Resolving the J/\psi RHIC puzzles at LHC

Experiments with gold-gold collisions at RHIC have revealed (i) stronger suppression of charmonium production at forward rapidity than at midrapidity and (ii) the similarity between the suppression degrees at RHIC and SPS energies. To describe these findings we employ the model that includes nuclear shadowing effects, calculated within the Glauber-Gribov theory, rapidity-dependent absorptive mechanism, caused by energy-momentum conservation, and dissociation and recombination of the charmonium due to interaction with co-moving matter. The free parameters of the model are tuned and fixed by comparison with experimental data at lower energies. A good agreement with the RHIC results concerning the rapidity and centrality distributions is obtained for both heavy Au+Au and light Cu+Cu colliding system. For pA and A+A collisions at LHC the model predicts stronger suppression of the charmonium and bottomonium yields in stark contrast to thermal model predictions.Comment: SQM2008 proceedings, 6 page

Nuclear suppression at RHIC and LHC in Glauber-Gribov approach

The approach to problem of nuclear shadowing based on Gribov Reggeon calculus is presented. Here the total cross section of $h A$ interaction is found in a parameter-free description, employing the new data on the gluon density of the Pomeron, measured with high precision at HERA, as input. The model is then applied for calculation of $J/\psi$ production in $d Au$ collisions at top RHIC energy. It is shown that the theoretical estimates are in a very good agreement with the PHENIX data, and further predictions for the $J/\psi$ suppression in $p Pb$ collisions at coming soon LHC are made.Comment: SQM2007 proceedings, 6 page

Anisotropic flow of charged and identified hadrons in the quark-gluon string model for Au+Au collisions at sqrt(s) = 200 GeV

The pseudorapidity behaviour of the azimuthal anisotropy parameters v_1 and v_2 of inclusive charged hadrons and their dependence on the centrality has been studied in Au+Au collisions at full RHIC energy of sqrt(s) = 200 GeV within the microscopic quark-gluon string model. The QGSM simulation results for the directed flow v_1 show antiflow alignment within the pseudorapidity range |eta| < 2 in a fair agreement with the experimental v_1(eta) data, but cannot reproduce the further development of the antiflow up to |eta| around 3.5. The eta dependence of the elliptic flow v_2 extracted from the simulations agrees well with the experimental data in the whole pseudorapidity range for different centrality classes. The centrality dependence of the integrated elliptic flow of charged hadrons in the QGSM almost coincides with the PHOBOS experimental distribution. The transverse momentum dependence of the elliptic flow of identified and inclusive charged hadrons is studied also. The model reproduces quantitatively the low p_T part of the distributions rather good, but underestimates the measured elliptic flow for transverse momenta p_T > 1 GeV/c. Qualitatively, however, the model is able to reproduce the saturation of the v_2(p_T) spectra with rising p_T as well as the crossing of the elliptic flow for mesons and baryons.Comment: REVTeX, 10 pages, 10 figures, v2: extended discussion of the model results, accepted for publication in Phys. Rev.

Large deviations of the maximal eigenvalue of random matrices

We present detailed computations of the 'at least finite' terms (three dominant orders) of the free energy in a one-cut matrix model with a hard edge a, in beta-ensembles, with any polynomial potential. beta is a positive number, so not restricted to the standard values beta = 1 (hermitian matrices), beta = 1/2 (symmetric matrices), beta = 2 (quaternionic self-dual matrices). This model allows to study the statistic of the maximum eigenvalue of random matrices. We compute the large deviation function to the left of the expected maximum. We specialize our results to the gaussian beta-ensembles and check them numerically. Our method is based on general results and procedures already developed in the literature to solve the Pastur equations (also called "loop equations"). It allows to compute the left tail of the analog of Tracy-Widom laws for any beta, including the constant term.Comment: 62 pages, 4 figures, pdflatex ; v2 bibliography corrected ; v3 typos corrected and preprint added ; v4 few more numbers adde

Finite-dimensional reductions of the discrete Toda chain

The problem of construction of integrable boundary conditions for the discrete Toda chain is considered. The restricted chains for properly chosen closure conditions are reduced to the well known discrete Painlev\'e equations $dP_{III}$, $dP_{V}$, $dP_{VI}$. Lax representations for these discrete Painlev\'e equations are found.Comment: Submitted to Jornal of Physics A: Math. Gen., 14 page

