Temperature dependence of η/s of strongly interacting matter: Effects of the equation of state and the parametric form of (η/s)(T)

We investigate the temperature dependence of the shear viscosity to entropy density ratio $\ensuremath{\eta}/s$ using a piecewise linear parametrization. To determine the optimal values of the parameters and the associated uncertainties, we perform a global Bayesian model-to-data comparison on $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{{s}_{\mathrm{NN}}}=200$ GeV and $\mathrm{Pb}+\mathrm{Pb}$ collisions at 2.76 TeV and 5.02 TeV, using a $2+1\mathrm{D}$ hydrodynamical model with the Eskola-Kajantie-Ruuskanen-Tuominen (EKRT) initial state. We provide three new parametrizations of the equation of state (EoS) based on contemporary lattice results and hadron resonance gas, and use them and t…

Transition from ideal to viscous Mach cones in a kinetic transport approach

Using a microscopic transport model we investigate the evolution of conical structures originating from the supersonic projectile moving through the hot matter of ultrarelativistic particles. Using different scenarios for the interaction between projectile and matter, and different transport properties of the matter, we study the formation and structure of Mach cones. Especially, a dependence of the Mach cone angle on the details and rate of the energy deposition from projectile to the matter is investigated. Furthermore, the two-particle correlations extracted from the numerical calculations are compared to an analytical approximation. We find that the propagation of a high energetic parti…

Pinning down QCD-matter shear viscosity in A + A collisions via EbyE fluctuations using pQCD + saturation + hydrodynamics

We compute the initial energy densities produced in ultrarelativistic heavy-ion collisions from NLO perturbative QCD using a saturation conjecture to control soft particle production, and describe the subsequent space-time evolution of the system with hydrodynamics, event by event. The resulting centrality dependence of the low-$p_T$ observables from this pQCD + saturation + hydro ("EKRT") framework are then compared simultaneously to the LHC and RHIC measurements. With such an analysis we can test the initial state calculation, and constrain the temperature dependence of the shear viscosity-to-entropy ratio $\eta/s$ of QCD matter. Using these constraints from the current RHIC and LHC measu…

Transverse Spectra of Hadrons in Central $AA$ Collisions at RHIC and LHC from pQCD+Saturation+Hydrodynamics and from pQCD+Energy Losses

We study the transverse spectra of hadrons in nearly central $AA$ collisions at RHIC and LHC in a broad transverse momentum range Low-$p_T$ spectra are calculated by using boost-invariant hydrodynamics with initial energy and net-baryon densities from the EKRT pQCD+saturation model. High-$p_T$ spectra are obtained from pQCD jet calculation including the energy loss of the parton in the matter prior to its fragmentation to final hadrons.

Elliptic flow from event-by-event hydrodynamics with fluctuating initial state

We develop an event-by-event ideal hydrodynamical framework where initial state density fluctuations are present and where we use a similar flow-analysis method as in the experiments to make a one-to-one $v_2$ comparison with the measured data. Our studies also show that the participant plane is quite a good approximation for the event plane.

Event-by-event fluctuations in a perturbative QCD + saturation + hydrodynamics model: Determining QCD matter shear viscosity in ultrarelativistic heavy-ion collisions

We introduce an event-by-event perturbative-QCD + saturation + hydro (“EKRT”) framework for ultrarelativistic heavy-ion collisions, where we compute the produced fluctuating QCD-matter energy densities from next-to-leading-order perturbative QCD using a saturation conjecture to control soft-particle production and describe the space-time evolution of the QCD matter with dissipative fluid dynamics, event by event. We perform a simultaneous comparison of the centrality dependence of hadronic multiplicities, transverse momentum spectra, and flow coefficients of the azimuth-angle asymmetries against the LHC and RHIC measurements. We compare also the computed event-by-event probability distribut…

