Coupled Boltzmann calculation of mixed axion/neutralino cold dark matter production in the early universe

We calculate the relic abundance of mixed axion/neutralino cold dark matter which arises in R-parity conserving supersymmetric (SUSY) models wherein the strong CP problem is solved by the Peccei-Quinn (PQ) mechanism with a concommitant axion/saxion/axino supermultiplet. By numerically solving the coupled Boltzmann equations, we include the combined effects of 1. thermal axino production with cascade decays to a neutralino LSP, 2. thermal saxion production and production via coherent oscillations along with cascade decays and entropy injection, 3. thermal neutralino production and re-annihilation after both axino and saxion decays, 4. gravitino production and decay and 5. axion production both thermally and via oscillations. For SUSY models with too high a standard neutralino thermal abundance, we find the combined effect of SUSY PQ particles is not enough to lower the neutralino abundance down to its measured value, while at the same time respecting bounds on late-decaying neutral particles from BBN. However, models with a standard neutralino underabundance can now be allowed with either neutralino or axion domination of dark matter, and furthermore, these models can allow the PQ breaking scale f(a) to be pushed up into the 10(14) - 10(15) GeV range, which is where it is typically expected to be in string theory models.

Integrable Models: from Dynamical Solutions to String Theory

We review the status of integrable models from the point of view of their dynamics and integrability conditions. A few integrable models are discussed in detail. We comment on the use it is made of them in string theory. We also discuss the SO(6) symmetric Hamiltonian with SO(6) boundary. This work is especially prepared for the 70th anniversaries of Andr, Swieca (in memoriam) and Roland Koberle.

On the Milnor fibre and L numbers of semi-weighted homogeneous arrangements

Inthispaperwestudygermsofpolynomialsformedbytheproductofsemi-weighted homogeneous polynomials of the same type, which we call semi-weighted homogeneous arrangements. It is shown how the L numbers of such polynomials are computed using only their weights and degree of homogeneity. A key point of the main theorem is to find the number called polar ratio of this polynomial class. An important consequence is the description of the Euler characteristic of the Milnor fibre of such arrangements only depending on their weights and degree of homogeneity. The constancy of the L numbers in families formed by such arrangements is shown, with the deformed terms having weighted degree greater than the weighted degree of the initial germ. Moreover, using the results of Massey applied to families of function germs, we obtain the constancy of the homology of the Milnor fibre in this family of semi-weighted homogeneous arrangements.

The discriminants associated to isotropy representations of symmetric spaces

We consider a generalized discriminant associated to a symmetric space which generalizes the discriminant of real symmetric matrices, and note that it can be written as a sum of squares of real polynomials. A method to estimate the minimum number of squares required to represent the discrimininant is developed and applied in examples.

Definite integrals and operational methods

An operational method, already employed to formulate a generalization of the Ramanujan master theorem, is applied to the evaluation of integrals of various types. This technique provides a very flexible and powerful tool yielding new results encompassing different aspects of the special function theory. Crown Copyright (C) 2012 Published by Elsevier Inc. All rights reserved.

W Z plus missing-E-T signal from gaugino pair production at LHC7

LHC searches for supersymmetry currently focus on strongly produced sparticles, which are copiously produced if gluinos and squarks have masses of a few hundred GeV. However, in supersymmetric models with heavy scalars, as favored by the decoupling solution to the SUSY flavor and CP problems, and m((g) over tilde) greater than or similar to 500 GeV as indicated by recent LHC results, chargino-neutralino ((W) over tilde (+/-)(1)(Z) over tilde (2)) production is the dominant cross section for m((W) over tilde1) similar to m((Z) over tilde2) < m(<(g)over tilde>)/3 at LHC with root s = 7 TeV (LHC7). Furthermore, if m((Z) over tilde1) + (m (Z) over tilde) less than or similar to m((Z) over tilde2) less than or similar to m((Z) over tilde1) + m(h), then (Z) over tilde (2) dominantly decays via (Z) over tilde (2) -> (Z) over tilde (1)Z, while (W) over tilde (1) decays via (W) over tilde (1) -> (Z) over tilde W-1. We investigate the LHC7 reach in the W Z + (sic)T channel (for both leptonic and hadronic decays of the W boson) in models with and without the assumption of gaugino mass universality. In the case of the mSUGRA/CMSSM model with heavy squark masses, the LHC7 discovery reach in the W Z+ (sic)T channel becomes competetive with the reach in the canonical (sic)T + jets channel for integrated luminosities similar to 30 fb(-1). We also present the LHC7 reach for a simplified model with arbitrary m((Z) over tilde1) and m((W) over tilde1) similar to m((Z) over tilde2). Here, we find a reach of up to m((W) over tilde1) similar to 200 (250) GeV for 10 (30) fb(-1).

