Ultra-relativistic Heavy-Ion Collision (HIC) generates very strong initial magnetic field ( B) inducing a vorticity in the reaction plane. The high B influences the evolution dynamics that is opposed by the large Faraday current due to electric field generated by the time varying B. We show that the resultant effects entail a significantly large directed flow (v1) of charm quarks (CQs) compared to light quarks due to a combination of several favorable conditions for CQs, mainly: (i) unlike light quarks formation time scale of CQs, τ f ≃ 0.1fm/c is comparable to the time scale when B attains its maximum value and (ii) the kinetic relaxation time of CQs is similar to the QGP lifetime, this helps the CQ to retain the initial kick picked up from the electromagnetic field in the transverse direction. The effect is also odd under charge exchange allowing to distinguish it from the vorticity of the bulk matter due to the initial angular momentum conservation; conjointly thanks to its mass, Mc >> ΛQCD, there should be no mixing with the chiral magnetic dynamics. Hence CQs provide very crucial and independent information on the strength of the magnetic field produced in HIC. 24.85.+p; 05.20.Dd; 12.38.Mh PACS

The two key observables related to heavy quarks that have been measured in RHIC and LHC energies are the nuclear suppression factor RAA and the elliptic flow v2. Simultaneous description of these two observables is a top challenge for all the existing models. We have highlighted how a consistent combination of four ingredients i.e the temperature dependence of the energy loss, full solution of the Boltzmann collision integral for the momentum evolution of heavy quark, hadronization by coalescence, then the hadronic rescattering, responsible to address a large part of such a puzzle. We have considered four different models to evaluate the temperature dependence of drag coefficients of the heavy quark in QGP. All these four different models are set to reproduce the same RAA as of the experiments. We have shown that for the same RAA, the v2 could be quite different depending on the interaction dynamics as well as other ingredients.

The shear viscosity η has been calculated by using the Green-Kubo relation in the framework of a partonic transport approach solved at cascade level. We compare the numerical results for η obtained from the Green-Kubo correlator with the analytical formulas in both the Relaxation Time Approximation (RTA) and the Chapman-Enskog approximation (CE). We investigate and emphasize the differences between the isotropic and anisotropic cross sections and between the massless and massive particles. We show that in the range of temperature explored in a Heavy Ion collision and for pQCD-like cross section the RTA significantly underestimates the viscosity by about a factor of 2-3, while a good agreement is found between the CE approximation and GreeKubo relation already at first order of approximation. The agreement with the CE approximation supplies an analytical formula that allows to develop kinetic transport theory at fixed shear viscosity to entropy density ratio, η/s. This open the possibility to explore dissipative non-equilibrium evolution of the distribution functions vs T-dependent η/s and particle momenta in the dynamics of the Quark-Gluon Plasma created in ultra-relativistic heavy-ion collisions.

We describe the propagation of charm quarks in the quark-gluon plasma (QGP) by means of a Boltzmann transport approach. Non-perturbative interaction between heavy quarks and light quarks have been taken into account through a quasi-particle approach in which light partons are dressed with thermal masses tuned to lQCD thermodynamics. Such a model is able to describe the main feature of the non-perturbative dynamics: the enhancement of the interaction strength near Tc. We show that the resulting charm in-medium evolution is able to correctly predict simultaneously the nuclear suppression factor, RAA, and the elliptic flow, v2, at both RHIC and LHC energies and at different centralities. The hadronization of charm quarks is described by mean of an hybrid model of fragmentation plus coalescence and plays a key role toward the agreeement with experimental data.We also performed calculations within the Langevin approach which can lead to very similar RAA(pT ) as Boltzmann, but the charm drag coefficient as to be reduced by about a 30% and also generates an elliptic flow v2(pT ) is about a 15% smaller. We finally compare the space diffusion coefficient 2πT Ds extracted by our phenomenological approach to lattice QCD results, finding a satisfying agreement within the present systematic uncertainties. Our analysis implies a charm thermalization time, in the p → 0 limit, of about 4 − 6 f m/c which is smaller than the QGP lifetime at LHC energy. 24.85.+p; 05.20.Dd; 12.38.Mh PACS

