, producing the world's most sensitive search for e 01by excluding masses up to 149 GeV=c2 for e 01 lifetimes much less than 1 ns.

Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Physics and Astronomy." Includes bibliographical references (p. 165-172).

Thesis (Ph. D.)--University of Texas at Austin, 2001. / Vita. Includes bibliographical references (leaves 150-160). Available also in a digital version from Dissertation Abstracts.

published_or_final_version / Physics / Master / Master of Philosophy

This work aims to understand how cosmic inflation embeds into larger models of particle physics and string theory. Our work operates within a weakened version of the Landscape paradigm, wherein it is assumed that the set of possible Lagrangians is vast enough to admit the notion of a generic model. By focusing on slow-roll inflation, we examine the roles of both the scalar potential and the space of couplings which determine its precise form. In particular, we focus on the structural properties of the scalar potential, and find a surprising result: inflection point inflation emerges as an important —and under certain assumptions, dominant — possibility in the context of generic scalar potentials. We begin by a systematic coarse graining over the set of possible inflection point inflation models using V.I. Arnold’s ADE classification of singularities. Similar to du Val’s pioneering work on surface singularities, these determine structural classes for inflection point inflation which depened on a distinct number of control parameters. We consider both single and multifield inflation, and show how the various structural classes embed within each other. We also show how such control parameters influence the larger physical models in to which inflation is embedded. These techniques are then applied to both MSSM inflation and KKLT-type models of string cosmology. In the former case, we find that the scale of inflation can be entirely encoded within the super- potential of supersymmetric quantum field theories. We show how this relieves the fine-tuning required in such models by upwards of twelve orders of magnitude. Moreover, unnatural tuning between SUSY breaking and SUSY preserving sectors is eliminated without the explicit need for any hidden sector dynamics. In the later case, we discuss how structural stability vastly generalizes — and addresses — the Kallosh-Linde problem. Implications for the spectrum of SUSY breaking soft terms are then discussed, with an emphasis on how they may assist in constraining the inflationary scalar potential. We then pivot to a general discussion of the FLRW-scalar phase space, and show how inflection points induce caustics — or dynamical fixed points — amongst the space of possible trajectories. These fixed points are then used to argue that for uninformative priors on the space of couplings, the likelihood of inflection point inflation scales with the inverse cube of the number of e-foldings. We point out the geometric origin for the known ambiguity in the Liouville measure, and demonstrate of inflection point inflation ameliorates this problem. Finally we investigate the effect of the fixed point structure on the spectrum of density perturbations. We show how an anomaly in the Cosmic Mircowave Background data — low power at large scales — can be explained as a by product of the fixed point dynamics.

The Minimally Supersymmetric Standard Model (MSSM) provides us with a WIMP dark matter candidate particle, the neutralino. Neutralinos from the dark matter halo can potentially become captured by the sun and concentrated in the core, where they can undergo self-annihilation and so produce a distinct neutrino signal. The IceCube Neutrino Observatory has the potential to detect this neutrino signal and thus give indirect evidence of the presence and properties of neutralino dark matter. Although the full, unconstrained MSSM has 105 parameters this can be reduced to 25 parameters by the application of physically motivated assumptions. Scans of this MSSM-25 parameter space are conducted using the DarkSUSY software package and an adaptive scanning technique based on the Monte-Carlo VEGAS algorithm. The IceCube exclusion confidence level is then calculated for a set of points produced by these scans. Results indicate that the detection capability of IceCube exceeds that of current direct detection methods in certain regions of the parameter space. The use of a 25 dimensional parameter space reveals that there are new regions of observables with high exclusion confidence levels compared to earlier simulations performed with a seven dimensional parameter space.

