Quarkonia and Heavy-Quark Relaxation Times in the Quark-Gluon Plasma

A thermodynamic T-matrix approach for elastic 2-body interactions is employed to calculate spectral functions of open and hidden heavy-quark systems in the Quark-Gluon Plasma. This enables the evaluation of quarkonium bound-state properties and heavy-quark diffusion on a common basis and thus to obtain mutual constraints. The two-body interaction kernel is approximated within a potential picture for spacelike momentum transfers. An effective field-theoretical model combining color-Coulomb and confining terms is implemented with relativistic corrections and for different color channels. Four pertinent model parameters, characterizing the coupling strengths and screening, are adjusted to reproduce the color-average heavy-quark free energy as computed in thermal lattice QCD. The approach is tested against vacuum spectroscopy in the open (D, B) and hidden (Psi and Upsilon) flavor sectors, as well as in the high-energy limit of elastic perturbative QCD scattering. Theoretical uncertainties in the static reduction scheme of the 4-dimensional Bethe-Salpeter equation are elucidated. The quarkonium spectral functions are used to calculate Euclidean correlators which are discussed in light of lattice QCD results, while heavy-quark relaxation rates and diffusion coefficients are extracted utilizing a Fokker-Planck equation.Comment: 33 pages, 28 figure

Fixed-Angle Elastic Hadron Scattering

The scattering amplitude in the dual model with Mandelstam analyticity and trajectory $\alpha (s)=\alpha_{0}-\gamma \ln [ (1+\beta \sqrt{s_{0} -s})/(1+ \beta \sqrt{s_{0}})]$ is studied in the limit $s,|t|\to \infty, s/t=const.$ By using the saddle point method, a series decomposition for the scattering amplitude is obtained, with the leading and two sub-leading terms calculated explicitly.Comment: 15 pages, LaTeX, 2 figures with eps file

Gauge Dependence in Chern-Simons Theory

We compute the contribution to the modulus of the one-loop effective action in pure non-Abelian Chern-Simons theory in an arbitrary covariant gauge. We find that the results are dependent on both the gauge parameter ($\alpha$) and the metric required in the gauge fixing. A contribution arises that has not been previously encountered; it is of the form $(\alpha / \sqrt{p^2}) \epsilon _{\mu \lambda \nu} p^\lambda$. This is possible as in three dimensions $\alpha$ is dimensionful. A variant of proper time regularization is used to render these integrals well behaved (although no divergences occur when the regularization is turned off at the end of the calculation). Since the original Lagrangian is unaltered in this approach, no symmetries of the classical theory are explicitly broken and $\epsilon_{\mu \lambda \nu}$ is handled unambiguously since the system is three dimensional at all stages of the calculation. The results are shown to be consistent with the so-called Nielsen identities which predict the explicit gauge parameter dependence using an extension of BRS symmetry. We demonstrate that this $\alpha$ dependence may potentially contribute to the vacuum expectation values of products of Wilson loops.Comment: 17 pp (including 3 figures). Uses REVTeX 3.0 and epsfig.sty (available from LANL). Latex thric

Convergence rate for a curse-ofdimensionality-free method for a class of HJB PDEs

Abstract. In previous work of the first author and others, max-plus methods have been explored for solution of firstorder, nonlinear Hamilton-Jacobi-Bellman partial differential equations (HJB PDEs) and corresponding nonlinear control problems. Although max-plus basis expansion and max-plus finite-element methods can provide substantial computationalspeed advantages, they still generally suffer from the curse-of-dimensionality. Here we consider HJB PDEs where the Hamiltonian takes the form of a (pointwise) maximum of linear/quadratic forms. The approach to solution will be rather general, but in order to ground the work, we consider only constituent Hamiltonians corresponding to long-run averagecost-per-unit-time optimal control problems for the development. We consider a previously obtained numerical method not subject to the curse-of-dimensionality. The method is based on construction of the dual-space semigroup corresponding to the HJB PDE. This dual-space semigroup is constructed from the dual-space semigroups corresponding to the constituent linear/quadratic Hamiltonians. The dual-space semigroup is particularly useful due to its form as a max-plus integral operator with kernel obtained from the originating semigroup. One considers repeated application of the dual-space semigroup to obtain the solution. Although previous work indicated that the method was not subject to the curse-of-dimensionality, it did not indicate any error bounds or convergence rate. Here, we obtain specific error bounds. Key words. partial differential equations, curse-of-dimensionality, dynamic programming, max-plus algebra, Legendre transform, Fenchel transform, semiconvexity, Hamilton-Jacobi-Bellman equations, idempotent analysis. AMS subject classifications. 49LXX, 93C10, 35B37, 35F20, 65N99, 47D99 1. Introduction. A robust approach to the solution of nonlinear control problems is through the general method of dynamic programming. For the typical class of problems in continuous time and continuous space, with the dynamics governed by finite-dimensional, ordinary differential equations, this leads to a representation of the problem as a first-order, nonlinear partial differential equation, the Hamilton-Jacobi-Bellman equation -or the HJB PDE. If one has an infinite time-horizon problem, then the HJB PDE is a steady-state equation, and this PDE is over a space (or some subset thereof) whose dimension is the dimension of the state variable of the control problem. Due to the nonlinearity, the solutions are generally nonsmooth, and one must use the theory of viscosity solution

