## Parton Equilibration

Since the beginning of the search for a quark gluon plasma and the emergence of high energy nuclear collisions, the issues related to thermal and chemical equilibration have always been a focal point of many theoretical investigations. These issues are critical for experimental detection of a quark gluon plasma in high energy nuclear collisions, because most of our knowledge of the plasma and its signals has been based on the assumption that it is in both thermal and chemical equilibrium. In the last few years, it was realized that hard or semihard processes will dominate the collision dynamics and constitute most of the initial energy deposition in the central region of ultrarelativistic nuclear collisions. Since the initially produced partons carry relatively large transverse momenta, it becomes possible to estimate the initial energy density and the equilibration time scales using perturbative QCD. To stimulate studies in this new field, the first workshop on parton dynamics was held here at LBNL from August 23 to September 3, 1993. The proceedings, edited by X.-N. Wang, was published as a special LBL report .

Based on the HIJING Monte Carlo model which was developed at LBL, we studied the space-time structure of the initial parton production in ultrarelativistic heavy ion collisions. We found \cite{W2} that the parton production time is in the order of 0.5 fm/c and another 0.5 fm/c later local isotropy is achieved by simple free streaming. An approach to the problem of QCD cascading was also made analytically. An example of radiative dilepton production was studied \cite{W3}. This study has clarified some problems related to Monte Carlo simulations of the problem \cite{W4}. The subsequent evolution of the dense partonic gas to a thermally and chemically equilibrated quark-gluon plasmas is also investigated \cite{W5}. Associated with this process, medium effects such as color screening, multiple scattering, and interference have also been investigated and incorporated. We find that gluons can achieve equilibrium when their initial density is high enough, but quarks cannot reach chemical equilibrium within the life-time of the partonic system which has serious consequences for detecting QGP. However, the pre-equilibrium parton interactions can be studied by measuring observables such as open charm production \cite{W6}. The existence of the produced partons via semihard scatterings will also influence the underlying soft particle production. It is shown \cite{W7} that the produced partons will damp rapidly the chromoelectric fields in the plasma in analog to ohmic heating. This damping is shown to suppress pair production in the context of flux tube model and decrease transverse energy production.

The most important factor which controls the gluon equilibration time is the initial density. One of the uncertainties in estimating the initial parton production is closed related to the initial parton structure function of nuclei. We have taken a perturbative approach to the problem of nuclear modification of gluon structure function \cite{W8,W9}. We found that gluon shadowing can be generated perturbatively from gluon fusion in perturbative QCD. Another uncertainty is due to the validity of perturbative QCD at small transverse momentum transfer. HIJING (Heavy Ion Jet INteraction Generator) Monte Carlo model developed here at LBL was designed to combine hard QCD processes with soft interactions. The detailed description of the program has been provided \cite{W10} for experimentalists to use the program to guide their design of detectors for the forthcoming RHIC collider ( and proposed LHC). Detailed systematic comparison of HIJING results with a very wide range of data demonstrates for the first time the interplay between soft dynamics and hard QCD interaction. However, the uncertainties related to the division of hard and soft processes cannot be constrained by current data but will affect predictions for future heavy ion collisions. In order to pin down the uncertainties related to minijet production in high-energy hadron and nuclear collisions, two-particle correlation functions in azimuthal angle $\phi$ and their $p_T$ dependence were proposed to measure the contribution to particle production from minijets \cite{W11}. Once measured experimentally, this will greatly reduce the uncertainties we are facing in parton and transverse energy production in high-energy nuclear collisions.

We also plan to continue investigating a variety of physics topics with HIJING including $pA\rightarrow$ dihadron reactions and back-to-back two-particle correlations. The long range objective is to develop a space-time parton shower program that utilizes HIJING as the initial condition prior to hadronization. This latter development is coupled to both the field theoretic and phenomenological studies as described in the next section. The space-time cascade can only be done after a proper understanding of how interference phenomena leading to the Landau-Pomeranchuk-Migdal effect can be included in a classical cascade simulation, and how hard partons affect the underlining soft interactions. \noindent Field Theory One area of field theoretic studies is on radiative energy loss by fast partons inside a QGP. The hard part of this problem is to incorporate correctly the destructive interference phenomena leading to the LPM effect. We have began and plan to continue in the future a systematic study of multiple scatterings and radiation within the frame work of pQCD. Due to the unique feature of QCD, the interference pattern of multiple radiation induced by multiple scatterings is very different from QED. We have confirmed the validity of LPM effect in QCD \cite{W12,W13}. Our results show that the radiative energy loss could be much larger than the elastic contribution. Because of the LPM effect however, it is highly sensitive to the infrared cutoff scale. We are investigating whether that extra sensitivity could be exploited as a tool to "measure" that unknown scale in the vicinity of the QGP transition \cite{W14}.

Another area of field theoretic studies involved high temperature perturbative QCD calculations of transport properties. The transport properties of relativistic quark-gluon and electron-photon plasmas have been described in the weak coupling limit by including the Debye electric and dynamical screening for the magnetic parts of the interactions. Rates of momentum and thermal relaxation, electrical conductivity, viscosities, flavor and spin diffusion have been calculated for both high temperature \cite{W15,W16} and degenerate plasmas \cite{W17}; these transport coefficients have been applied to RHIC collisions and the early universe, where temperatures are high, as well as degenerate quark matter in neutron stars, where temperatures are low. The transport times in high temperature plasmas are typically $\tau\sim(\alpha_s^2\ln(1/\alpha_s)T)^{-1}$. In degenerate plasmas the temperature dependences differ from standard Fermi liquid results. The diffusion of color in quark-gluon plasmas is, however, found to be much slower than the diffusion of spin and flavor because color is easily exchanged by the gluons in the very singular forward scattering processes \cite{W18}. If the infrared divergence is cut off by a magnetic mass, $m_{mag}\sim \alpha_sT$, the color diffusion is $D_{color}\sim (\alpha_s\ln(1/\alpha_s)T)^{-1}$, a factor $\alpha_s$ smaller than spin and flavor diffusion. A similar effect is espected in electroweak plasmas above $M_W$ due to $W^\pm$ exchanges. The color conductivity in quark-gluon plasmas and the electrical conductivity in electroweak plasmas are correspondingly small in relativistic heavy ion collisions and the very early universe. The color diffusion coefficient and color conductivity calculated are in qualitative agreement with recent results on diffusion in color space by Gyulassy and Selikhov.

A new area of research in field theory was started in collaboration with a postdoctoral fellow in the Physics Division. The possibility of produce a large domain of chirally disoriented pion field is investigated. The size of the domain in spatial rapidity was found to be around two units of rapidity, which could lead to some measurable clusters of chiral ordered pions in phase space \cite{W19}. We are currently investigating how to detect such domain if the there are many but small such domains.

\noindent Phenomenology The phenomenological aspect of our relativistic nuclear physics program tries not only to provide constraints for the development of a realistic model at both low and high energies but also to explain the current experimental data. Though HIJING has be tested against and explained a wide range of data in $pp$, $pA$ and $AA$ collisions, further studies of additional observables, like two-pion correlation function \cite{W11}, are still necessary to reduce the uncertaintied for the predictions for the future high energy collisions. We also plan to study high energy $pA$ collisions at Fermilab energies using HIJING model.