LHC discovery potential for supersymmetry with root s=7 TeV and 5-30 fb(-1)

We extend our earlier results delineating the supersymmetry reach of the CERN Large Hadron Collider operating at a center-of-mass energy root s = 7 TeV to integrated luminosities in the range 5-30 fb(-1). Our results are presented within the paradigm minimal supergravity model or constrained minimal supersymmetric standard model. Using a six-dimensional grid of cuts for the optimization of signal to background ratio-including missing E-T-we find for m((g) over tilde) similar to m((q) over tilde) an LHC 5 sigma supersymmetry discovery reach of m((g) over tilde) similar to 1:3, 1.4, 1.5, and 1.6 TeV for 5, 10, 20, and 30 fb(-1), respectively. For m((q) over tilde) >> m((g) over tilde), the corresponding reach is instead m((g) over tilde) similar to 0: 8, 0.9, 1.0, and 1.05 TeV, for the same integrated luminosities.

GENERALIZED FINITE ELEMENT METHOD ON NONCONVENTIONAL HYBRID-MIXED FORMULATION

The generalized finite element method (GFEM) is applied to a nonconventional hybrid-mixed stress formulation (HMSF) for plane analysis. In the HMSF, three approximation fields are involved: stresses and displacements in the domain and displacement fields on the static boundary. The GFEM-HMSF shape functions are then generated by the product of a partition of unity associated to each field and the polynomials enrichment functions. In principle, the enrichment can be conducted independently over each of the HMSF approximation fields. However, stability and convergence features of the resulting numerical method can be affected mainly by spurious modes generated when enrichment is arbitrarily applied to the displacement fields. With the aim to efficiently explore the enrichment possibilities, an extension to GFEM-HMSF of the conventional Zienkiewicz-Patch-Test is proposed as a necessary condition to ensure numerical stability. Finally, once the extended Patch-Test is satisfied, some numerical analyses focusing on the selective enrichment over distorted meshes formed by bilinear quadrilateral finite elements are presented, thus showing the performance of the GFEM-HMSF combination.

Probing neutralino properties in minimal supergravity with bilinear R-parity violation

Supersymmetric models with bilinear R-parity violation can account for the observed neutrino masses and mixing parameters indicated by neutrino oscillation data. We consider minimal supergravity versions of bilinear R-parity violation where the lightest supersymmetric particle is a neutralino. This is unstable, with a large enough decay length to be detected at the CERN Large Hadron Collider. We analyze the Large Hadron Collider potential to determine the lightest supersymmetric particle properties, such as mass, lifetime and branching ratios, and discuss their relation to neutrino properties.

Bayesian analysis of random regression models using B-splines to model test-day milk yield of Holstein cattle in Brazil

The objective of this paper is to model variations in test-day milk yields of first lactations of Holstein cows by RR using B-spline functions and Bayesian inference in order to fit adequate and parsimonious models for the estimation of genetic parameters. They used 152,145 test day milk yield records from 7317 first lactations of Holstein cows. The model established in this study was additive, permanent environmental and residual random effects. In addition, contemporary group and linear and quadratic effects of the age of cow at calving were included as fixed effects. Authors modeled the average lactation curve of the population with a fourth-order orthogonal Legendre polynomial. They concluded that a cubic B-spline with seven random regression coefficients for both the additive genetic and permanent environment effects was to be the best according to residual mean square and residual variance estimates. Moreover they urged a lower order model (quadratic B-spline with seven random regression coefficients for both random effects) could be adopted because it yielded practically the same genetic parameter estimates with parsimony. (C) 2012 Elsevier B.V. All rights reserved.

Random regression analyses using B-spline functions to model growth of Nellore cattle

The objective of this study was to estimate (co)variance components using random regression on B-spline functions to weight records obtained from birth to adulthood. A total of 82 064 weight records of 8145 females obtained from the data bank of the Nellore Breeding Program (PMGRN/Nellore Brazil) which started in 1987, were used. The models included direct additive and maternal genetic effects and animal and maternal permanent environmental effects as random. Contemporary group and dam age at calving (linear and quadratic effect) were included as fixed effects, and orthogonal Legendre polynomials of age (cubic regression) were considered as random covariate. The random effects were modeled using B-spline functions considering linear, quadratic and cubic polynomials for each individual segment. Residual variances were grouped in five age classes. Direct additive genetic and animal permanent environmental effects were modeled using up to seven knots (six segments). A single segment with two knots at the end points of the curve was used for the estimation of maternal genetic and maternal permanent environmental effects. A total of 15 models were studied, with the number of parameters ranging from 17 to 81. The models that used B-splines were compared with multi-trait analyses with nine weight traits and to a random regression model that used orthogonal Legendre polynomials. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most appropriate and parsimonious model to describe the covariance structure of the data. Selection for higher weight, such as at young ages, should be performed taking into account an increase in mature cow weight. Particularly, this is important in most of Nellore beef cattle production systems, where the cow herd is maintained on range conditions. There is limited modification of the growth curve of Nellore cattle with respect to the aim of selecting them for rapid growth at young ages while maintaining constant adult weight.