Latest predictions from the EbyE NLO EKRT model

We present the latest results from the NLO pQCD + saturation + viscous hydrodynamics (EbyE NLO EKRT) model. The parameters in the EKRT saturation model are fixed by the charged hadron multiplicity in the 0-5 \% 2.76 TeV Pb+Pb collisions. The $\sqrt{s}$, $A$ and centrality dependence of the initial particle production follows then from the QCD dynamics of the model. This allows us to predict the $\sqrt{s}$ and $A$ dependence of the particle production. We show that our results are in an excellent agreement with the low-$p_T$ data from 2.76 TeV and 5.02 TeV Pb+Pb collisions at the LHC as well as with the data from the 200 GeV Au+Au collisions at RHIC. In particular, we study the centrality de…

Correlated gluonic hot spots meet symmetric cumulants data at LHC energies

We present a systematic study on the influence of spatial correlations between the proton constituents, in our case gluonic hot spots, their size and their number on the symmetric cumulant SC(2, 3), at the eccentricity level, within a Monte Carlo Glauber framework [1]. When modeling the proton as composed by 3 gluonic hot spots, the most common assumption in the literature, we find that the inclusion of spatial correlations is indispensable to reproduce the negative sign of SC(2, 3) in the highest centrality bins as dictated by data. Further, the subtle interplay between the different scales of the problem is discussed. To conclude, the possibility of feeding a 2+1D viscous hydrodynamic sim…

Event-by-event distributions of azimuthal asymmetries in ultrarelativistic heavy-ion collisions

Relativistic dissipative fluid dynamics is a common tool to describe the space-time evolution of the strongly interacting matter created in ultrarelativistic heavy-ion collisions. For a proper comparison to experimental data, fluid-dynamical calculations have to be performed on an event-by-event basis. Therefore, fluid dynamics should be able to reproduce, not only the event-averaged momentum anisotropies, $$, but also their distributions. In this paper, we investigate the event-by-event distributions of the initial-state and momentum anisotropies $\epsilon_n$ and $v_n$, and their correlations. We demonstrate that the event-by-event distributions of relative $v_n$ fluctuations are almost eq…

Exploring the applicability of dissipative fluid dynamics to small systems by comparison to the Boltzmann equation

[Background] Experimental data from heavy-ion experiments at RHIC-BNL and LHC-CERN are quantitatively described using relativistic fluid dynamics. Even p+A and p+p collisions show signs of collective behavior describable in the same manner. Nevertheless, small system sizes and large gradients strain the limits of applicability of fluid-dynamical methods. [Purpose] The range of applicability of fluid dynamics for the description of the collective behavior, and in particular of the elliptic flow, of small systems needs to be explored. [Method] Results of relativistic fluid-dynamical simulations are compared with solutions of the Boltzmann equation in a longitudinally boost-invariant picture. …

Predictions for multiplicities and flow harmonics in 5.44 TeV Xe+Xe collisions at the CERN Large Hadron Collider

We present the next-to-leading-order event-by-event EKRT model predictions for the centrality dependence of the charged hadron multiplicity in the pseudorapidity interval $|\eta|\le 0.5$, and for the centrality dependence of the charged hadron flow harmonics $v_n\{2\}$ obtained from 2-particle cumulants, in $\sqrt{s_{NN}}=5.44$ TeV Xe+Xe collisions at the CERN Large Hadron Collider. Our prediction for the 0-5 \% central charged multiplicity is $dN_{\rm ch}/d\eta =1218\pm 46$. We also predict $v_n\{2\}$ in Xe+Xe collisions to increase more slowly from central towards peripheral collisions than those in a Pb+Pb system. We find that at $10 \dots 50$\% centralities $v_2\{2\}$ is smaller and $v_…

