A Machine Checked Model of Idempotent MGU Axioms For Lists of Equational Constraints

We present formalized proofs verifying that the first-order unification algorithm defined over lists of satisfiable constraints generates a most general unifier (MGU), which also happens to be idempotent. All of our proofs have been formalized in the Coq theorem prover. Our proofs show that finite maps produced by the unification algorithm provide a model of the axioms characterizing idempotent MGUs of lists of constraints. The axioms that serve as the basis for our verification are derived from a standard set by extending them to lists of constraints. For us, constraints are equalities between terms in the language of simple types. Substitutions are formally modeled as finite maps using the Coq library Coq.FSets.FMapInterface. Coq's method of functional induction is the main proof technique used in proving many of the axioms.Comment: In Proceedings UNIF 2010, arXiv:1012.455

Neutralino Dark Matter, b-tau Yukawa Unification and Non-Universal Sfermion Masses

We study the implications of minimal non-Universal Boundary Conditions in the sfermion Soft SUSY Breaking (SSB) masses of mSUGRA. We impose asymptotic b-tau Yukawa coupling Unification and we resort to a parameterization of the deviation from Universality in the SSB motivated by the multiplet structure of SU(5) GUT. A set of cosmo-phenomenological constraints, including the recent results from WMAP, determines the allowed parameter space of the models under consideration. We highlight a new coannihilation corridor where neutralino-sbottom and neutralino-tau sneutrino-stau coannihilations significantly contribute to the reduction of the neutralino relic density.Comment: 38 pages, 27 Figures, Latex; Version accepted for publication in PR

The pMSSM Interpretation of LHC Results Using Rernormalization Group Invariants

The LHC has started to constrain supersymmetry-breaking parameters by setting bounds on possible colored particles at the weak scale. Moreover, constraints from Higgs physics, flavor physics, the anomalous magnetic moment of the muon, as well as from searches at LEP and the Tevatron have set additional bounds on these parameters. Renormalization Group Invariants (RGIs) provide a very useful way of representing the allowed parameter space by making direct connection with the values of these parameters at the messenger scale. Using a general approach, based on the pMSSM parametrization of the soft supersymmetry-breaking parameters, we analyze the current experimental constraints to determine the probability distributions for the RGIs. As examples of their application, we use these distributions to analyze the question of Gaugino Mass Unification and to probabilistically determine the parameters of General and Minimal Gauge Mediation with arbitrary Higgs mass parameters at the Messenger Scale.Comment: 38 pages, 10 figure

CAutoCSD-evolutionary search and optimisation enabled computer automated control system design

This paper attempts to set a unified scene for various linear time-invariant (LTI) control system design schemes, by transforming the existing concept of 'Computer-Aided Control System Design' (CACSD) to the novel 'Computer-Automated Control System Design' (CAutoCSD). The first step towards this goal is to accommodate, under practical constraints, various design objectives that are desirable in both time and frequency-domains. Such performance-prioritised unification is aimed to relieve practising engineers from having to select a particular control scheme and from sacrificing certain performance goals resulting from pre-committing to the adopted scheme. With the recent progress in evolutionary computing based extra-numeric, multi-criterion search and optimisation techniques, such unification of LTI control schemes becomes feasible, analytically and practically, and the resultant designs can be creative. The techniques developed are applied to, and illustrated by, three design problems. The unified approach automatically provides an integrator for zero-steady state error in velocity control of a DC motor, meets multiple objectives in designing an LTI controller for a non-minimum phase plant and offers a high-performing LTI controller network for a nonlinear chemical process

Leptophobic U(1)'s and the R_b - R_c Crisis

In this paper, we investigate the possibility of explaining both the R_b excess and the R_c deficit reported by the LEP experiments through Z-Z' mixing effects. We have constructed a set of models consistent with a restrictive set of principles: unification of the Standard Model (SM) gauge couplings, vector- like additional matter, and couplings which are both generation-independent and leptophobic. These models are anomaly-free, perturbative up to the GUT scale, and contain realistic mass spectra. Out of this class of models, we find three explicit realizations which fit the LEP data to a far better extent than the unmodified SM or MSSM and satisfy all other phenomenological constraints which we have investigated. One realization, the \eta-model coming from E_6, is particularly attractive, arising naturally from geometrical compactifications of heterotic string theory. This conclusion depends crucially on the inclusion of a U(1) kinetic mixing term, whose value is correctly predicted by renormalization group running in the E_6 model given one discrete choice of spectra.Comment: LaTeX, 26 pages, 5 embedded EPSF figures. Version to be published in Phys. Rev.

Indirect signals from light neutralinos in supersymmetric models without gaugino mass unification

We examine indirect signals produced by neutralino self-annihilations, in the galactic halo or inside celestial bodies, in the frame of an effective MSSM model without gaugino-mass unification at a grand unification scale. We compare our theoretical predictions with current experimental data of gamma-rays and antiprotons in space and of upgoing muons at neutrino telescopes. Results are presented for a wide range of the neutralino mass, though our discussions are focused on light neutralinos. We find that only the antiproton signal is potentially able to set constraints on very low-mass neutralinos, below 20 GeV. The gamma-ray signal, both from the galactic center and from high galactic latitudes, requires significantly steep profiles or substantial clumpiness in order to reach detectable levels. The up-going muon signal is largely below experimental sensitivities for the neutrino flux coming from the Sun; for the flux from the Earth an improvement of about one order of magnitude in experimental sensitivities (with a low energy threshold) can make accessible neutralino masses close to O, Si and Mg nuclei masses, for which resonant capture is operative.Comment: 17 pages, 1 tables and 5 figures, typeset with ReVTeX4. The paper may also be found at http://www.to.infn.it/~fornengo/papers/indirect04.ps.gz or through http://www.astroparticle.to.infn.it/. Limit from BR(Bs--> mu+ mu-) adde

Naturalness and the Status of Supersymmetry

For decades, the unnaturalness of the weak scale has been the dominant problem motivating new particle physics, and weak-scale supersymmetry has been the dominant proposed solution. This paradigm is now being challenged by a wealth of experimental data. In this review, we begin by recalling the theoretical motivations for weak-scale supersymmetry, including the gauge hierarchy problem, grand unification, and WIMP dark matter, and their implications for superpartner masses. These are set against the leading constraints on supersymmetry from collider searches, the Higgs boson mass, and low-energy constraints on flavor and CP violation. We then critically examine attempts to quantify naturalness in supersymmetry, stressing the many subjective choices that impact the results both quantitatively and qualitatively. Finally, we survey various proposals for natural supersymmetric models, including effective supersymmetry, focus point supersymmetry, compressed supersymmetry, and R-parity-violating supersymmetry, and summarize their key features, current status, and implications for future experiments.Comment: 38 pages, to appear in Annual Review of Nuclear and Particle Science; v2: fixed typos, updated Higgs results, added references and a parable, published versio