Quark and gluon distribution functions in a viscous quark-gluon plasma medium and dilepton production via $q\overline{q}$ annihilation

Viscous modifications to the thermal distributions of quark-antiquarks and gluons have been studied in a quasiparticle description of the quark-gluon-plasma medium created in relativistic heavy-ion collision experiments. The model is described in terms of quasipartons that encode the hot QCD medium effects in their respective effective fugacities. Both shear and bulk viscosities have been taken in to account in the analysis, and the modifications to thermal distributions have been obtained by modifying the energy-momentum tensor in view of the nontrivial dispersion relations for the gluons and quarks. The interactions encoded in the equation of state induce significant modifications to the thermal distributions. As an implication, the dilepton production rate in the $q\overline{q}$ annihilation process has been investigated. The equation of state is found to have a significant impact on the dilepton production rate along with the viscosities.

Figure 1

Behavior of $I_{gg}$ and $I_{qq}$ as functions of $T/T_c$. The temperature dependences of the $z_g$ and $z_q$ are taken from Ref. [32]. Clearly, the modifications induced by the EoS are quite significant even at higher temperatures as compared to the ideal QGP EoS.

Figure 2

The behavior of $z_q^2$ as a function of $T/T_c$ is shown along with its SB limit ($z_q\to 1$). The temperature dependence of the effective quark fugacity, $z_q$, is taken from Ref. [32].

Figure 3

The behavior of $R_q$ (the modification factor to the viscous contribution to the dilepton rate induced by the realistic EoS) as function of $T/T_c$ is shown along with its SB limit [$R_q\to 1/\zeta (5)$]. The temperature dependence of the effective quark fugacity, $z_q$, is taken from Ref. [32]. Here, we assume that $\eta$ and $\zeta$ are the phenomenological parameters for the QGP and assumed to be same for realistic and ideal QGP EoSs.

Figure 4

Thermal dilepton yield from viscous quark-gluon plasma at RHIC energies for different dilepton-invariant masses using the modified distribution functions. Dotted curves represent the rates calculated ignoring the EoS modifications on the thermal distribution functions.

Figure 5

Transverse momentum spectra for the thermal dileptons (with invariant mass $M=0.525\mathrm{GeV}$) from the viscous quark-gluon plasma produced in RHIC energies. The effect of viscosities is highlighted.