Dilepton Production In The Viscous Quark-Gluon Plasma

In1964, Gell-Mann and Zwcig pointed out that hadrons were consists of quarks and gluons. Quantum chromodynamics (QCD) predicts that deconfined phase tran-sition, a phase transition from normal hadron gas to quark-gluon plasma (QGP), will occur at high temperature and/or high density. QGP is a new state of mat-ter-consisting of a large amount of deconfined quarks, antiquarks and gluons. The Relativistic Heavy Ion Collider (RHIC) in Brookheaven National Laboratory (BNL) in U.S. provides the created environment for the formation of QGP.Howcvcr, QGP maybe produced in the earlier stage of high energy heavy ion collisions,people can only observe the information from experiment for hadronized hadronic matter after QGP evolution, great interests have still been absorbed in the topics of the forma-tion conditions of QGP,the evolution of QGP and the probes of QGP. One of the most convincing probes is the dilcpton production. Since QGP is a strongly coupled and nearly perfect quark-gluon fluid with a very small viscosity. The hydrodynamics model can describe the space-time evolution of QGP system well.At first, we will briefly introduce some primary findings at RHIC, such as strangeness increase and J/ψ,jet quenching,collective flow and dilepton production and so on. Then we will review the foundations of finite temperature field the-ory, in this frame, the propagators of Bosons and Fermions could be expressed in Keldysh Form. Based on the theoretical tool of the Hard Thermal Loops(HTL) re-summation,we present the resummed photon self energy including one-and two-loops in Coulomb gauge.Then we will present the2+1D viscous hydrodynamics model. Based on this model we studied the time evolution of the viscous QGP system, i.e., temperature, the square of the sound speed, ratio of the shear viscosity to entropy(η/s) etc. We found that,the evolution of the system evolves slower than the ideal case; and after applying the viscous correction to the fluid dynamics, the larger the viscosity is, the slower the evolution of the temperature evolves.Basing on those information obtained from the evolution of the viscous QGP sys tem,we can study the rate of the dilepton production in viscous QGP.We calculate the imaginary part of self energy of photon with HTL in real time formalism. In-tegrating the space-time of the dilepton production rate, we get the invariant mass spectrum of dilepton of the annihilation processqqâ†'ll. We found that with a small η/s, the invariant mass spectrum of dilepton increased deviates from the ideal case (η/s=0).With the increase of η/s, its deviation becomes larger. It also comes out that different equations of state don’t affect the distribution of the invariant mass spectrum obviously.Similar to the preceding treatment of the qq annihilation process, we can also discuss the other sources of dilcpton production. This will be left for our future work...