Abstract:A new class of accelerating, exact, explicit and simple solutions of relativistic hydrodynamics is presented. Since these new solutions yield a finite rapidity distribution, they lead to an advanced estimate of the initial energy density and life-time of high energy heavy ion collisions. Accelerating solutions are also given for spherical expansions in arbitrary number of spatial dimensions.
“…For λ > 1, we obtain several classes of accelerating solutions, described in Refs. [26][27][28]41]. For example, 1+1 dimensional hydrodynamical solutions are obtained for any real value of λ, for the special EoS of κ = 1.…”
Section: Rapidity Distributions From Hydrodynamicsmentioning
confidence: 99%
“…It is important to observe that in order to describe the majority of experimental data, besides rapidity distributions, pseudorapidity distributions (with pseudorapidity defined as η = 0.5 ln ((p + p z )/(p − p z ))) have to be calculated as well [26][27][28]41]. This can be done by using an average transverse momentum (p t ) value and making a transformation from pseudorapidity η to rapidity y.…”
Section: Rapidity Distributions From Hydrodynamicsmentioning
confidence: 99%
“…The size of this slab is estimated by the radius R of the colliding hadrons or nuclei, them the initial volume is dV = (R 2 π)τ 0 dη 0 , with τ 0 dη S0 being the longitudinal size, while dη S0 is the space-time rapidity width at τ 0 , as detailed in Refs. [26][27][28]41]. The energy contained in this volume is dE = E dN , where dN is the number of particles and E is their average energy near y = 0.…”
Section: Energy Density Estimationmentioning
confidence: 99%
“…In Refs. [26][27][28]41] we performed fits to BRAHMS pseudo-rapidity distributions from Ref. [48], and these fits indicate that corr ≈ 10 GeV/fm 3 in √ s NN = 200 GeV Au+Au collisions at RHIC.…”
Section: Energy Density Estimationmentioning
confidence: 99%
“…Besides these efforts, there is also an interest in models where exact, explicit and parametric solutions of the hydrodynamical equations are used, and where the initial state may be inferred directly from matching the parameters of the solution to the data. Several famous hydrodynamical solutions were developed to describe high energy collisions [22][23][24], but also advanced relativistic solutions were found in the last decade [25][26][27][28][29][30][31][32], when a revival of this sub-field was seen.…”
Abstract:Results from the Relativistic Heavy Ion Colloder (RHIC) and the Large Hadron Collider (LHC) experiments show that in relativistic heavy ion collisions, a new state of matter, a strongly interacting perfect fluid, is created. Accelerating, exact and explicit solutions of relativistic hydrodynamics allow for a simple and natural description of this medium. A finite rapidity distribution arises from these solutions, leading to an advanced estimate of the initial energy density of high energy collisions. These solutions can be utilized to describe various aspects of proton-proton collisions, as originally suggested by Landau. We show that an advanced estimate based on hydrodynamics yields an initial energy density in √ s = 7 and 8 TeV proton-proton (p-p) collisions at the LHC on the same order as the critical energy density from lattice Quantum Chromodynamics (QCD). The advanced estimate yields a corresponding initial temperature that is around the critical temperature from QCD and the Hagedorn temperature. The multiplicity dependence of the estimated initial energy density suggests that in high multiplicity p-p collisions at the LHC, there is large enough initial energy density to create a non-hadronic perfect fluid.
“…For λ > 1, we obtain several classes of accelerating solutions, described in Refs. [26][27][28]41]. For example, 1+1 dimensional hydrodynamical solutions are obtained for any real value of λ, for the special EoS of κ = 1.…”
Section: Rapidity Distributions From Hydrodynamicsmentioning
confidence: 99%
“…It is important to observe that in order to describe the majority of experimental data, besides rapidity distributions, pseudorapidity distributions (with pseudorapidity defined as η = 0.5 ln ((p + p z )/(p − p z ))) have to be calculated as well [26][27][28]41]. This can be done by using an average transverse momentum (p t ) value and making a transformation from pseudorapidity η to rapidity y.…”
Section: Rapidity Distributions From Hydrodynamicsmentioning
confidence: 99%
“…The size of this slab is estimated by the radius R of the colliding hadrons or nuclei, them the initial volume is dV = (R 2 π)τ 0 dη 0 , with τ 0 dη S0 being the longitudinal size, while dη S0 is the space-time rapidity width at τ 0 , as detailed in Refs. [26][27][28]41]. The energy contained in this volume is dE = E dN , where dN is the number of particles and E is their average energy near y = 0.…”
Section: Energy Density Estimationmentioning
confidence: 99%
“…In Refs. [26][27][28]41] we performed fits to BRAHMS pseudo-rapidity distributions from Ref. [48], and these fits indicate that corr ≈ 10 GeV/fm 3 in √ s NN = 200 GeV Au+Au collisions at RHIC.…”
Section: Energy Density Estimationmentioning
confidence: 99%
“…Besides these efforts, there is also an interest in models where exact, explicit and parametric solutions of the hydrodynamical equations are used, and where the initial state may be inferred directly from matching the parameters of the solution to the data. Several famous hydrodynamical solutions were developed to describe high energy collisions [22][23][24], but also advanced relativistic solutions were found in the last decade [25][26][27][28][29][30][31][32], when a revival of this sub-field was seen.…”
Abstract:Results from the Relativistic Heavy Ion Colloder (RHIC) and the Large Hadron Collider (LHC) experiments show that in relativistic heavy ion collisions, a new state of matter, a strongly interacting perfect fluid, is created. Accelerating, exact and explicit solutions of relativistic hydrodynamics allow for a simple and natural description of this medium. A finite rapidity distribution arises from these solutions, leading to an advanced estimate of the initial energy density of high energy collisions. These solutions can be utilized to describe various aspects of proton-proton collisions, as originally suggested by Landau. We show that an advanced estimate based on hydrodynamics yields an initial energy density in √ s = 7 and 8 TeV proton-proton (p-p) collisions at the LHC on the same order as the critical energy density from lattice Quantum Chromodynamics (QCD). The advanced estimate yields a corresponding initial temperature that is around the critical temperature from QCD and the Hagedorn temperature. The multiplicity dependence of the estimated initial energy density suggests that in high multiplicity p-p collisions at the LHC, there is large enough initial energy density to create a non-hadronic perfect fluid.
We review several facets of the hydrodynamic description of the relativistic heavy ion collisions, starting from the historical motivation to the present understandings of the observed collective aspects of experimental data, especially those of the most recent RHIC and LHC results. In this report, we particularly focus on the conceptual questions and the physical foundations of the validity of the hydrodynamic approach itself. We also discuss recent efforts to clarify some of the points in this direction, such as the various forms of derivations of relativistic hydrodynamics together with the limitations intrinsic to the traditional approaches, variational approaches, known analytic solutions for special cases, and several new theoretical developments. Throughout this review, we stress the role of course-graining procedure in the hydrodynamic description and discuss its relation to the physical observables through the analysis of a hydrodynamic mapping of a microscopic transport model. Several questions to be answered to clarify the physics of collective phenomena in the relativistic heavy ion collisions are pointed out.
We review some theoretical challenges in the quest for understanding quark matter. Several contributions to the Strangeness in Quark Matter 2007 Conference indicated problems to be solved and methods to be developed further. This summary gives an individual review of questions held to be important by the author.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.