Jet Quenching with Parton Evolution
We report the evolution effects on jet energy loss with detailed balance. The initial conditions and parton evolution based on perturbative QCD in the chemical non-equilibrated medium and Bjorken expanding medium at RHIC are determined. The parton evolution affect the jet energy loss evidently. This will increase the energy and propagating distance dependence of the parton energy loss and will affect the shape of suppression of moderately high hadron spectra.
keywords:initial conditions, parton evolution, jet quenching
One of the challenging goals of heavy-ion physics is to detect quark-gluon plasma (QGP). Jet quenching WG1992 () or suppression of large hadrons, caused by the energy loss of a propagating parton in a dense medium, has become a powerful tool for the study of properties of QGP. In the heavy ion collisions, the two nuclei pass through each other, interact, and then produce a dense plasma of quarks and gluons. As the initial parton density is large and the partons suffer many collisions in a very short time, the initial partonic system may attain kinetic equilibrium. But does it attain chemical equilibrium? From the numerical studies of parton cascade model, which is based on the concept of inside-outside cascade Anishetty:1980sf (); Hwa:1986sf (); Balizt:1987 () and evolve parton distributions by Monte-Carlo simulation of a relativistic transport equation involving lowest order perturbative QCD scattering and parton fragmentations, it is believed that QGP likely to be formed in such collisions are far from chemical equilibrium. So that the effect of parton chemical equilibration on jet energy loss need to be studied.
We consider here a thermal equilibrated, but chemical non-equilibrated system, and write the parton distribution as an approximation in the factorized Bose or Fermi-Dirac form with non-equilibrium fugacities which gives the measure of derivation from chemical equilibrium,
In general, chemical reactions among partons can be quite complicated because of the possibility of initial and final-state gluon radiations. Here we are interested in understanding the basic mechanisms, so we restrict our consideration to the dominant reaction mechanisms , for the equilibration of each parton flavorBiro:1994sf (). Restricting to reactions, the evolution of the parton densities is governed by the master equations,
If we assume that parton scatterings are sufficiently rapid to maintain local thermal equilibrium, and therefore we can neglect effects of viscosity due to elastic and inelastic scatterings, we can have the hydrodynamic equation, and the baryon number conservation . Then with the master equations above, if the four equations can be solved, we can determine the evolution of , and towards chemical equilibrium, once initial conditions are known. So the input of the initial condition play an important role to investigate the effects of the evolution for the parton system.
Using the momentum distribution discussed above, we can obtain the transverse energy per unit rapidity and parton evolution as shown in Fig.1. It implies that the initial temperature is , is for the central events of Au-Au collisions at RHIC. Using the same method, we get that the initial temperature is for Bjorken expansion() for thermal and chemical equilibrium system. The initial condition determined is showed to be consistent with that from the particle multiplicities.
From the evolution, the Debye screening mass, mean free path, cross section and opacity can be obtained from the perturbative QCD at finite temperature in a thermal equilibrated, but chemical non-equilibrated mediumCheng ().
Since the contribution of the first order opacity is dominant, by including the interference between the process of the rescattering and non-rescattering, we obtain the energy loss for stimulated emission and energy gain for thermal absorption as
where , the factor reflects the destructive interference arising from the non-Abelian LPM effect. Averaging over the longitudinal target profile is defined as , where . is the normalized distribution of momentum transfer from the scattering centers.
The propagating distance dependence of the energy loss for stimulated emission and the ratio of the calculated parton energy loss with and without thermal absorption as functions of parton energy value and propagating distance in a chemical non-equilibrated medium is shown in Fig. 2. It is shown that, by taking into account the evolution of the temperature and fugacity, the energy loss from stimulated emission is proportional to in the chemical non-equilibrated medium and Bjorken expanding medium rather than -dependence on the propagating distance in the static mediumGLV (). The energy loss in the chemical non-equilibrated medium is a bit less than that in Bjorken expanding medium. The energy absorption can not be neglected at intermediate jet energies and small propagating distance of the energetic parton in contrast with that it is important only at intermediate jet energy in the static mediumEnke ().
In summary, we determined the initial conditions and parton evolution and proposed the evolution effects on parton energy loss. The evolution of the medium modifies the jet energy loss in the intermediate energy region and affect the shape of suppression intermediate high hadrons spectrum.
This work was supported by NSFC of China under Projects No. 10825523, No. 10635020, by MOE of China under Projects No. IRT0624, by MOST of China under Project No. 2008CB317106; and by MOE and SAFEA of China under Project No. PITDU-B08033.
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