On the notion of potential in quantum gravity

The problem of consistent definition of the quantum corrected gravitational field is considered in the framework of the $S$-matrix method. Gauge dependence of the one-particle-reducible part of the two-scalar-particle scattering amplitude, with the help of which the potential is usually defined, is investigated at the one-loop approximation. The $1/r^2$-terms in the potential, which are of zero order in the Planck constant $\hbar,$ are shown to be independent of the gauge parameter weighting the gauge condition in the action. However, the $1/r^3$-terms, proportional to $\hbar,$ describing the first proper quantum correction, are proved to be gauge-dependent. With the help of the Slavnov identities, their dependence on the weighting parameter is calculated explicitly. The reason the gauge dependence originates from is briefly discussed.Comment: LaTex 2.09, 16 pages, 5 ps figure

The thermal model on the verge of the ultimate test: particle production in Pb-Pb collisions at the LHC

We investigate the production of hadrons in nuclear collisions within the framework of the thermal (or statistical hadronization) model. We discuss both the ligh-quark hadrons as well as charmonium and provide predictions for the LHC energy. Even as its exact magnitude is dependent on the charm production cross section, not yet measured in Pb-Pb collisions, we can confidently predict that at the LHC the nuclear modification factor of charmonium as a function of centrality is larger than that observed at RHIC and compare the experimental results to these predictions.Comment: 4 pages, 3 figures; proceedings of QM201

Quark Matter and Nuclear Collisions: A Brief History of Strong Interaction Thermodynamics

The past fifty years have seen the emergence of a new field of research in physics, the study of matter at extreme temperatures and densities. The theory of strong interactions, quantum chromodynamics (QCD), predicts that in this limit, matter will become a plasma of deconfined quarks and gluons -- the medium which made up the early universe in the first 10 microseconds after the big bang. High energy nuclear collisions are expected to produce short-lived bubbles of such a medium in the laboratory. I survey the merger of statistical QCD and nuclear collision studies for the analysis of strongly interacting matter in theory and experiment.Comment: 24 pages, 14 figures Opening Talk at the 5th Berkeley School on Collective Dynamics in High Energy Collisions, LBNL Berkeley/California, May 14 - 18, 201

Gauge dependence of effective gravitational field

The problem of gauge independent definition of effective gravitational field is considered from the point of view of the process of measurement. Under assumption that dynamics of the measuring apparatus can be described by the ordinary classical action, effective Slavnov identities for the generating functionals of Green functions corresponding to a system of arbitrary gravitational field measured by means of scalar particles are obtained. With the help of these identities, the total gauge dependence of the non-local part of the one-loop effective apparatus action, describing the long-range quantum corrections, is calculated. The value of effective gravitational field inferred from the effective apparatus action is found to be gauge-dependent. A probable explanation of this result, referring to a peculiarity of the gravitational interaction, is given.Comment: Revised version as publishe

Contribution of matter fields to the Gell-Mann-Low function for N=1 supersymmetric Yang-Mills theory, regularized by higher covariant derivatives

Contribution of matter fields to the Gell-Mann-Low function for N=1 supersymmetric Yang-Mills theory, regularized by higher covariant derivatives, is obtained using Schwinger-Dyson equations and Slavnov-Tailor identities. A possible deviation of the result from the corresponding contribution in the exact Novikov, Shifman, Vainshtein and Zakharov $\beta$-function is discussed.Comment: 20 pages, 4 figure