The "Ridge" in Proton-Proton Scattering at 7 TeV

One of the most important experimental results for proton-proton scattering at the LHC is the observation of a so-called "ridge" structure in the two particle correlation function versus the pseudorapidity difference $\Delta\eta$ and the azimuthal angle difference $\Delta\phi$. One finds a strong correlation around $\Delta\phi=0$, extended over many units in $\Delta\eta$. We show that a hydrodynamical expansion based on flux tube initial conditions leads in a natural way to the observed structure. To get this result, we have to perform an event-by-event calculation, because the effect is due to statistical fluctuations of the initial conditions, together with a subsequent collective expansion. This is a strong point in favour of a fluid-like behavior even in $pp$ scattering, where we have to deal with length scales of the order of 0.1 fm.Comment: 5 pages, 4 figure

Dynamical freeze-out in event-by-event hydrodynamics

In hydrodynamical modeling of the ultrarelativistic heavy-ion collisions the freeze-out is typically performed at a constant temperature or density. In this work we apply a dynamical freeze-out criterion, which compares the hydrodynamical expansion rate with the pion scattering rate. Recently many calculations have been done using event-by-event hydrodynamics where the initial density profile fluctuates from event to event. In these event-by-event calculations the expansion rate fluctuates strongly as well, and thus it is interesting to check how the dynamical freeze-out changes hadron distributions with respect to the constant temperature freeze-out. We present hadron spectra and elliptic flow calculated using (2+1)-dimensional ideal hydrodynamics, and show the differences between constant temperature and dynamical freeze-out criteria. We find that the differences caused by different freeze-out criteria are small in all studied cases.Comment: 8 pages, 11 figures, to be published in the proceedings of the 28th Winter Workshop on Nuclear Dynamics, Puerto Rico, April 7-14, 201

Sound Mode Hydrodynamics from Bulk Scalar Fields

We study the hydrodynamic sound mode using gauge/gravity correspondence by examining a generic black brane background's response to perturbations. We assume that the background is generated by a single scalar field, and then generalize to the case of multiple scalar fields. The relevant differential equations obeyed by the gauge invariant variables are presented in both cases. Finally, we present an analytical solution to these equations in a special case; this solution allows us to determine the speed of sound and bulk viscosity for certain special metrics. These results may be useful in determining sound mode transport coefficients in phenomenologically motivated holographic models of strongly coupled systems.Comment: 17 pages. Corrections made to one of the gauge invariant equations (66). This equation was not used in the other main conclusions of the paper, so the rest of the results are unchange

Effects of fluctuations on the initial eccentricity from the Color Glass Condensate in heavy ion collisions

We introduce a modified form of the Kharzeev-Levin-Nardi (KLN) approach for nuclear collisions. The new ansatz for the unintegrated gluon distribution function preserves factorization, and the saturation scale is bound from below by that for a single nucleon. It also reproduces the correct scaling with the number of collisions at high transverse momentum. The corresponding Monte Carlo implementation allows us to account for fluctuations of the hard sources (nucleons) in the transverse plane. We compute various definitions of the eccentricity within the new approach, which are relevant for the interpretation of the elliptic flow. Our approach predicts breaking of the scaling of the eccentricity with the Glauber eccentricity at the level of about 30%.Comment: 9 pages, 10 figures, Updated version as accepted by Phys.Rev.

Results on Identified Hadrons from the PHENIX Experiment at RHIC

Recent results on identified hadrons from the PHENIX experiment in Au+Au collisions at mid-rapidity at $\sqrt{s_{NN}}$ = 200 GeV are presented. The centrality dependence of transverse momentum distributions and particle ratios for identified charged hadrons are studied. The transverse flow velocity and freeze-out temperature are extracted from $p_{T}$ spectra within the framework of a hydrodynamic collective flow model. Two-particle HBT correlations for charged pions are measured in different centrality selections for a broad range of transverse momentum of the pair. Results on elliptic flow measurements with respect to the reaction plane for identified particles are also presented.Comment: 10 pages, 10 figures. Talk presented at Quark Matter 2002, Nantes, France, July 18-24, 2002. To appear in the proceedings (Nucl. Phys. A