On Darboux Integrable Semi-Discrete Chains

Differential-difference equation $\frac{d}{dx}t(n+1,x)=f(x,t(n,x),t(n+1,x),\frac{d}{dx}t(n,x))$ with unknown $t(n,x)$ depending on continuous and discrete variables $x$ and $n$ is studied. We call an equation of such kind Darboux integrable, if there exist two functions (called integrals) $F$ and $I$ of a finite number of dynamical variables such that $D_xF=0$ and $DI=I$, where $D_x$ is the operator of total differentiation with respect to $x$, and $D$ is the shift operator: $Dp(n)=p(n+1)$. It is proved that the integrals can be brought to some canonical form. A method of construction of an explicit formula for general solution to Darboux integrable chains is discussed and for a class of chains such solutions are found.Comment: 19 page

Thermodynamic limit of random partitions and dispersionless Toda hierarchy

We study the thermodynamic limit of random partition models for the instanton sum of 4D and 5D supersymmetric U(1) gauge theories deformed by some physical observables. The physical observables correspond to external potentials in the statistical model. The partition function is reformulated in terms of the density function of Maya diagrams. The thermodynamic limit is governed by a limit shape of Young diagrams associated with dominant terms in the partition function. The limit shape is characterized by a variational problem, which is further converted to a scalar-valued Riemann-Hilbert problem. This Riemann-Hilbert problem is solved with the aid of a complex curve, which may be thought of as the Seiberg-Witten curve of the deformed U(1) gauge theory. This solution of the Riemann-Hilbert problem is identified with a special solution of the dispersionless Toda hierarchy that satisfies a pair of generalized string equations. The generalized string equations for the 5D gauge theory are shown to be related to hidden symmetries of the statistical model. The prepotential and the Seiberg-Witten differential are also considered.Comment: latex2e using amsmath,amssymb,amsthm packages, 55 pages, no figure; (v2) typos correcte

Operator product expansion of higher rank Wilson loops from D-branes and matrix models

In this paper we study correlation functions of circular Wilson loops in higher dimensional representations with chiral primary operators of N=4 super Yang-Mills theory. This is done using the recently established relation between higher rank Wilson loops in gauge theory and D-branes with electric fluxes in supergravity. We verify our results with a matrix model computation, finding perfect agreement in both the symmetric and the antisymmetric case.Comment: 28 pages, latex; v2: minor misprints corrected, references adde

Second virial coefficients of light nuclear clusters and their chemical freeze-out in nuclear collisions

Here we develop a new strategy to analyze the chemical freeze-out of light (anti)nuclei produced in high energy collisions of heavy atomic nuclei within an advanced version of the hadron resonance gas model. It is based on two different, but complementary approaches to model the hard-core repulsion between the light nuclei and hadrons. The first approach is based on an approximate treatment of the equivalent hard-core radius of a roomy nuclear cluster and pions, while the second approach is rigorously derived here using a self-consistent treatment of classical excluded volumes of light (anti)nuclei and hadrons. By construction, in a hadronic medium dominated by pions, both approaches should give the same results. Employing this strategy to the analysis of hadronic and light (anti)nuclei multiplicities measured by ALICE at $\sqrt{s_{NN}} =2.76$ TeV and by STAR at $\sqrt{s_{NN}} =200$ GeV, we got rid of the existing ambiguity in the description of light (anti)nuclei data and determined the chemical freeze-out parameters of nuclei with high accuracy and confidence. At ALICE energy the nuclei are frozen prior to the hadrons at the temperature $T = 175.1^{+2.3}_{-3.9}$ MeV, while at STAR energy there is a single freeze-out of hadrons and nuclei at the temperature $T = 167.2 \pm 3.9$ MeV. We argue that the found chemical freeze-out volumes of nuclei can be considered as the volumes of quark-gluon bags that produce the nuclei at the moment of hadronization.Comment: 15 pages, 4 figures, 3 table

A survey of Hirota's difference equations

A review of selected topics in Hirota's bilinear difference equation (HBDE) is given. This famous 3-dimensional difference equation is known to provide a canonical integrable discretization for most important types of soliton equations. Similarly to the continuous theory, HBDE is a member of an infinite hierarchy. The central point of our exposition is a discrete version of the zero curvature condition explicitly written in the form of discrete Zakharov-Shabat equations for M-operators realized as difference or pseudo-difference operators. A unified approach to various types of M-operators and zero curvature representations is suggested. Different reductions of HBDE to 2-dimensional equations are considered. Among them discrete counterparts of the KdV, sine-Gordon, Toda chain, relativistic Toda chain and other typical examples are discussed in detail.Comment: LaTeX, 43 pages, LaTeX figures (with emlines2.sty