Color-octet scalar effects on Higgs boson production in gluon fusion

We compute the next-to-next-to-leading order QCD corrections to the gluon-fusion production of a Higgs boson in models with massive color-octet scalars in the ${\bf (8,1)_0}$ representation using an effective-theory approach. We derive a compact analytic expression for the relevant Wilson coefficient, and explain an interesting technical aspect of the calculation that requires inclusion of the quartic-scalar interactions at next-to-next-to-leading order. We perform a renormalization-group analysis of the scalar couplings to derive the allowed regions of parameter space, and present phenomenological results for both the Tevatron and the LHC. The modifications of the Higgs production cross section are large at both colliders, and can increase the Standard Model rate by more than a factor of two in allowed regions of parameter space. We estimate that stringent constraints on the color-octet scalar parameters can be obtained using the Tevatron exclusion limit on Higgs production.Comment: 18 pages, 6 figures, 3 table

The impact of a deep convection on sulfate transport and redistribution

International audienceA three-dimensional compressible cloud model was used to simulate the processes related to dynamics, microphysics and chemistry of continental non-polluted and continental polluted clouds. The chemical components are formulated in terms of continuity equations for different chemical species in the aqueous phase within the cloud. Their evolution in this model came from not only by the processes of advection and turbulence transport, but also the chemical reactions and microphysical transfers. The model includes a method of kinetic uptake limitations. Gases with low solubility H* 3 mol dm-3 atm-1 are in Henry's law equilibrium with temperature dependence of Henry's law coefficients. Seven pollutant groups are currently included in the chemistry parameterization scheme: S(IV), S(VI), (H2O2), (O3), N(V), (NH3), (CO2). The present model contains explicit treatment of SO2 and O3, a kinetic method of gas uptake as well as an improved microphysical parameterization scheme. The primary objective of this model is to study the impact of the deep convection on the pollutant transport, redistribution and deposition. It is done through chemical reactions, oxidation, scavenging of aerosol particles and transfer via microphysical transitions among water categories. Two base run simulation parameters are used to initialize the model. The first model run is for the 6 July 1995 event, characterized by intensive convective cloud activity and a large amount of precipitation, manifested as a flashflood. The second one is related to transboundary dust transport and sulfate wet deposition. The chemical field initialization is based on the vertical distribution profiles of gases and aerosols for continental non-polluted and continental polluted background. The study has revealed the importance of considering interactions between dynamics, microphysics and cloud chemistry. Deep convection in the first analyzed case generates rapid upward and downward transport of pollutants. It stimulates the impact of scavenging processes and microphysical conversions, pollutant redistribution and wet deposition. We find good agreement between calculated and observed rainfall, pH, sulfate concentration and wet deposition, in the second simulated case. Aerosol particles partially dissolved in precipitation changed their qualitative and quantitative features, acidity and increment of all chemical components. A lot of sensitivity tests of the terms included in the chemistry parameterization scheme indicate that assumption of Henry's law equilibrium leads to a factor 2 to 3 underestimate of a soluble gas in cloud water and 3 to 5 in rainwater, respectively. Our calculations demonstrate that assumption of Henry's law leads to a factor of about 1.0 to 1.3 overestimation of the integrated sulfur mass removed by wet deposition. Analysis of the relative contribution of some parameters implies that 20% - 24% of total sulfur mass deposited belongs to both nucleation and impact scavenging. Liquid phase oxidation contributed 22% and 28% of the total sulfur mass deposited for continental non-polluted and continental polluted background, respectively. Neglecting liquid-ice phase chemical reactions leads to underestimation of the total sulfur mass deposited by about a factor of 1.0 to 1.2 for continental non-polluted and continental polluted distributions, relative to the base run

On a modular property of N=2 superconformal theories in four dimensions

In this note we discuss several properties of the Schur index of N=2 superconformal theories in four dimensions. In particular, we study modular properties of this index under SL(2,Z) transformations of its parameters.Comment: 23 page, 2 figure

Raising and lowering operators, factorization and differential/difference operators of hypergeometric type

Starting from Rodrigues formula we present a general construction of raising and lowering operators for orthogonal polynomials of continuous and discrete variable on uniform lattice. In order to have these operators mutually adjoint we introduce orthonormal functions with respect to the scalar product of unit weight. Using the Infeld-Hull factorization method, we generate from the raising and lowering operators the second order self-adjoint differential/difference operator of hypergeometric type.Comment: LaTeX, 24 pages, iopart style (late submission

Determinants of elliptic hypergeometric integrals

We start from an interpretation of the BC_(2)-symmetric “Type I” (elliptic Dixon) elliptic hypergeometric integral evaluation as a formula for a Casoratian of the elliptic hypergeometric equation and then generalize this construction to higher-dimensional integrals and higher-order hypergeometric functions. This allows us to prove the corresponding formulas for the elliptic beta integral and symmetry transformation in a new way, by proving that both sides satisfy the same difference equations and that these difference equations satisfy a needed Galois-theoretic condition ensuring the uniqueness of the simultaneous solution

Quasi-exactly solvable problems and the dual (q-)Hahn polynomials

A second-order differential (q-difference) eigenvalue equation is constructed whose solutions are generating functions of the dual (q-)Hahn polynomials. The fact is noticed that these generating functions are reduced to the (little q-)Jacobi polynomials, and implications of this for quasi-exactly solvable problems are studied. A connection with the Azbel-Hofstadter problem is indicated.Comment: 15 pages, LaTex; final version, presentation improved, title changed, to appear in J.Math.Phy

Solitons and Normal Random Matrices

We discuss a general relation between the solitons and statistical mechanics and show that the partition function of the normal random matrix model can be obtained from the multi-soliton solutions of the two-dimensional Toda lattice hierarchy in a special limit

S-duality and 2d Topological QFT

We study the superconformal index for the class of N=2 4d superconformal field theories recently introduced by Gaiotto. These theories are defined by compactifying the (2,0) 6d theory on a Riemann surface with punctures. We interpret the index of the 4d theory associated to an n-punctured Riemann surface as the n-point correlation function of a 2d topological QFT living on the surface. Invariance of the index under generalized S-duality transformations (the mapping class group of the Riemann surface) translates into associativity of the operator algebra of the 2d TQFT. In the A_1 case, for which the 4d SCFTs have a Lagrangian realization, the structure constants and metric of the 2d TQFT can be calculated explicitly in terms of elliptic gamma functions. Associativity then holds thanks to a remarkable symmetry of an elliptic hypergeometric beta integral, proved very recently by van de Bult.Comment: 25 pages, 11 figure