Resistive dissipative magnetohydrodynamics from the Boltzmann-Vlasov equation

We derive the equations of motion of relativistic, resistive, second-order dissipative magnetohydrodynamics from the Boltzmann-Vlasov equation using the method of moments. We thus extend our previous work [Phys. Rev. D 98, 076009 (2018)], where we only considered the non-resistive limit, to the case of finite electric conductivity. This requires keeping terms proportional to the electric field $E^\mu$ in the equations of motions and leads to new transport coefficients due to the coupling of the electric field to dissipative quantities. We also show that the Navier-Stokes limit of the charge-diffusion current corresponds to Ohm's law, while the coefficients of electrical conductivity and cha…

Extracting qˆ in event-by-event hydrodynamics and the centrality/energy puzzle

In our analysis, we combine event-by-event hydrodynamics, within the EKRT formulation, with jet quenching -ASW Quenching Weights- to obtain high- for charged particles at RHIC and LHC energies for different centralities. By defining a K-factor that quantifies the departure of from an ideal estimate, , we fit the single-inclusive experimental data for charged particles. This K-factor is larger at RHIC than at the LHC but, surprisingly, it is almost independent of the centrality of the collision. peerReviewed

Temperature dependence of η / s of strongly interacting matter: Effects of the equation of state and the parametric form of ( η / s ) ( T )

We investigate the temperature dependence of the shear viscosity to entropy density ratio η/s using a piecewise linear parametrization. To determine the optimal values of the parameters and the associated uncertainties, we perform a global Bayesian model-to-data comparison on Au+Au collisions at √sNN=200 GeV and Pb+Pb collisions at 2.76 TeV and 5.02 TeV, using a 2+1D hydrodynamical model with the Eskola-Kajantie-Ruuskanen-Tuominen (EKRT) initial state. We provide three new parametrizations of the equation of state (EoS) based on contemporary lattice results and hadron resonance gas, and use them and the widely used s95p parametrization to explore the uncertainty in the analysis due to the c…

Constraints from $v_2$ fluctuations for the initial state geometry of heavy-ion collisions

The ability to accurately compute the series of coefficients $v_n$ characterizing the momentum space anisotropies of particle production in ultrarelativistic heavy ion collisions as a function of centrality is widely regarded as a triumph of fluid dynamics as description of the bulk matter evolution. A key ingredient to fluid dynamical modeling is however the initial spatial distribution of matter as created by a yet not completely understood equilibration process. A measurement directly sensitive to this initial state geometry is therefore of high value for constraining models of pre-equilibrium dynamics. Recently, it has been shown that such a measurement is indeed possible in terms of th…

Derivation of transient relativistic fluid dynamics from the Boltzmann equation

In this work we present a general derivation of relativistic fluid dynamics from the Boltzmann equation using the method of moments. The main difference between our approach and the traditional 14-moment approximation is that we will not close the fluid-dynamical equations of motion by truncating the expansion of the distribution function. Instead, we keep all terms in the moment expansion. The reduction of the degrees of freedom is done by identifying the microscopic time scales of the Boltzmann equation and considering only the slowest ones. In addition, the equations of motion for the dissipative quantities are truncated according to a systematic power-counting scheme in Knudsen and inve…

Diffusion processes involving multiple conserved charges: a first study from kinetic theory and implications to the fluid-dynamical modeling of heavy ion collisions

The bulk nuclear matter produced in heavy ion collisions carries a multitude of conserved quantum numbers: electric charge, baryon number, and strangeness. Therefore, the diffusion processes associated to these conserved charges cannot occur independently and must be described in terms of a set of coupled diffusion equations. This physics is implemented by replacing the traditional diffusion coefficients for each conserved charge by a diffusion coefficient matrix, which quantifies the coupling between the conserved quantum numbers. The diagonal coefficients of this matrix are the usual charge diffusion coefficients, while the off-diagonal entries describe the diffusive coupling of the charg…

Event-by-event fluctuations in a perturbative QCD plus saturation plus hydrodynamics model : Determining QCD matter shear viscosity in ultrarelativistic heavy-ion collisions

