Coherent states for compact Lie groups and their large-N limits

The first two parts of this article surveys results related to the heat-kernel coherent states for a compact Lie group K. I begin by reviewing the definition of the coherent states, their resolution of the identity, and the associated Segal-Bargmann transform. I then describe related results including connections to geometric quantization and (1+1)-dimensional Yang--Mills theory, the associated coherent states on spheres, and applications to quantum gravity. The third part of this article summarizes recent work of mine with Driver and Kemp on the large-N limit of the Segal--Bargmann transform for the unitary group U(N). A key result is the identification of the leading-order large-N behavior of the Laplacian on "trace polynomials."Comment: Submitted to the proceeding of the CIRM conference, "Coherent states and their applications: A contemporary panorama.

Isolation and characterization of a laminin-binding protein from rat and chick muscle.

A major laminin-binding protein (LBP), distinct from previously described LBPs, has been isolated from chick and rat skeletal muscle (Mr 56,000 and 66,000, respectively). The purified LBPs from the two species were shown to be related antigenically and to have similar NH2-terminal amino acid sequences and total amino acid compositions. Protein blots using laminin and laminin fragments provided evidence that this LBP interacts with the major heparin-binding domain, E3, of laminin. Studies on the association of this LBP with muscle membrane fractions and reconstituted lipid vesicles indicate that this protein can interact with lipid bilayers and has properties of a peripheral, not an integral membrane protein. These properties are consistent with its amino acid sequence, determined from cDNAs (Clegg et al., 1988). Examination by light and electron microscopy of the LBP antigen distribution in skeletal muscle indicated that the protein is localized primarily extracellularly, near the extracellular matrix and myotube plasmalemma. While a form of this LBP has been identified in heart muscle, it is present at low or undetectable levels in other tissues examined by immunocytochemistry indicating that it is probably a muscle-specific protein. As this protein is localized extracellularly and can bind to both membranes and laminin, it may mediate myotube interactions with the extracellular matrix

Amino acid sequence and distribution of mRNA encoding a major skeletal muscle laminin binding protein: an extracellular matrix-associated protein with an unusual COOH-terminal polyaspartate domain.

Two cDNAs encoding an abundant chicken muscle extracellular matrix (ECM)-associated laminin-binding protein (LBP) have been isolated and sequenced. The predicted primary amino acid sequence includes a probable signal peptide and a site for N-linked glycosylation, but lacks a hydrophobic segment long enough to span the membrane. The COOH terminus consists of an unusual repeat of 33 consecutive aspartate residues. Comparison with other sequences indicates that this protein is different from previously described LBPs and ECM receptors. RNA blot analysis of LBP gene expression showed that LBP mRNA was abundant in skeletal and heart muscle, but barely detectable in other tissues. Blots of chicken genomic DNA suggest that a single gene encodes this LBP. The amino acid sequence and mRNA distribution are consistent with the biochemical characterization described by Hall and co-workers (Hall, D. E., K. A. Frazer, B. C. Hahn, and L. F. Reichardt. 1988. J. Cell Biol. 107:687-697). These analyses indicate that LBP is an abundant ECM-associated muscle protein with an unusually high negative charge that interacts with both membranes and laminin, and has properties of a peripheral, not integral membrane protein. Taken together, our studies show that muscle LBP is a secreted, peripheral membrane protein with an unusual polyaspartate domain. Its laminin and membrane binding properties suggest that it may help mediate muscle cell interactions with the extracellular matrix. We propose the name "aspartactin" for this LBP

The impact of the ATLAS zero-lepton, jets and missing momentum search on a CMSSM fit

Recent ATLAS data significantly extend the exclusion limits for supersymmetric particles. We examine the impact of such data on global fits of the constrained minimal supersymmetric standard model (CMSSM) to indirect and cosmological data. We calculate the likelihood map of the ATLAS search, taking into account systematic errors on the signal and on the background. We validate our calculation against the ATLAS determinaton of 95% confidence level exclusion contours. A previous CMSSM global fit is then re-weighted by the likelihood map, which takes a bite at the high probability density region of the global fit, pushing scalar and gaugino masses up.Comment: 16 pages, 7 figures. v2 has bigger figures and fixed typos. v3 has clarified explanation of our handling of signal systematic

Studying Wythoff and Zometool Constructions using Maple

We describe a Maple package that serves at least four purposes. First, one can use it to compute whether or not a given polyhedral structure is Zometool constructible. Second, one can use it to manipulate Zometool objects, for example to determine how to best build a given structure. Third, the package allows for an easy computation of the polytopes obtained by the kaleiodoscopic construction called the Wythoff construction. This feature provides a source of multiple examples. Fourth, the package allows the projection on Coxeter planesComment: 11 pages, 11 figure

