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The heavy quark collisional scattering on partons of the quark gluon plasma (QGP) is studied in a QCD medium at finite temperature and chemical potential. We evaluate the effects of finite parton masses and widths, finite temperature $T$ and quark chemical potential $\mu_q$ on the different elastic cross sections for dynamical quasi-particles (on- and off-shell particles in the QGP medium as described by the dynamical quasi-particles model "DQPM") using the leading order Born diagrams. Our results show clearly the decrease of the $qQ$ and $gQ$ total elastic cross sections when the temperature and the quark chemical potential increase. These effects are amplified for finite $\mu_q$ at temperatures lower than the corresponding critical temperature $T_c (\mu_q)$. Using these cross sections we, furthermore, estimate the energy loss and longitudinal and transverse momentum transfers of a heavy quark propagating in a finite temperature and chemical potential medium. Accordingly, we have shown that the transport properties of heavy quarks are sensitive to the temperature and chemical potential variations. Our results provide some basic ingredients for the study of charm physics in heavy-ion collisions at Beam Energy Scan (BES) at RHIC and CBM experiment at FAIR., Comment: 19 pages, 28 figures

In this paper we study the azimuthal correlations of heavy quarks in $\mathrm{Pb}+\mathrm{Pb}$ collisions with $\sqrt{s}=2.76$ TeV at the Large Hadron Collider. Due to the interaction with the medium, heavy quarks and antiquarks are deflected from their original direction and the initial correlation of the pair is broadened. We investigate this effect for different transverse momentum classes. Low-momentum heavy-quark pairs lose their leading-order back-to-back initial correlation, while a significant residual correlation survives at large momenta. Due to the larger acquired average deflection from their original directions the azimuthal correlations of heavy-quark pairs are broadened more efficiently in a purely collisional energy loss mechanism compared to that including radiative corrections. This discriminatory feature survives when next-to-leading-order production processes are included.

We study the heavy quark scattering on partons of the quark gluon plasma (QGP) being especially interested in the collisional (elastic) scattering processes of heavy quarks on quarks and gluons. We calculate the different cross sections for perturbative partons (massless on-shell particles in the vacuum) and for dynamical quasi-particles (off-shell particles in the QGP medium as described by the dynamical quasi-particles model "DQPM") using the leading order Born diagrams. Our results show clearly the effect of a finite parton mass and width on the perturbative elastic $(q(g) Q \rightarrow q (g) Q)$ cross sections which depend on temperature $T$, energy density $\epsilon$, the invariant energy $\sqrt{s}$ and the scattering angle $\theta$. Our detailed comparisons demonstrate that the finite width of the quasi-particles in the DQPM - which encodes the multiple partonic scattering - has little influence on the cross section for $q Q \rightarrow q Q$ as well as $g Q \rightarrow g Q$ scattering except close to thresholds. Thus when studying the dynamics of energetic heavy quarks in a QGP medium the spectral width of the degrees-of-freedom may be discarded. We have, furthermore, compared the cross sections from the DQPM with corresponding results from hard-thermal-loop (HTL) approaches. The HTL inspired models - essentially fixing the regulators by elementary vacuum cross sections and decay amplitudes instead of properties of the QGP at finite temperature - provide quite different results especially w.r.t. the temperature dependence of the $qQ$ and $gQ$ cross sections (in all settings). Accordingly, the transport properties of heavy quarks will be very different as a function of temperature when compared to DQPM results., Comment: 28 pages, 32 figures

We have measured the proton elliptic flow excitation function for the Au + Au system spanning the beam energy range 2 -- 8 AGeV. The excitation function shows a transition from negative to positive elliptic flow at a beam energy, $E_{tr} \sim$ 4 AGeV. Detailed comparisons with calculations from a relativistic Boltzmann-equation are presented. The comparisons suggest a softening of the nuclear equation of state (EOS) from a stiff form (K \sim 380 MeV) at low beam energies (E_{Beam} \le 2 AGeV) to a softer form (K \sim 210 MeV) at higher energies (E_{Beam} \ge $ 4 AGeV) where the calculated baryon density $ \rho \sim 4 \rho_0$.

We investigate how the possible existence of hadronic bound states above the deconfinement transition temperature ${T}_{c}$ affects heavy-quark observables, such as the nuclear modification factor, the elliptic flow, and azimuthal correlations. Lattice QCD calculations suggest that above ${T}_{c}$ the effective degrees of freedom might not be exclusively partonic but that a certain fraction of hadronic degrees of freedom might already form at higher temperatures. This is an interesting question by itself but also has a strong influence on other probes of the strongly interacting matter produced in ultrarelativistic heavy-ion collisions. A substantial fraction of hadronic bound states above ${T}_{c}$ reduces on average the interaction of the heavy quarks with colored constituents of the medium. We find that all studied observables are highly sensitive to the active degrees of freedom in the quark-gluon plasma.

The energy loss of a relativistic charge undergoing multiple scatterings while traversing an infinite, polarizable and absorptive plasma is investigated. Polarization and damping mechanisms in the medium are phenomenologically modelled by a complex index of refraction. Apart from the known Ter-Mikaelian effect related to the dielectric polarization of matter, we find an additional, substantial reduction of the energy loss due to damping of radiation. The observed effect is more prominent for larger damping and/or larger energy of the charge. A conceivable analog of this phenomenon in QCD could influence the study of jet quenching phenomena in ultra-relativistic heavy-ion collisions at RHIC and LHC., Comment: Sep 2012. 4pp. 3 figures. Revised journal version - Erratum

High transverse momentum (p{sub T}) single nonphotonic electrons which have been measured in the RHIC experiments come dominantly from heavy meson decay. The ratio of their p{sub T} spectra in pp and AA collisions [R{sub AA}(p{sub T})] reveals the energy loss of heavy quarks in the environment created by AA collisions. Using a fixed coupling constant and the Debye mass (m{sub D}{approx_equal}gT) as the infrared regulator, perturbative QCD (pQCD) calculations are not able to reproduce the data, neither the energy loss nor the azimuthal (v{sub 2}) distribution. Employing a running coupling constant and replacing the Debye mass by a more realistic hard thermal loop (HTL) calculation, we find a substantial increase in the collisional energy loss, which brings the v{sub 2}(p{sub T}) distribution as well as R{sub AA}(p{sub T}) to values close to the experimental ones without excluding a contribution from radiative energy loss.

We discuss charmonium production in proton-nucleus collisions at RHIC energies under the assumption of xF and x2 scaling. We find that all the ambiguities due to energy loss are gone at this energy and therefore data will reveal the scaling law, if any. These p-A data will also be crucial to interpret nucleus-nucleus data with respect to a possible formation of a quark gluon plasma because the extrapolations for charmonium production from the present p-A data to RHIC energies, based on the two scaling laws, differ by a factor of four.