We introduce an event-by-event perturbative-QCD + saturation + hydro ("EKRT") framework for ultrarelativistic heavy-ion collisions, where we compute the produced fluctuating QCD-matter energy densities from next-to-leading-order perturbative QCD using a saturation conjecture to control soft-particle production and describe the space-time evolution of the QCD matter with dissipative fluid dynamics, event by event. We perform a simultaneous comparison of the centrality dependence of hadronic multiplicities, transverse momentum spectra, and flow coefficients of the azimuth-angle asymmetries against the LHC and RHIC measurements. We compare also the computed event-by-event probability distribut…

Jet quenching as a probe of the initial stages in heavy-ion collisions

Jet quenching provides a very flexible variety of observables which are sensitive to different energy- and time-scales of the strongly interacting matter created in heavy-ion collisions. Exploiting this versatility would make jet quenching an excellent chronometer of the yoctosecond structure of the evolution process. Here we show, for the first time, that a combination of jet quenching observables is sensitive to the initial stages of heavy-ion collisions, when the approach to local thermal equilibrium is expected to happen. Specifically, we find that in order to reproduce at the same time the inclusive particle production suppression, $R_{AA}$, and the high-$p_T$ azimuthal asymmetries, $v…

Multicomponent relativistic dissipative fluid dynamics from the Boltzmann equation

We derive multicomponent relativistic second-order dissipative fluid dynamics from the Boltzmann equations for a reactive mixture of $N_{\text{spec}}$ particle species with $N_q$ intrinsic quantum numbers (e.g. electric charge, baryon number, and strangeness) using the method of moments. We obtain the continuity equations for multiple conserved charges as well as the conservation equations for the total energy and momentum in the single-fluid approximation. These $4+N_q$ conservation laws are closed by deriving the second-order equations of motion for the dissipative quantities in the $(10+4N_q)$-moment approximation. The resulting fluid-dynamical equations are formally similar to those of …

Transverse spectra of hadrons at RHIC

We present results on spectra of pions, kaons and (anti)protons from a study of heavy ion collisions using the perturbative QCD + saturation model to calculate the production of initial (transverse) energy and baryon number followed by a hydrodynamic description of the expansion of produced matter. In particular, we study how the hadron spectra and multiplicities depend on the decoupling temperature $\Tdec$ when the low temperature phase contains all hadrons and and hadron resonances with mass below 2 GeV. We show that the spectra and multiplicities of pions, kaons and (anti)protons measured at RHIC in central Au+Au collisions with $\sqrt s=130$ GeV can be obtained with a single decoupling …

Pinning down QCD-matter shear viscosity in ultrarelativistic heavy-ion collisions via EbyE fluctuations using pQCD + saturation + hydrodynamics

We introduce an event-by-event pQCD + saturation + hydro ("EKRT") framework for high-energy heavy-ion collisions, where we compute the produced fluctuating QCD-matter energy densities from next-to-leading order (NLO) perturbative QCD (pQCD) using saturation to control soft particle production, and describe the space-time evolution of the QCD matter with viscous hydrodynamics, event by event (EbyE). We compare the computed centrality dependence of hadronic multiplicities, p_T spectra and flow coefficients v_n against LHC and RHIC data. We compare also the computed EbyE probability distributions of relative fluctuations of v_n, as well as correlations of 2 and 3 event-plane angles, with LHC d…

Predictions for low-pTand high-pThadron spectra in nearly central Pb+Pb collisions atsNN=5.5TeV tested atsNN=130and 200 GeV

We study the hadron spectra in nearly central $A+A$ collisions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) in a broad transverse momentum range. We cover the low-${p}_{T}$ spectra using longitudinally boost-invariant hydrodynamics with initial energy and net-baryon number densities from the perturbative QCD (pQCD)+saturation model. Buildup of the transverse flow and sensitivity of the spectra to a single decoupling temperature ${T}_{\mathrm{dec}}$ are studied. Comparison with RHIC data at $\sqrt{{s}_{\mathit{NN}}}=130$ and 200 GeV suggests a rather high value ${T}_{\mathrm{dec}}=150$ MeV. The high-${p}_{T}$ spectra are computed using factorized pQCD cro…