Yukawa unification in SO(10) with light sparticle spectrum

We investigate supersymmetric SO(10) GUT model with \mu<0. The requirements of top-bottom-tau Yukawa unification, correct radiative electroweak symmetry breaking and agreement with the present experimental data may be met when the soft masses of scalars and gauginos are non-universal. We show how appropriate non-universalities can easily be obtained in the SO(10) GUT broken to the Standard Model. We discuss how values of BR(b-->s \gamma) and (g-2)_\mu simultaneously in a good agreement with the experimental data can be achieved in SO(10) model with \mu<0. In the region of the parameter space preferred by our analysis there are two main mechanisms leading to the LSP relic abundance consistent with the WMAP results. One is the co-annihilation with the stau and the second is the resonant annihilation via exchange of the Z boson or the light Higgs scalar. A very interesting feature of SO(10) models with negative \mu is that they predict relatively light sparticle spectra. Even the heaviest superpartners may easily have masses below 1.5 TeV in contrast to multi-TeV particles typical for models with positive \mu.Comment: 23 pages, 5 figure

A Profile Likelihood Analysis of the Constrained MSSM with Genetic Algorithms

The Constrained Minimal Supersymmetric Standard Model (CMSSM) is one of the simplest and most widely-studied supersymmetric extensions to the standard model of particle physics. Nevertheless, current data do not sufficiently constrain the model parameters in a way completely independent of priors, statistical measures and scanning techniques. We present a new technique for scanning supersymmetric parameter spaces, optimised for frequentist profile likelihood analyses and based on Genetic Algorithms. We apply this technique to the CMSSM, taking into account existing collider and cosmological data in our global fit. We compare our method to the MultiNest algorithm, an efficient Bayesian technique, paying particular attention to the best-fit points and implications for particle masses at the LHC and dark matter searches. Our global best-fit point lies in the focus point region. We find many high-likelihood points in both the stau co-annihilation and focus point regions, including a previously neglected section of the co-annihilation region at large m_0. We show that there are many high-likelihood points in the CMSSM parameter space commonly missed by existing scanning techniques, especially at high masses. This has a significant influence on the derived confidence regions for parameters and observables, and can dramatically change the entire statistical inference of such scans.Comment: 47 pages, 8 figures; Fig. 8, Table 7 and more discussions added to Sec. 3.4.2 in response to referee's comments; accepted for publication in JHE

The generalised NMSSM at one loop: fine tuning and phenomenology

We determine the degree of fine tuning needed in a generalised version of the NMSSM that follows from an underlying Z4 or Z8 R symmetry. We find that it is significantly less than is found in the MSSM or NMSSM and extends the range of Higgs mass that have acceptable fine tuning up to Higgs masses of mh ~ 130 GeV. For universal boundary conditions analogous to the CMSSM the phenomenology is rather MSSM like with the singlet states typically rather heavy. For more general boundary conditions the singlet states can be light, leading to interesting signatures at the LHC and direct detection experiments.Comment: 20 pages, 9 figures, matches published versio

General Gauge Mediation at the Weak Scale

We completely characterize General Gauge Mediation (GGM) at the weak scale by solving all IR constraints over the full parameter space. This is made possible through a combination of numerical and analytical methods, based on a set of algebraic relations among the IR soft masses derived from the GGM boundary conditions in the UV. We show how tensions between just a few constraints determine the boundaries of the parameter space: electroweak symmetry breaking (EWSB), the Higgs mass, slepton tachyons, and left-handed stop/sbottom tachyons. While these constraints allow the left-handed squarks to be arbitrarily light, they place strong lower bounds on all of the right-handed squarks. Meanwhile, light EW superpartners are generic throughout much of the parameter space. This is especially the case at lower messenger scales, where a positive threshold correction to $m_h$ coming from light Higgsinos and winos is essential in order to satisfy the Higgs mass constraint.Comment: 43 pages, 20 figures, mathematica package included in the sourc

Interpreting a 1 fb^-1 ATLAS Search in the Minimal Anomaly Mediated Supersymmetry Breaking Model

Recent LHC data significantly extend the exclusion limits for supersymmetric particles, particularly in the jets plus missing transverse momentum channels. The most recent such data have so far been interpreted by the experiment in only two different supersymmetry breaking models: the constrained minimal supersymmetric standard model (CMSSM) and a simplified model with only squarks and gluinos and massless neutralinos. We compare kinematical distributions of supersymmetric signal events predicted by the CMSSM and anomaly mediated supersymmetry breaking (mAMSB) before calculating exclusion limits in mAMSB. We obtain a lower limit of 900 GeV on squark and gluino masses at the 95% confidence level for the equal mass limit, tan(beta)=10 and mu>0.Comment: 18 pages, 11 figure