Well motivated theoretical models predict the annihilation of dark matter (DM) into standard model particles, a phenomenon which could be a significant source of photons in the gamma-ray sky. With its unprecedented sensitivity and its broad energy range (20 MeV to more than 300 GeV) the main instrument on board the Fermi satellite, the Large Area Telescope (LAT), might be able to detect an indirect signature of DM annihilations. In this work we revisit several interesting claims of extended dark matter emission made from analyses of Fermi-LAT data: First, based on three years of Fermi Large Area Telescope (LAT) gamma-ray data of the Virgo cluster, evidence for an extended emission associated with dark matter pair annihilation in the bb̄ channel has been reported by Han et al. (arxiv:1201.1003). After an in depth spatial and temporal analysis, we argue that the tentative evidence for a gamma-ray excess from the Virgo cluster is mainly due to the appearance of a population of previously unresolved gamma-ray point sources in the region of interest. These point sources are not part of the LAT second source catalogue (2FGL), but are found to be above the standard detection significance threshold when three or more years of LAT data is included. Second, we confirm the detection of a spatially extended excess of 2-5 GeV gamma rays from the Galactic Center (GC), consistent with the emission expected from annihilating dark matter or an unresolved population of about 10³ milisecond pulsars. However, there are significant uncertainties in the diffuse galactic background at the GC. We have performed a revaluation of these two models for the extended gamma ray source at the GC by accounting for the systematic uncertainties of the Galactic diffuse emission model. We also marginalize over point source and diffuse background parameters in the region of interest. We show that the excess emission is significantly more extended than a point source. We find that the DM (or pulsars population) signal is larger than the systematic errors and therefore proceed to determine the sectors of parameter space that provide an acceptable fit to the data. We found that a population of order a 10³ MSPs with parameters consistent with the average spectral shape of Fermi-LAT measured MSPs was able to fit the GC excess emission. For DM, we found that a pure τ⁺τ⁻ annihilation channel is not a good fit to the data. But a mixture of τ⁻τ⁻ and bb̄ with a (σν) of order the thermal relic value and a DM mass of around 20 to 60 GeV provides an adequate fit. We also consider the possibility that the GeV excess is due to nonthermal bremsstrahlung produced by a population of electrons interacting with neutral gas in molecular clouds. The millisecond pulsars and dark matter alternatives have spatial templates well fitted by the square of a generalized Navarro-Frenk-White (NFW) profile with inner slope γ = 1.2. We model the third option with a 20-cm continuum emission Galactic Ridge template. A template based on the HESS residuals is shown to give similar results. The gamma-ray excess is found to be best fit by a combination of the generalized NFW squared template and a Galactic Ridge template. We also find the spectra of each template is not significantly affected in the combined fit and is consistent with previous single template fits. That is, the generalized NFW squared spectrum can be fit by either of order 10³ unresolved MSPs or DM with mass around 30 GeV, a thermal cross section, and mainly annihilating to bb̄ quarks. While the Galactic Ridge continues to have a spectrum consistent with a population of nonthermal electrons whose spectrum also provides a good fit to synchrotron emission measurements. We also show that the current DM fit may be hard to test, even with 10 years of Fermi-LAT data, especially if there is a mixture of DM and MSPs contributing to the signal, in which case the implied DM cross section will be suppressed.

We study the conjectured equivalence between the O(3) Gross-Neveu model and the supersymmetric sine-Gordon model under a naive application of the bosonization rules. We start with a review of the equivalence between sine-Gordon model and the massive Thirring model. We study the models by perturbation theory and then determine the equivalence. We find that the dependence of the identifications on the couplings can change according to the definition of the vector current. With the operator identifications of the special case corresponding to a free fermionic theory, known as the bosonization rules, we describe the equivalence between the massless Thirring model and the model of a compactified free boson field. For the massless Thirring model, or equivalently the O(2) Gross-Neveu model, we study the conservation laws for the vector current and the axial current by employing a generalized point-splitting method which allows a one-parameter family of definitions of the vector current. With this parameter, we can make contact with different approaches that can be found in the literature; these approaches differ mainly because of the specific definition of the current that was used. We also find the Sugawara form of the stress-energy tensor and its commutation relations. Further, we rewrite the identifications between sine-Gordon and Thirring models in our generalized framework. For the O(3) Gross-Neveu model, we extend our point-splitting method to determine the exact expression for the supercurrent. Using this current, we compute the superalgebra which determines three quantum components of the stress-energy tensor. With an Ansatz for the undetermined component, we find the trace anomaly and the first beta-function coefficient. The central charge which can be computed without using our point-splitting method is independent of the coupling constant, in fact, it is always zero. For the supersymmetric sine-Gordon model, we review its supersymmetry in the context of models derived from a scalar multiplet in two dimensions. We then obtain the central charge and discover an extra term that was missing in the original derivation. We also analyze how normal ordering modifies the central charge. Finally, we discuss the conjectured equivalence of the O(3) Gross-Neveu model and the supersymmetric sine-Gordon model under the naive application of the bosonization rules. Comparing our results of the central charges and the supercurrents for these models, we find that they disagree; consequently the models should be generically inequivalent. We also conclude that the naive application of the bosonization rules at the Lagrangian level does not always lead to an equivalent theory.

We compute the exact partition function of two dimensional N=(2,2) supersymmetric gauge theories on S². For theories with SU(2|1)_A invariance, the partition function admits two equivalent representations corresponding to localization on the Coulomb branch or the Higgs branch, which includes vortex and anti-vortex excitations at the poles. For SU(2|1)_B invariant gauge theories, the partition function is localized to the Higgs branch which is generically a Kähler quotient manifold. The resulting partition functions are invariant under the renormalization group flow. For gauge theories that flow in the infrared to Calabi-Yau nonlinear sigma models, the partition functions for the SU(2|1)_A (resp SU(2|1)_B) invariant theories compute the Kähler potential on the Kähler moduli (resp. complex structure moduli) of the Calabi-Yau manifold. We also compute the elliptic genus of such theories in the presence of Stückelberg fields and show that they are modular completions of mock Jacobi forms.