The propagation of heavy quarks in the quark-gluon plasma (QGP) has been often treated within the framework of the Langevin equation (LV), i.e. assuming the momentum transfer is small or the scatterings are sufficiently forward peaked, small screening mass mD. We address a direct comparison between the Langevin dynamics and the Boltzmann collisional integral (BM) when a bulk medium is in equilibrium at fixed temperature. We show that unless the cross section is quite forward peaked (mD ∼ = T ) or the mass to temperature ratio is quite large (MHQ/T > ∼ 8 − 10) there are significant differences in the evolution of the p−spectra and consequently on nuclear modification factor RAA(pT ). However for charm quark we find that very similar RAA(pT ) between the LV and BM can be obtained, but with a modified diffusion coefficient by about ∼ 15 − 50% depending on the angular dependence of the cross section which regulates the momentum transfer. Studying also the momentum spread suffered by a single heavy quarks we see that at temperatures T > ∼ 250 MeV the dynamics of the scatterings is far from being of Brownian type for charm quarks. In the case of bottom quarks we essentially find no differences in the time evolution of the momentum spectra between the LV and the BM dynamics independently of the angular dependence of the cross section, at least in the range of temperature relevant for ultra-relativistic heavy-ion collisions. Finally, we have shown the possible impact of this study on RAA(pT ) and v2(pT ) for a realistic simulation of relativistic HIC. For larger mD the elliptic flow can be about 50% larger for the Boltzmann dynamics with respect to the Langevin. This is helpful for a simultaneous reproduction of RAA(pT ) and v2(pT ). 24.85.+p; 05.20.Dd; 12.38.Mh PACS

In this article we report on our results about the computation of the elliptic flow of the quark-gluon plasma produced in relativistic heavy-ion collisions, simulating the expansion of the fireball by solving the relativistic Boltzmann equation for the parton distribution function tuned at a fixed shear-viscosity to entropy-density ratio η/s. Our main goal is to put emphasis on the role of a saturation scale in the initial gluon spectrum, which makes the initial distribution far from a thermalized one. We find that the presence of the saturation scale reduces the efficiency in building up the elliptic flow, even if the thermalization process is quite fast τ therm ≈ 0.8 fm/c and the pressure isotropization is even faster τ isotr ≈ 0.5 fm/c. The impact of the nonequilibrium implied by the saturation scale manifests for noncentral collisions and can modify the estimate of the viscosity with respect to the assumption of full thermalization in p T space. We find that the estimate of η/s is modified from η/s ≈ 2/4π to η/s ≈ 1/4π at the Relativistic Heavy-Ion Collider and from η/s ≈ 3/4π to η/s ≈ 2/4π at the Large Hadron Collider. We complete our investigation with a study of the thermalization and isotropization times of the fireball for different initial conditions and values of η/s showing how the latter affects both isotropization and thermalization. Last, we have seen that the range of values explored by the phase-space distribution function f is such that at p T < 0.5 GeV the inner part of the fireball stays with occupation number significantly larger than unity despite the fast longitudinal expansion, which might suggest the possibility of the formation of a transient Bose-Einstein condensate.

A current goal of relativistic heavy ion collisions experiments is the search for a Color Glass Condensate (CGC) as the limiting state of QCD matter at very high density. In viscous hydrodynamics simulations, a standard Glauber initial condition leads to estimate 4πη/s ∼ 1, while employing the Kharzeev-Levin-Nardi (KLN) modeling of the glasma leads to at least a factor of 2 larger η/s. Within a kinetic theory approach based on a relativistic Boltzmann-like transport simulation, our main result is that the out-of-equilibrium initial distribution reduces the efficiency in building-up the elliptic flow. At RHIC energy we find the available data on v2 are in agreement with a 4πη/s ∼ 1 also for KLN initial conditions. More generally, our study shows that the initial non-equilibrium in p-space can have a significant impact on the build-up of anisotropic flow.

We have developed a relativistic kinetic transport approach that incorporates initial state fluctuations allowing to study the build up of elliptic flow v2 and high order harmonics v3, v4 and v5 for a fluid at fixed η/s(T ). We study the effect of the η/s ratio and its T dependence on the build up of the vn(pT ) for two different beam energies: RHIC for Au+Au at √ s = 200 GeV and LHC for P b + P b at √ s = 2.76 T eV . We find that for the two different beam energies considered the suppression of the vn(pT ) due to the viscosity of the medium have different contributions coming from the cross over or QGP phase. Our study reveals that only in ultra-central collisions (0 − 0.2%) the vn(pT ) have a stronger sensitivity to the T dependence of η/s in the QGP phase and this sensitivity increases with the order of the harmonic n. Moreover, the study of the correlations between the initial spatial anisotropies ǫn and the final flow coefficients vn shows that at LHC energies there is more correlation than at RHIC energies. The degree of correlation increases from peripheral to central collisions, but only in ultra-central collisions at LHC, we find that the linear correlation coefficient C(n, n) ≈ 1 for n = 2, 3, 4 and 5. This suggests that the final correlations in the (vn,vm) space reflect the initial correlations in the (ǫn,ǫm) space.