Fluid dynamics with saturated minijet initial conditions in ultrarelativistic heavy-ion collisions

Using next-to-leading order perturbative QCD and a conjecture of saturation to suppress the production of low-energy partons, we calculate the initial energy densities and formation times for the dissipative fluid dynamical evolution of the quark-gluon plasma produced in ultrarelativistic heavy-ion collisions. We identify the framework uncertainties and demonstrate the predictive power of the approach by a good global agreement with the measured centrality dependence of charged particle multiplicities, transverse momentum spectra and elliptic flow simultaneously for the Pb+Pb collisions at the LHC and Au+Au at RHIC. In particular, the shear viscosity in the different phases of QCD matter is…

Corrigendum to “Transition from ideal to viscous Mach cones in a kinetic transport approach” [Phys. Lett. B 710 (4–5) (2012) 641]

Longitudinal dynamics of multiple conserved charges

Abstract It is the goal of the RHIC BES program and the future FAIR and NICA facilities to produce compressed baryonic matter. In experiments such as these, strong gradients in baryon density are expected, and therefore the diffusion of baryon number could play a major role in the description of the fireball. The constituents of the produced matter carry a multitude of conserved charges, namely the baryon number, strangeness and electric charge, so that the diffusion currents of conserved charge couple with each other. Therefore, baryon density gradients in the above-mentioned high-density collision experiments will generate equalizing currents in all conserved charges. In common fluid dyna…

Event-by-event hydrodynamics and elliptic flow from fluctuating initial states

We develop a framework for event-by-event ideal hydrodynamics to study the differential elliptic flow which is measured at different centralities in Au+Au collisions at Relativistic Heavy Ion Collider (RHIC). Fluctuating initial energy density profiles, which here are the event-by-event analogues of the eWN profiles, are created using a Monte Carlo Glauber model. Using the same event plane method for obtaining $v_2$ as in the data analysis, we can reproduce both the measured centrality dependence and the $p_T$ shape of charged-particle elliptic flow up to $p_T\sim2$~GeV. We also consider the relation of elliptic flow to the initial state eccentricity using different reference planes, and di…

Influence of temperature-dependent shear viscosity on elliptic flow at backward and forward rapidities in ultrarelativistic heavy-ion collisions

We explore the influence of a temperature-dependent shear viscosity over entropy density ratio $\eta/s$ on the azimuthal anisotropies v_2 and v_4 of hadrons at various rapidities. We find that in Au+Au collisions at full RHIC energy, $\sqrt{s_{NN}}=200$ GeV, the flow anisotropies are dominated by hadronic viscosity at all rapidities, whereas in Pb+Pb collisions at the LHC energy, $\sqrt{s_{NN}}=2760$ GeV, the flow coefficients are affected by the viscosity both in the plasma and hadronic phases at midrapidity, but the further away from midrapidity, the more dominant the hadronic viscosity is. We find that the centrality and rapidity dependence of the elliptic and quadrangular flows can help…

Elliptic flow in nuclear collisions at ultrarelativistic energies available at the CERN Large Hadron Collider

We use perfect-fluid hydrodynamical model to predict the elliptic flow coefficients in $\mathrm{Pb}+\mathrm{Pb}$ collisions at the Large Hadron Collider (LHC). The initial state for the hydrodynamical calculation for central $A+A$ collisions is obtained from the perturbative QCD $+$ saturation model. The centrality dependence of the initial state is modeled by the optical Glauber model. We show that the baseline results obtained from the framework are in good agreement with the data from the Relativistic Heavy Ion Collider and show predictions for the ${p}_{T}$ spectra and elliptic flow of pions in $\mathrm{Pb}+\mathrm{Pb}$ collisions at the LHC. Also mass and multiplicity effects are discu…

Fluid dynamical response to initial state fluctuations

Abstract We investigate a fluid dynamical response to the fluctuations and geometry of the initial state density profiles in ultrarelativistic heavy ion collisions.