Chemical freeze-out temperature in hydrodynamical description of Au+Au collisions at sqrt(s_NN) = 200 GeV

We study the effect of separate chemical and kinetic freeze-outs to the ideal hydrodynamical flow in Au+Au collisions at RHIC (sqrt(s_NN) = 200 GeV energy). Unlike in earlier studies we explore how these effects can be counteracted by changes in the initial state of the hydrodynamical evolution. We conclude that the reproduction of pion, proton and antiproton yields necessitates a chemical freeze-out temperature of T = 150 MeV instead of T = 160 - 170 MeV motivated by thermal models. Unlike previously reported, this lower temperature makes it possible to reproduce the p_T-spectra of hadrons if one assumes very small initial time, tau_0 = 0.2 fm/c. However, the p_T-differential elliptic flow, v_2(p_T) remains badly reproduced. This points to the need to include dissipative effects (viscosity) or some other refinement to the model.Comment: 8 pages, 7 figures; Accepted for publication in European Physical Journal A; Added discussion about the effect of weak decays to chemical freeze-out temperature and a figure showing isentropic curves in T-mu plan

Second order hydrodynamics for a special class of gravity duals

The sound mode hydrodynamic dispersion relation is computed up to order $q^3$ for a class of gravitational duals which includes both Schwarzschild $AdS$ and Dp-Brane metrics. The implications for second order transport coefficients are examined within the context of Israel-Stewart theory. These sound mode results are compared with previously known results for the shear mode. This comparison allows one to determine the third order hydrodynamic contributions to the shear mode for the class of metrics considered here.Comment: 20 page

Influence of a temperature-dependent shear viscosity on the azimuthal asymmetries of transverse momentum spectra in ultrarelativistic heavy-ion collisions

We study the influence of a temperature-dependent shear viscosity over entropy density ratio $\eta/s$, different shear relaxation times $\tau_\pi$, as well as different initial conditions on the transverse momentum spectra of charged hadrons and identified particles. We investigate the azimuthal flow asymmetries as a function of both collision energy and centrality. The elliptic flow coefficient turns out to be dominated by the hadronic viscosity at RHIC energies. Only at higher collision energies the impact of the viscosity in the QGP phase is visible in the flow asymmetries. Nevertheless, the shear viscosity near the QCD transition region has the largest impact on the collective flow of the system. We also find that the centrality dependence of the elliptic flow is sensitive to the temperature dependence of $\eta/s$.Comment: 13 pages, 20 figure

On the formation of Hubble flow in Little Bangs

A dynamical appearance of scaling solutions in the relativistic hydrodynamics applied to describe ultra-relativistic heavy-ion collisions is studied. We consider the boost-invariant cylindrically symmetric systems and the effects of the phase transition are taken into account by using a temperature dependent sound velocity inferred from the lattice simulations of QCD. We find that the transverse flow acquires the scaling form r/t within the short evolution times, 10 - 15 fm, only if the initial transverse flow originating from the pre-equilibrium collective behavior is present at the initial stage of the hydrodynamic evolution. The amount of such pre-equilibrium flow is correlated with the initial pressure gradient; larger gradients require smaller initial flow. The results of the numerical calculations support the phenomenological parameterizations used in the Blast-Wave, Buda-Lund, and Cracow models of the freeze-out process.Comment: 11 page

v4: A small, but sensitive observable for heavy ion collisions

Higher order Fourier coefficients of the azimuthally dependent single particle spectra resulting from noncentral heavy ion collisions are investigated. For intermediate to large transverse momenta, these anisotropies are expected to become as large as 5 %, and should be clearly measurable. The physics content of these observables is discussed from two different extreme but complementary viewpoints, hydrodynamics and the geometric limit with extreme energy loss.Comment: as published: typos corrected, Fig. 3 slightly improved in numerics and presentatio