Heavy quark scattering and quenching in a QCD medium at finite temperature and chemical potential

The heavy quark collisional scattering on partons of the quark gluon plasma (QGP) is studied in a quantum chromodynamics 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 quasiparticles (on- and off-shell particles in the QGP medium as described by the dynamical quasiparticle 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 $T_c\left({\mu }_q\right)$. 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 at RHIC and CBM experiment at FAIR.

Figure 1

(left) The DQPM running coupling ${\alpha }_s(T,{\mu }_q)=g^2(T^{☆}/T_c\left({\mu }_q\right))/\left(4\pi \right)$ as a function of $T$ in the lQCD for $N_f=0$ (red spheres) [54] and in the DQPM at zero chemical potential for $N_f=0$ (black line) and $N_f=3$ (dashed brown line). The result for the DQPM at finite quark chemical potential (${\mu }_q=0.2$ GeV) for $N_f=3$ is given by the orange thin line, (right) 3D plot of ${\alpha }_s(T,{\mu }_q)$.

Figure 2

The DQPM pole masses and widths for the gluons $(M_g,{\gamma }_g)$ (left) and light quarks $(M_q,{\gamma }_q)$ (right) given by (2.1) and (2.7) as a function of temperature for different values of the quark chemical potential ${\mu }_q$.

Figure 3

Feynman diagrams for the $qQ\to qQ$ and $gQ\to gQ$ scattering process. Latin (Greek) subscripts denote color (spin) indices. $k_i$, respectively, $p_i$ ($k_f$, respectively, $p_f$) denote the initial (final) 4-momentum of the light quark or the gluon, respectively, the heavy quark. The invariant energy squared is given by $s={(p_i+k_i)}^2,t={(p_i-p_f)}^2,u={(p_i-k_f)}^2$.

Figure 4

Differential (a) and total (b) elastic cross section for $uc\to uc$ elastic scattering for off-shell (black lines) and on-shell partons (orange lines) at three different values of the quark chemical potential ${\mu }_q$ (see legend) at $T=0.2$ GeV. We consider the DQPM pole masses for the on-shell partons and the DQPM spectral functions for the off-shell degrees of freedom.

Figure 5

Elastic cross section of $uc\to uc$ (a) and $gc\to gc$ (b) scattering as a function of the temperature $T$ and the invariant energy above threshold $\sqrt{s}-\sqrt{s_0}$, where $\sqrt{s_0}$ is the threshold energy, for on-shell partons as described by the DpQCD approach at ${\mu }_q=0$.

Figure 6

Thermal transition rate $\omega$ of $uc\to uc$ (a) and $gc\to gc$ (b) as a function of the temperature $T$ and quark chemical potential ${\mu }_q$ for on-shell partons as described by the DpQCD approach.

Figure 7

(a) Temperature $T$ as a function of the energy density $\varepsilon$ from the DQPM for different values of the quark chemical potential ${\mu }_q$. (b) Thermal transition rate for $uc\to uc$ scattering for off-shell (IEHTL) and on-shell (DpQCD) partons as a function of the energy density $\varepsilon$.

Figure 8

The total elastic interaction rate $R$ of $c$ quarks in the plasma rest frame in the IEHTL and DpQCD models as a function of the heavy quark momentum $p$ for three different values of the quark chemical potential ${\mu }_q=0,0.2,0.3$ GeV at $T=0.3$ GeV (a). (b) 3D plot of the total elastic interaction rate $R$ within DpQCD as a function of $T$ and ${\mu }_q$.

Figure 9

The total elastic interaction rate $R$ of $c$ quarks in the plasma rest frame as a function of the temperature $T$ and quark chemical potential ${\mu }_q$ from the scattering with light quarks (a), light antiquarks (b), and gluons (c). The on-shell heavy quark momentum in all cases is $p=5$ GeV.

Figure 10

The $c$-quark energy loss, $dE/dx$, in the plasma rest frame from the DpQCD and IEHTL models as a function of the heavy quark momentum $p$ at $T=0.2$ GeV for different values of the quark chemical potential ${\mu }_q$.

Figure 11

The $c$-quark energy loss, $dE/dx$, in the plasma rest frame from the DpQCD approach as a function of the temperature $T$ and quark chemical potential ${\mu }_q$ for the heavy quark momentum $p=1$ GeV (a) and $p=5$ GeV (b).

Figure 12

The energy loss $dE/dx$ of $c$ quarks in the plasma rest frame as a function of the temperature $T$ and the quark chemical potential ${\mu }_q$ from the scattering with light quarks (a), light antiquarks (b), and gluons (c). The on-shell heavy quark momentum in this case is $p=5$ GeV.

Figure 13

$c$-quark drag coefficient (6.1) and (6.2) (a), and $\widehat{q}$ (6.4) and (6.6) (b) in the plasma rest frame as a function of the heavy quark momentum $p$ for $T=2$ GeV.

Figure 14

$c$-quark drag (a) and $\widehat{q}$ (b) in the plasma rest frame from the DpQCD approach as a function of the temperature $T$ and quark chemical potential ${\mu }_q$ for the heavy quark momentum $p=5$ GeV.