Next-to-leading order improved perturbative QCD + saturation + hydrodynamics model for A + A collisions

We calculate initial conditions for the hydrodynamical evolution in ultrarelativistic heavy-ion collisions at the LHC and RHIC in an improved next-to-leading order perturbative QCD + saturation framework. Using viscous relativistic hydrodynamics, we show that we obtain a good simultaneous description of the centrality dependence of charged particle multiplicities, transverse momentum spectra and elliptic flow at the LHC and at RHIC. In particular, we discuss how the temperature dependence of the shear viscosity is constrained by these data.

Relative importance of second-order terms in relativistic dissipative fluid dynamics

[Introduction] In Denicol et al. [Phys. Rev. D 85 , 114047 (2012)], the equations of motion of relativistic dissipative fluid dynamics were derived from the relativistic Boltzmann equation. These equations contain a multitude of terms of second order in the Knudsen number, in the inverse Reynolds number, or their product. Terms of second order in the Knudsen number give rise to nonhyperbolic (and thus acausal) behavior and must be neglected in (numerical) solutions of relativistic dissipative fluid dynamics. The coefficients of the terms which are of the order of the product of Knudsen and inverse Reynolds numbers have been explicitly computed in the above reference, in the limit of a massl…

Temperature dependence of η/s : uncertainties from the equation of state

We perform a global model-to-data comparison on Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV and Pb+Pb collisions at $2.76$ TeV and $5.02$ TeV, using a 2+1D hydrodynamics model with the EKRT initial state and a shear viscosity over entropy density ratio $(\eta/s)(T)$ with a linear $T$ dependence. To quantify the amount of uncertainty due to the choice of the equation of state (EoS), we compare analysis results based on four different EoSs: the well known $s95p$ parametrisation, an updated parametrisation based on the same list of particles in hadron resonance gas, but using recent lattice results for the partonic part of the EoS, and two new parametrisations based on the Particle Data Group …

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 t…

Temperature dependence of eta/s of strongly interacting matter : Effects of the equation of state and the parametric form of (eta/s)(T)

We investigate the temperature dependence of the shear viscosity to entropy density ratio $\eta/s$ using a piecewise linear parametrization. To determine the optimal values of the parameters and the associated uncertainties, we perform a global Bayesian model-to-data comparison on Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV and Pb+Pb collisions at $2.76$ TeV and $5.02$ TeV, using a 2+1D hydrodynamical model with the EKRT initial state. We provide three new parametrizations of the equation of state (EoS) based on contemporary lattice results and hadron resonance gas, and use them and the widely used $s95p$ parametrization to explore the uncertainty in the analysis due to the choice of the eq…

Solving the heat-flow problem with transient relativistic fluid dynamics

Israel-Stewart theory is a causal, stable formulation of relativistic dissipative fluid dynamics. This theory has been shown to give a decent description of the dynamical behavior of a relativistic fluid in cases where shear stress becomes important. In principle, it should also be applicable to situations where heat flow becomes important. However, it has been shown that there are cases where Israel-Stewart theory cannot reproduce phenomena associated with heat flow. In this paper, we derive a relativistic dissipative fluid-dynamical theory from kinetic theory which provides a good description of all dissipative phenomena, including heat flow. We explicitly demonstrate this by comparing th…

Dependence of hadron spectra on decoupling temperature and resonance contributions

Using equilibrium hydrodynamics with initial conditions for the energy and net baryon number densities from the perturbative QCD + saturation model, a good simultaneous description of the measured pion, kaon and (anti)proton spectra in central Au+Au collisions at $\sqrt s=130 A$GeV is found with a single decoupling temperature $\Tdec=150...160$ MeV. The interplay between the resonance content of the EoS and the development of the transverse flow leads to inverse slopes and $$ of hadrons which increase with decreasing $\Tdec$. The origin of this result is discussed.

