Mohammad Nopoush

Bulk viscous evolution within anisotropic hydrodynamics

Abstract We derive a system of moment-based dynamical equations that describe the 1+1d space-timeevolution of a cylindrically symmetric massive gas undergoing boost-invariant longitudinal expan-sion. Extending previous work, we introduce an explicit degree of freedom associated with thebulk pressure of the system. The resulting form generalizes the ellipsoidal one-particle distributionfunction appropriate for massless particles to massive particles. Using this generalized form, weobtain a system of partial di erential equations that can be solved numerically. In order to assessthe performance of this scheme, we compare the resulting anisotropic hydrodynamics solutionswith the exact solution of the 0+1d Boltzmann equation in the relaxation time approximation.We nd that the inclusion of the bulk degree of freedom improves agreement between anisotropichydrodynamics and the exact solution for a massive gas. PACS numbers: 12.38.Mh, 24.10.Nz, 25.75.-q, 51.10.+y, 52.27.NyKeywords: Relativistic heavy-ion collisions, Relativistic hydrodynamics, Relativistic transport, Boltzmannequation

(3+1)D Quasiparticle Anisotropic Hydrodynamics for Ultrarelativistic Heavy-Ion Collisions

We present the first comparisons of experimental data with phenomenological results from (3+1)D quasiparticle anisotropic hydrodynamics (aHydroQP). We compare particle spectra, average transverse momentum, and elliptic flow. The dynamical equations used for the hydrodynamic stage utilize aHydroQP, which naturally includes both shear and bulk viscous effects. The (3+1)D aHydroQP evolution obtained is self-consistently converted to hadrons using anisotropic Cooper-Frye freeze-out. Hadron production and decays are modeled using a customized version of therminator 2. In this first study, we utilized smooth Glauber-type initial conditions and a single effective freeze-out temperature T_{FO}=130  MeV with all hadronic species in full chemical equilibrium. With this rather simple setup, we find a very good description of many heavy-ion observables.

Leading-order anisotropic hydrodynamics for central collisions

We use leading-order anisotropic hydrodynamics to study an azimuthally-symmetric boost-invariant quark-gluon plasma. We impose a realistic lattice-based equation of state and perform self-consistent anisotropic freeze-out to hadronic degrees of freedom. We then compare our results for the full spatiotemporal evolution of the quark-gluon plasma and its subsequent freeze-out to results obtained using 1+1d Israel-Stewart second-order viscous hydrodynamics. We find that for small shear viscosities, 4 pi eta/s ~ 1, the two methods agree well for nucleus-nucleus collisions, however, for large shear viscosity to entropy density ratios or proton-nucleus collisions we find important corrections to the Israel-Stewart results for the final particle spectra and the total number of charged particles. Finally, we demonstrate that the total number of charged particles produced is a monotonically increasing function of 4 pi eta/s in Israel-Stewart viscous hydrodynamics whereas in anisotropic hydrodynamics it has a maximum at 4 pi eta/s ~ 10. For all 4 pi eta/s > 0, we find that for Pb-Pb collisions Israel-Stewart viscous hydrodynamics predicts more dissipative particle production than anisotropic hydrodynamics.

Quasiparticle anisotropic hydrodynamics for central collisions

We use quasiparticle anisotropic hydrodynamics to study an azimuthally-symmetric boost-invariant quark-gluon plasma including the effects of both shear and bulk viscosities. In quasiparticle anisotropic hydrodynamics, a single finite-temperature quasiparticle mass is introduced and fit to the lattice data in order to implement a realistic equation of state. We compare results obtained using the quasiparticle method with the standard method of imposing the equation of state in anisotropic hydrodynamics and viscous hydrodynamics. Using these three methods, we extract the primordial particle spectra, total number of charged particles, and average transverse momentum for various values of the shear viscosity to entropy density ratio eta/s. We find that the three methods agree well for small shear viscosity to entropy density ratio, eta/s, but differ at large eta/s. We find, in particular, that when using standard viscous hydrodynamics, the bulk-viscous correction can drive the primordial particle spectra negative at large p_T which is clearly unphysical. Such a behavior is not seen in either anisotropic hydrodynamics approach, irrespective of the value of eta/s.

Anisotropic hydrodynamic modeling of 2.76 TeV Pb-Pb collisions

We compare phenomenological results from 3+1d quasiparticle anisotropic hydrodynamics (aHydroQP) with experimental data collected in LHC 2.76 TeV Pb-Pb collisions. In particular, we present comparisons of particle spectra, average transverse momentum, elliptic flow, and HBT radii. The aHydroQP model relies on the introduction of a single temperature-dependent quasiparticle mass which is fit to lattice QCD data. By taking moments of the resulting Boltzmann equation, we obtain the dynamical equations used in the hydrodynamic stage which include the effects of both shear and bulk viscosities. At freeze-out, we use anisotropic Cooper-Frye freeze-out performed on a fixed-energy-density hypersurface to convert to hadrons. To model the production and decays of the hadrons we use THERMINATOR 2 which is customized to sample from ellipsoidal momentum-space distribution functions. Using smooth Glauber initial conditions, we find very good agreement with many heavy-ion collision observables.

