Observation of Higgs boson decays to τ\tau lepton pairs

A search for Higgs boson decays to $\tau$ leptons is performed using events recorded in proton-proton collisions by the CMS experiment at the LHC at a center-of-mass energy of 13 TeV. The data set corresponds to an integrated luminosity of 35.9 $fb^{-1}$. An excess of events is observed over the expected background prediction with a significance of 4.9 standard deviations, to be compared to an expected significance of 4.7 standard deviations.Comment: Proceedings of poster at LHCP1

Search for exotic decays of the Higgs boson

Searches for exotic decays of the 125 GeV Higgs boson performed with data collected by the CMS experiment are presented. Three classes of searches are detailed: searches for invisible decays of the Higgs boson, searches for lepton flavor violating Higgs decays, and searches for decays to the Higgs boson to light pseudoscalars decaying to SM particle pairs. These analyses are based on data collected at center-of-mass energies of 8 and 13 TeV.Comment: Proceedings of LHCP1

The Diffusion Equation on a Hypersphere

We study the diffusion equation on the surface of a 4D sphere and obtain a Kubo formula for the diffusion coefficient

Statistical field theory for simple fluids: the collective variables representation

An alternative representation of an exact statistical field theory for simple fluids, based on the method of collective variables, is presented. The results obtained are examined from the point of another version of theory that was developed recently by performing a Hubbard-Stratonovich transformation of the configurational Boltzmann factor [J.-M. Caillol, Mol. Phys. 101 (2003) 1617]. The analytical expressions for the pressure and the free energy are derived in two-loop approximation for both versions of theory and it is shown that they are indeed equivalent.The results yield a new type approximation within an untested approximation scheme

Some applications of the Lambert W function to classical statistical mechanics

We apply the recently defined Lambert W function to some problems of classical statistical mechanics, i.e. the Tonks gas and a fluid of classical particles interacting via repulsive pair potentials. The latter case is considered both from the point of view of the standard theory of liquids and in the framework of a field theoretical description. Some new mathematical properties of the Lambert W function are obtained by passing

Sine-Gordon Theory for the Equation of State of Classical Hard-Core Coulomb systems. III Loopwise Expansion

We present an exact field theoretical representation of an ionic solution made of charged hard spheres. The action of the field theory is obtained by performing a Hubbard-Stratonovich transform of the configurational Boltzmann factor. It is shown that the Stillinger-Lovett sum rules are satisfied if and only if all the field correlation functions are short range functions. The mean field, Gaussian and two-loops approximations of the theory are derived and discussed. The mean field approximation for the free energy constitutes a rigorous lower bound for the exact free energy, while the mean field pressure is an upper bound. The one-loop order approximation is shown to be identical with the random phase approximation of the theory of liquids. Finally, at the two-loop order and in the pecular case of the restricted primitive model, one recovers results obtained in the framework of the mode expansion theory.Comment: 35 pages, 3 figure

Random Walks on Hyperspheres of Arbitrary Dimensions

We consider random walks on the surface of the sphere $S_{n-1}$ ($n \geq 2$) of the $n$-dimensional Euclidean space $E_n$, in short a hypersphere. By solving the diffusion equation in $S_{n-1}$ we show that the usual law $\varpropto t$ valid in $E_{n-1}$ should be replaced in $S_{n-1}$ by the generic law $\varpropto \exp(-t/\tau)$, where $\theta$ denotes the angular displacement of the walker. More generally one has $\varpropto \exp(-t/ \tau(L,n))$ where $C^{n/2-1}_{L}$ a Gegenbauer polynomial. Conjectures concerning random walks on a fractal inscribed in $S_{n-1}$ are given tentatively.Comment: 10 page

The non-perturbative renormalization group in the ordered phase

We study some analytical properties of the solutions of the non perturbative renormalization group flow equations for a scalar field theory with $Z_2$ symmetry in the ordered phase, i.e. at temperatures below the critical temperature. The study is made in the framework of the local potential approximation. We show that the required physical discontinuity of the magnetic susceptibility $\chi(M)$ at $M=\pm M_0$ ($M_0$ spontaneous magnetization) is reproduced only if the cut-off function which separates high and low energy modes satisfies to some restrictive explicit mathematical conditions; we stress that these conditions are not satisfied by a sharp cut-off in dimensions of space $d<4$.Comment: 27 pages, 14 figures, 7 table

Parametric instabilities of circularly polarized small-amplitude Alfvén waves in Hall plasmas

We study the stability of circularly polarized Alfvén waves (pump waves) in Hall plasmas. First we re-derive the dispersion equation governing the pump wave stability without making an ad hoc assumption about the dependences of perturbations on time and the spatial variable. Then we study the stability of pump waves with small non-dimensional amplitude a (a 1) analytically, restricting our analysis to b < 1, where b is the ratio of the sound and Alfvén speed. Our main results are the following. The stability properties of right-hand polarized waves are qualitatively the same as in ideal MHD. For any values of b and the dispersion parameter τ they are subject to decay instability that occurs for wave numbers from a band with width of order a. The instability increment is also of order a. The left-hand polarized waves can be subject, in general, to three different types of instabilities. The first type is the modulational instability. It only occurs when b is smaller than a limiting value that depends on τ. Only perturbations with wave numbers smaller than a limiting value of order a are unstable. The instability increment is proportional to a2. The second type is the decay instability. It has the same properties as in the case of right-hand polarized waves; however, it occurs only when b < 1 τ. The third type is the beat instability. It occurs for any values of b and τ, and only perturbations with the wave numbers from a narrow band with the width of order a2 are unstable. The increment of this instability is proportional to a2, except for τ close to τc when it is proportional to a, where τc is a function of b

Liquid-Vapor Transition and Critical Behavior of The Ultrasoft Restricted Primitive Model of Polyelectrolytes : a Monte Carlo Study

We present a Monte-Carlo study of the liquid-vapor transition and the critical behavior of a model of polyelectrolytes with soft gaussian charge distributions introduced recently by Coslovich, Hansen, and Kahl [J. Chem. Phys. \textbf{134}, 244514 (2011)]. A finite size study involving four different volumes in the grand canonical ensemble yields a precise determination of the critical temperature, chemical potential, and density of the model. Attempts to determine the nature of the criticality and to obtain reliable values for the critical exponents are not conclusive.Comment: 14 pages, 4 figure