Density Fluctuations in the Quark-Gluon Plasma

Using the kinetic theory we discuss how the particle and energy densities of the quark-gluon plasma fluctuate in a space-time cell. The fluctuations in the equilibrium plasma and in that one from the early stage of ultrarelativistic heavy-ion collisions are estimated. Within the physically interesting values of the parameters involved the fluctuations appear sizeable in both cases.Comment: 8 pages, no macro

p_T-fluctuations in high-energy p-p and A-A collisions

The event-by-event p_T-fluctuations in proton-proton and central Pb-Pb collisions, which have been experimentally studied by means of the so-called Phi-measure, are analyzed. The contribution due to the correlation which couples the average p_T to the event multiplicity is computed. The correlation appears to be far too weak to explain the preliminary experimental value of Phi (p_T) in p-p interactions. The significance of the result is discussed.Comment: 5 pages, 2 figures, minor improvement

Thermalization vs. Isotropization & Azimuthal Fluctuations

Hydrodynamic description requires a local thermodynamic equilibrium of the system under study but an approximate hydrodynamic behaviour is already manifested when a momentum distribution of liquid components is not of equilibrium form but merely isotropic. While the process of equilibration is relatively slow, the parton system becomes isotropic rather fast due to the plasma instabilities. Azimuthal fluctuations observed in relativistic heavy-ion collisions are argued to distinguish between a fully equilibrated and only isotropic parton system produced in the collision early stage.Comment: 12 pages, presented at `Correlations and Fluctuations in Relativistic Nuclear Collisions', MIT, April 05, minor correction

Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS

Event-by-event fluctuations and correlations in azimuthal angle are currently widely investigated in various experiments. In this paper the $\Phi$ measure (earlier used in experiments to evaluate fluctuations in transverse momentum) is now applied to azimuthal angle $\phi$. Properties of this $\Phi_{\phi}$ function are investigated through fast generators and with complex models such as Pythia, Hijing, and UrQMD. Preliminary results of NA49 on $\Phi_{\phi}$ are also presented. The system size dependence (p+p, C+C, Si+Si and 6 centralities of Pb+Pb) at the highest SPS energy (158$A$ GeV) is shown, as well as the energy dependence (20$A$ - 158$A$ GeV) for the 7.2\% most central Pb+Pb interactions.Comment: Proceedings from Hot Quarks 2010,June 21-2

Energy Loss of a Heavy Fermion in an Anisotropic QED Plasma

We compute the leading-order collisional energy loss of a heavy fermion propagating in a QED plasma with an electron distribution function which is anisotropic in momentum space. We show that in the presence of such anisotropies there can be a significant directional dependence of the heavy fermion energy loss with the effect being quite large for highly-relativistic velocities. We also repeat the analysis of the isotropic case more carefully and show that the final result depends on the intermediate scale used to separate hard and soft contributions to the energy loss. We then show that the canonical isotropic result is obtained in the weak-coupling limit. For intermediate-coupling we use the residual scale dependence as a measure of our theoretical uncertainty. We also discuss complications which could arise due to the presence of unstable soft photonic modes and demonstrate that the calculation of the energy loss is safe.Comment: 19 pages, 18 figures. v2 - Correction to normalization of numerical results; some figures modified as a result; discussion of role of unstable modes added along with two new figure