From minijet saturation to global observables in A + A collisions at the LHC and RHIC

We review the recent results from the computation of saturated next-to-leading order perturbative QCD minijet intial conditions combined with viscous hydrodynamical evolution of ultrarelativistic heavy-ion collisions at the LHC and RHIC. Comparison with experimental data is shown.

Predictions for 5.023 TeV Pb + Pb collisions at the CERN Large Hadron Collider

We compute predictions for various low-transverse-momentum bulk observables in √sNN = 5.023 TeV Pb+Pb collisions at the CERN Large Hadron Collider (LHC) from the event-by-event next-to-leading-order perturbative-QCD + saturation + viscous hydrodynamics (“EKRT”) model. In particular, we consider the centrality dependence of charged hadron multiplicity, flow coefficients of the azimuth-angle asymmetries, and correlations of event-plane angles. The centrality dependencies of the studied observables are predicted to be very similar to those at 2.76 TeV, and the magnitudes of the flow coefficients and event-plane angle correlations are predicted to be close to those at 2.76 TeV. The flow coeffic…

Corrigendum to “Transition from ideal to viscous Mach cones in a kinetic transport approach”

Extractingqˆin event-by-event hydrodynamics and the centrality/energy puzzle

Abstract In our analysis, we combine event-by-event hydrodynamics, within the EKRT formulation, with jet quenching -ASW Quenching Weights- to obtain high- p T R AA for charged particles at RHIC and LHC energies for different centralities. By defining a K -factor that quantifies the departure of q ˆ from an ideal estimate, K = q ˆ / ( 2 ϵ 3 / 4 ) , we fit the single-inclusive experimental data for charged particles. This K -factor is larger at RHIC than at the LHC but, surprisingly, it is almost independent of the centrality of the collision.

Nonresistive dissipative magnetohydrodynamics from the Boltzmann equation in the 14-moment approximation

We derive the equations of motion of relativistic, non-resistive, second-order dissipative magnetohydrodynamics from the Boltzmann equation using the method of moments. We assume the fluid to be composed of a single type of point-like particles with vanishing dipole moment or spin, so that the fluid has vanishing magnetization and polarization. In a first approximation, we assume the fluid to be non-resistive, which allows to express the electric field in terms of the magnetic field. We derive equations of motion for the irreducible moments of the deviation of the single-particle distribution function from local thermodynamical equilibrium. We analyze the Navier-Stokes limit of these equati…

Relative importance of second-order terms in relativistic dissipative fluid dynamics

In Denicol et al., Phys. Rev. D 85, 114047 (2012), the equations of motion of relativistic dissipative fluid dynamics were derived from the relativistic Boltzmann equation. These equations contain a multitude of terms of second order in Knudsen number, in inverse Reynolds number, or their product. Terms of second order in Knudsen number give rise to non-hyperbolic (and thus acausal) behavior and must be neglected in (numerical) solutions of relativistic dissipative fluid dynamics. The coefficients of the terms which are of the order of the product of Knudsen and inverse Reynolds numbers have been explicitly computed in the above reference, in the limit of a massless Boltzmann gas. Terms of …

Constraining energy loss from high-pT azimuthal asymmetries

The nuclear modification factor $R_{\rm AA}$ has been satisfactorily described by various jet quenching models. Nonetheless, all these formalisms, until very recently, underpredicted the high-$p_{\rm T}$ (> 10 GeV) elliptic flow $v_2$. We find that the simultaneous description of these observables requires to strongly suppress the quenching for the first $\sim 0.6$ fm after the collision. This shows the potential of jet quenching observables to constrain the dynamics of the initial stages of the evolution.