Anisotropic hydrodynamics for conformal Gubser flow

Abstract In this proceedings contribution, we review the exact solution of the anisotropic hydrodynamics equations for a system subject to Gubser flow. For this purpose, we use the leading-order anisotropic hydrodynamics equations which assume that the distribution function is ellipsoidally symmetric in local-rest-frame momentum. We then prove that the SO(3)q symmetry in de Sitter space constrains the anisotropy tensor to be of spheroidal form with only one independent anisotropy parameter remaining. As a consequence, the exact solution reduces to the problem of solving two coupled non-linear differential equations. We show that, in the limit that the relaxation time goes to zero, one obtains Gubsers ideal hydrodynamic solution and, in the limit that the relaxation time goes to infinity, one obtains the exact free streaming solution obtained originally by Denicol et al. For finite relaxation time, we solve the equations numerically and compare to the exact solution of the relaxation-time-approximation Boltzmann equation subject to Gubser flow. Using this as our standard, we find that anisotropic hydrodynamics describes the spatio-temporal evolution of the system better than all currently known dissipative hydrodynamics approaches.

Exact solutions of the Boltzmann equation and optimized hydrodynamic approaches for relativistic heavy-ion collisions

Several recent results are reported from work aiming to improve the quantitative precision of relativistic viscous fluid dynamics for relativistic heavy-ion collisions. The dense matter created in such collisions expands in a highly anisotropic manner. Due to viscous effects this also renders the local momentum distribution anisotropic. Optimized hydrodynamic approaches account for these anisotropies already at leading order in a gradient expansion. Recently discovered exact solutions of the relativistic Boltzmann equation in anisotropically expanding systems provide a powerful testbed for such improved hydrodynamic approximations. We present the latest status of our quest for a formulation of relativistic viscous fluid dynamics that is optimized for applications to relativistic heavy-ion collisions.

The static hard-loop gluon propagator to all orders in anisotropy

A bstractWe calculate the (semi-)static hard-loop self-energy and propagator using the Keldysh formalism in a momentum-space anisotropic quark-gluon plasma. The static retarded, advanced, and Feynman (symmetric) self-energies and propagators are calculated to all orders in the momentum-space anisotropy parameter ξ. For the retarded and advanced self-energies/propagators, we present a concise derivation and comparison with previously-obtained results and extend the calculation of the self-energies to next-to-leading order in the gluon energy, ω. For the Feynman self-energy/propagator, we present new results which are accurate to all orders in ξ. We compare our exact results with prior expressions for the Feynman self-energy/propagator which were obtained using Taylor-expansions around an isotropic state. We show that, unlike the Taylor-expanded results, the all-orders expression for the Feynman propagator is free from infrared singularities. Finally, we discuss the application of our results to the calculation of the imaginary-part of the heavy-quark potential in an anisotropic quark-gluon plasma.

Relativistic anisotropic hydrodynamics

In this paper we review recent progress in relativistic anisotropic hydrodynamics. We begin with a pedagogical introduction to the topic which takes into account the advances in our understanding of this topic since its inception. We consider both conformal and non-conformal systems and demonstrate how one can implement a realistic equation of state using a quasiparticle approach. We then consider the inclusion of non-spheroidal (non-ellipsoidal) corrections to leading-order anisotropic hydrodynamics and present the findings of the resulting second-order viscous anisotropic hydrodynamics framework. We compare the results obtained in both the conformal and non-conformal cases with exact solutions to the Boltzmann equation and demonstrate that, in all known cases, anisotropic hydrodynamics best reproduces the exact solutions. Based on this success, we then discuss the phenomenological application of anisotropic hydrodynamics. Along these lines, we review techniques which can be used to convert a momentum-space anisotropic fluid into hadronic degrees of freedom by generalizing the original idea of Cooper-Frye freeze-out to momentum-space anisotropic systems. And, finally, we present phenomenological results of 3+1d quasiparticle anisotropic hydrodynamic simulations and compare them to experimental data produced in 2.76 TeV Pb-Pb collisions at the LHC. Our results indicate that anisotropic hydrodynamics provides a promising framework for describing the dynamics of the momentum-space anisotropic QGP created in heavy-ion collisions.

Quark self-energy in an ellipsoidally anisotropic quark-gluon plasma

We calculate the quark self-energy in a quark-gluon plasma that possesses an ellipsoidal momentum-space anisotropy in the local rest frame. By introducing additional transverse momentum anisotropy parameters into the parton distribution functions, we generalize previous results which were obtained for the case of a spheroidal anisotropy. Our results demonstrate that the presence of anisotropies in the transverse directions affects the real and imaginary parts of quark self-energy and, consequently, the self-energy depends on both the polar and azimuthal angles in the local rest frame of the matter. Our results for the quark self-energy set the stage for the calculation of the effects of ellipsoidal momentum-space anisotropy on quark-gluon plasma photon spectra and collective flow.