Fluctuating initial conditions in heavy-ion collisions from the Glauber approach

In the framework of the Glauber approach we analyze the shape parameters of the early-formed system and their event-by-event fluctuations. We test a variety of models: the conventional wounded nucleon model, a model admixing binary collisions to the wounded nucleons, a model with hot spots, as well as the hot-spot model where the deposition of energy occurs with a superimposed probability distribution. We look in detail at the so-called participant multipole moments, obtained by an averaging procedure where in each event the system is translated to its center of mass and aligned with the major principal axis of the ellipse of inertia. Quantitative comparisons indicate substantial relative effects for eccentricity in variants of Glauber models. On the other hand, the dependence of the scaled standard deviation of the participant eccentricity on the chosen model is weak. For all models the values range from about 0.5 for the central collisions to about 0.3-0.4 for peripheral collisions, both for the gold-gold and copper-copper collisions. They are dominated by statistics and change only by 10-15% from model to model. We provide an approximate analytic expansion for the multipole moments and their fluctuations given in terms of the fixed-axes moments. For central collisions and in the absence of correlations it gives the simple formula for the scaled standard deviation of the participant eccentricity: sqrt(4/pi-1). Similarly, we obtain expansions for the radial profiles of the multipole distributions. We investigate the relevance of the shape-fluctuation effects for jet quenching and find them important only for very central events. Finally, we argue how smooth hydro leads to the known result v_4 ~ v_2^2, and further to the prediction Delta v_4/v_4 = 2 Delta v_2/v_2.Comment: 20 pages, 15 figures, additions include comparison to the CGC result

New results from fluctuation analysis in NA49 at the CERN SPS

The exploration of the phase diagram of strongly interacting matter, particularly the study of the phase transition from hadronic to partonic matter and the search for a hypothetical critical endpoint of the first order transition line, is one of the most challenging tasks in present heavy ion physics. In this talk new results on chemical (particle ratio), transverse momentum, multiplicity and azimuthal angle fluctuations will be presented. We also discuss their connection to the onset of deconfinement and to the critical endpoint.Comment: The Proceedings of the International Conference "Critical Point and Onset of Deconfinement - CPOD 2011", Wuhan, November 7-11, 201

Perturbative and Nonperturbative Kolmogorov Turbulence in a Gluon Plasma

In numerical simulations of nonabelian plasma instabilities in the hard-loop approximation, a turbulent spectrum has been observed that is characterized by a phase-space density of particles $n(p)\sim p^{-\nu}$ with exponent $\nu\simeq 2$, which is larger than expected from relativistic $2\leftrightarrow 2$ scatterings. Using the approach of Zakharov, L'vov and Falkovich, we analyse possible Kolmogorov coefficients for relativistic $(m \ge 4)$-particle processes, which give at most $\nu=5/3$ perturbatively for an energy cascade. We discuss nonperturbative scenarios which lead to larger values. As an extreme limit we find the result $\nu=5$ generically in an inherently nonperturbative effective field theory situation, which coincides with results obtained by Berges et al.\ in large-$N$ scalar field theory. If we instead assume that scaling behavior is determined by Schwinger-Dyson resummations such that the different scaling of bare and dressed vertices matters, we find that intermediate values are possible. We present one simple scenario which would single out $\nu=2$.Comment: published versio

Contribution of α2\alpha^2-terms to the total interaction cross sections of relativistic elementary atoms with atoms of matter

It is shown that the corrections of $\alpha^2$ order to the total cross sections for interaction of elementary hydrogen-like atoms with target atoms, reported in the previously published paper [S.Mrowczynski, Phys.Rev. D36, 1520 (1987)], do not include some terms of the same order of magnitude. That results in a significant contribution of these corrections in particular cases. The full $\alpha^2$-corrections have been derived and it is shown that they are really small and could be omitted for most practical applications.Comment: 5 page

Measuring charge fluctuations in high-energy nuclear collisions

Various measures of charge fluctuations in heavy-ion collisions are discussed. Advantages of the Phi-measure are demonstrated and its relation to other fluctuation measures is established. To get the relation, Phi is expressed through the moments of multiplicity distribution. We study how the measures act in the case of a `background' model which represents the classical hadron gas in equilibrium. The model assumes statistical particle production constrained by charge conservation. It also takes into account both the effect of incomplete experimental apparatus acceptance and that of tracking inefficiency. The model is shown to approximately agree with the PHENIX and preliminary STAR data on the electric charge fluctuations. Finally, `background-free' measures are discussed.Comment: 12 pages, 6 figures, numerous but minor changes, Phys. Rev. C in prin