Derivation of transient relativistic fluid dynamics from the Boltzmann equation for a multi-component system

We derive the non-equilibrium single-particle momentum distribution function of a hadron resonance gas. We then study the effects that this newly derived expression can have in the freeze-out description of fluid-dynamical models of heavy ion collisions and compare it with the method traditionally employed, the 14-moment approximation.

Extracting $\hat{q}$ in event-by-event hydrodynamics and the centrality/energy puzzle

In our analysis, we combine event-by-event hydrodynamics, within the EKRT formulation, with jet quenching -ASW Quenching Weights- to obtain high-$p_T$ $R_{\rm AA}$ for charged particles at RHIC and LHC energies for different centralities. By defining a $K$-factor that quantifies the departure of $\hat{q}$ from an ideal estimate, $K = \hat{q}/(2\epsilon^{3/4})$, we fit the single-inclusive experimental data for charged particles. This $K$-factor is larger at RHIC than at the LHC but, surprisingly, it is almost independent of the centrality of the collision.

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Latest results from the EbyE NLO EKRT model

We review the results from the event-by-event next-to-leading order perturbative QCD + saturation + viscous hydrodynamics (EbyE NLO EKRT) model. With a simultaneous analysis of LHC and RHIC bulk observables we systematically constrain the QCD matter shear viscosity-to-entropy ratio eta/s(T), and test the initial state computation. In particular, we study the centrality dependences of hadronic multiplicities, pT spectra, flow coefficients, relative elliptic flow fluctuations, and various flow-correlations in 2.76 and 5.02 TeV Pb+Pb collisions at the LHC and 200 GeV Au+Au collisions at RHIC. Overall, our results match remarkably well with the LHC and RHIC measurements, and predictions for the…

Transition From Ideal To Viscous Mach Cones In A Partonic Transport Model

Using a partonic transport model we investigate the evolution of conical structures in ultrarelativistic matter. Using two different source terms and varying the transport properties of the matter we study the formation of Mach Cones. Furthermore, in an additional study we extract the two-particle correlations from the numerical calculations and compare them to an analytical approximation. The influence of the viscosity to the shape of Mach Cones and the corresponding two-particle correlations is studied by adjusting the cross section of the medium. peerReviewed

Hydrodynamical flow and hadron spectra in ultrarelativistic heavy ion collisions at RHIC and the LHC

Collective dynamics in relativistic nuclear collisions

Abstract I will review the current status of describing spacetime evolution of the relativistic nuclear collisions with fluid dynamics, and of determining the transport coefficients of strongly interacting matter. The fluid dynamical models suggest that shear viscosity to entropy density ratio of the matter is small. However, there are still considerable challenges in determining the transport coefficients, and especially their temperature dependence is still poorly constrained.

Elliptic flow from event-by-event hydrodynamics

We present an event-by-event hydrodynamical framework which takes into account the initial density fluctuations arising from a Monte Carlo Glauber model. The elliptic flow is calculated with the event plane method and a one-to-one comparison with the measured event plane $v_2$ is made. Both the centrality- and $p_T$-dependence of the $v_2$ are remarkably well reproduced. We also find that the participant plane is a quite good approximation for the event plane.

Zeroing in on the initial state — tomography using bulk, jets and photons

One of the unsolved problems in the current 'standard model' of heavy ion physics is the apparent rapid thermalization of QCD matter in the pre-equilibrium stage. While it is challenging to probe this mechanism directly, there are now several observables available which allow tomographic imaging of the initial state geometry, which is expected to carry remnant information of the equilibration mechanism. On the fluid dynamics side, scaled fluctuations in the momentum space anisotropy parameters v_n image the initial eccentricity fluctuations epsilon_n almost directly with only a weak dependence on the details of the fluid dynamical evolution. From a different direction, due to the strong non…