Stochastic quantization of the spherical model and supersymmetry.

In this work, we reported some results about the stochastic quantization of the spherical model. We started by reviewing some basic aspects of this method with emphasis in the connection between the Langevin equation and the supersymmetric quantum mechanics, aiming at the application of the corresponding connection to the spherical model. An intuitive idea is that when applied to the spherical model this gives rise to a supersymmetric version that is identified with one studied in Phys. Rev. E 85, 061109, (2012). Before investigating in detail this aspect, we studied the stochastic quantization of the mean spherical model that is simpler to implement than the one with the strict constraint. We also highlight some points concerning more traditional methods discussed in the literature like canonical and path integral quantization. To produce a supersymmetric version, grounded in the Nicolai map, we investigated the stochastic quantization of the strict spherical model. We showed in fact that the result of this process is an off-shell supersymmetric extension of the quantum spherical model (with the precise supersymmetric constraint structure). That analysis establishes a connection between the classical model and its supersymmetric quantum counterpart. The supersymmetric version in this way constructed is a more natural one and gives further support and motivations to investigate similar connections in other models of the literature.

Topics in geometry, analysis and inverse problems

The thesis consists of three independent parts. Part I: Polynomial amoebas We study the amoeba of a polynomial, as de ned by Gelfand, Kapranov and Zelevinsky. A central role in the treatment is played by a certain convex function which is linear in each complement component of the amoeba, which we call the Ronkin function. This function is used in two di erent ways. First, we use it to construct a polyhedral complex, which we call a spine, approximating the amoeba. Second, the Monge-Ampere measure of the Ronkin function has interesting properties which we explore. This measure can be used to derive an upper bound on the area of an amoeba in two dimensions. We also obtain results on the number of complement components of an amoeba, and consider possible extensions of the theory to varieties of codimension higher than 1. Part II: Differential equations in the complex plane We consider polynomials in one complex variable arising as eigenfunctions of certain differential operators, and obtain results on the distribution of their zeros. We show that in the limit when the degree of the polynomial approaches innity, its zeros are distributed according to a certain probability measure. This measure has its support on the union of nitely many curve segments, and can be characterized by a simple condition on its Cauchy transform. Part III: Radon transforms and tomography This part is concerned with different weighted Radon transforms in two dimensions, in particular the problem of inverting such transforms. We obtain stability results of this inverse problem for rather general classes of weights, including weights of attenuation type with data acquisition limited to a 180 degrees range of angles. We also derive an inversion formula for the exponential Radon transform, with the same restriction on the angle.

Serch for Neutralino Dark Matter with the AMANDA-II Neutrino Telescope

The annihilation of weakly interacting massive particles (WIMPs), accumulated in gravitational potentials (e.g., the core of the Earth, the Sun or the Galactic halo) would lead to neutrino production. This thesis investigates the possibility of searching for WIMPs in the form of the lightest supersymmetric particle (neutralino) trapped in the Sun using the AMANDA-II neutrino telescope. AMANDA-II is a large Cherenkov detector located deep in the ice at the geographical South Pole. The presented work is based on data taken during the year 2001. An analysis optimized to search for the neutralino-induced flux from the Sun has been developed. The observation of no excess with respect to the expected atmospheric neutrino background has been interpreted as an upper limit on the neutralino annihilation rate in the Sun and on the neutralino-induced muon flux in the vicinity of the detector.

A Dark Matter Search with AMANDA : Limits on the Muon Flux from Neutralino Annihilations at the Centre of the Earth with 1997-99 Data

The nature of the dark matter in the Universe is one of the greatest mysteries in modern astronomy. The neutralino is a nonbaryonic dark matter candidate in minimal supersymmetric extensions to the standard model of particle physics. If the dark matter halo of our galaxy is made up of neutralinos some would become gravitationally trapped inside massive bodies like the Earth. Their pair-wise annihilation produces neutrinos that can be detected by neutrino experiments looking in the direction of the centre of the Earth. The AMANDA neutrino telescope, currently the largest in the world, consists of an array of light detectors buried deep in the Antarctic glacier at the geographical South Pole. The extremely transparent ice acts as a Cherenkov medium for muons passing the array and using the timing information of detected photons it is possible to reconstruct the muon direction. A search has been performed for nearly vertically upgoing neutrino induced muons with AMANDA-B10 data taken over the three year period 1997-99. No excess above the atmospheric neutrino background expectation was found. Upper limits at the 90 % confidence level has been set on the annihilation rate of neutralinos at the centre of the Earth and on the muon flux induced by neutrinos created by the annihilation products.