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 thermodynamic behavior of QCD matter at high temperature is currently studied by lattice QCD theory. The main features are the fast rise of the energy density around the critical temperature T c and the large trace anomaly of the energy momentum tensor Θ µ µ = − 3P which hints at a strongly interacting system. Such features can be accounted for by employing a massive quasi-particle model with a temperature-dependent bag constant. Recent lattice QCD calculations with physical quark masses by the Wuppertal-Budapest group show a slower increase of and a smaller Θ µ µ peak with respect to previous results from the hotQCD collaboration. We investigate the implications of such differences from the point of view of a quasi-particle model, also discussing light and strange quark number susceptibilities. Furthermore, we predict the impact of these discrepancies on the temperature-dependence of the transport properties of matter, like the shear and bulk viscosities.

In a coalescence plus fragmentation approach we calculate the heavy baryon/meson ratio and the pT spectra of charmed hadrons D 0 , Ds and Λ + c in a wide range of transverse momentum from low pT up to about 10 GeV and discuss their ratios from RHIC to LHC energies without any change of the coalescence parameters. We have included the contribution from decays of heavy hadron resonances and also the one due to fragmentation of heavy quarks which do not undergo the coalescence process. The coalescence process is tuned to have all charm quarks hadronizing in the pT → 0 limit and at finite pT charm quarks not undergoing coalescence are hadronized by independent fragmentation. The pT dependence of the baryon/meson ratios are found to be sensitive to the masses of coalescing quarks, in particular the Λc/D 0 can reach values of about 1 ÷ 1.5 at pT ≈ 3 GeV, or larger, similarly to the light baryon/meson ratio like p/π and Λ/K, however a marked difference is a quite weak pT dependence with respect to the light case, such that a larger value at intermediate pT implies a relatively large value also for the integrated yields. A comparison with other coalescence model and with the prediction of thermal model is discussed.

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

We present numerical results of electric conductivity σ el of a fluid obtained solving the Relativistic Transport Boltzmann equation in a box with periodic boundary conditions. We compute σ el using two methods: the definition itself, i.e. applying an external electric field, and the evaluation of the Green-Kubo relation based on the time evolution of the current-current correlator. We find a very good agreement between the two methods.We also compare numerical results with analytic formulas in Relaxation Time Approximation (RTA) where the relaxation time for σ el is determined by the transport cross section σtr, i.e. the differential cross section weighted with the collisional momentum transfer. We investigate the electric conductivity dependence on the microscopic details of the 2-body scatterings: isotropic and anisotropic cross-section, and massless and massive particles. We find that the RTA underestimates considerably σ el ; for example at screening masses mD ∼ T such underestimation can be as large as a factor of 2. Furthermore, we study a more realistic case for a quark-gluon system (QGP) considering both a quasi-particle model, tuned to lQCD thermodynamics, as well as the case of a pQCD gas with running coupling. Also for these cases more directly related to the description of the QGP system, we find that RTA significantly underestimate the σ el by about a 60 − 80%.