Parton Production Via Vacuum Polarization

We discuss the production mechanism of partons via vacuum polarization during the very early, gluon dominated phase of an ultrarelativistic heavy-ion collision in the framework of the background field method of quantum chromodynamics.Comment: 3 pages, Latex, 3 figures (eps), to be published in JPhysG, SQM2001 proceeding

Fragmentation Function in Non-Equilibrium QCD Using Closed-Time Path Integral Formalism

In this paper we implement Schwinger-Keldysh closed-time path integral formalism in non-equilibrium QCD to the definition of Collins-Soper fragmentation function. We consider a high p_T parton in QCD medium at initial time t_0 with arbitrary non-equilibrium (non-isotropic) distribution function f(\vec{p}) fragmenting to hadron. We formulate parton to hadron fragmentation function in non-equilibrium QCD in the light-cone quantization formalism. It may be possible to include final state interactions with the medium via modification of the Wilson lines in this definition of the non-equilibrium fragmentation function. This may be relevant to study hadron production from quark-gluon plasma at RHIC and LHC.Comment: 15 pages latex, Accepted for Publication in European Physical Journal

Color Octet Contribution to High p_T J/\Psi Production in pp Collisions at \sqrt s = 500 and 200 GeV at RHIC

We compute \frac{d\sigma}{dp_T} of the J/\psi production in pp collisions at RHIC at \sqrt s = 500 and 200 GeV by using both the color octet and singlet models in the framework of non-relativistic QCD. The J/\psi we compute here includes the direct J/\psi from the partonic fusion processes and the J/\psi coming from the radiative decays of \chi_J's both in the color octet and singlet channel. The high p_T J/\psi production cross section is computed within the PHENIX detector acceptance ranges: -0.35 < \eta < 0.35 and 1.2 < \|\eta| < 2.4, the central electron and forward muon arms. It is found that the color octet contribution to J/\psi production is dominant at RHIC energy in comparison to the color singlet contributions. We compare our results with the recent preliminary data obtained by PHENIX detector for the high p_T J/\psi measurements. While the color singlet model fails to explain the data completely the color octet model is in agreement with the single data point above 2 GeV transverse momentum. A measurement of J/\psi production at RHIC in the next run with better statistics will allow us to determine the validity of the color octet model of J/\psi production at RHIC energies. This is very important because it is necessary to know the exact mechanism for J/\psi production in pp collisions at RHIC if one is to make predictions of J/\psi suppression as a signature of quark-gluon plasma. These mechanisms also play an important role in determining the polarized spin structure function of the proton at RHIC.Comment: 16 pages latex, 6 figure

Production and Equilibration of the Quark-Gluon Plasma with Chromoelectric Field and Minijets

Production and equilibration of quark-gluon plasma are studied within the color flux-tube model, at the RHIC and LHC energies. Non-Abelian relativistic transport equations for quarks, antiquarks and gluons, are solved in the extended phase space which includes coordinates, momenta and color. Before the chromoelectric field is formed, hard and semihard partons are produced via minijets which provide the initial conditions necessary to solve the transport equations. The model predicts that in spite of the vast difference between the RHIC and LHC incident energies, once the local equilibrium is reached, the energy densities, the number densities and the temperatures at the two machines may not be very different from each other. The minijet input significantly alters the evolution of the deconfined matter, unless the color field is too strong. For the input parameters used here the equilibration time is estimated to be $\sim 1$ fm at RHIC and $\sim 0.5$ fm at LHC, measured from the instant when the two colliding nuclei have just passed through each other. The temperature at equilibration is found to be $\sim 250$ MeV at RHIC and $\sim 300$ MeV at LHC.Comment: version to appear in Phys. Rev. C; discussion enlarged to include comparison with other models; conclusions unchanged; 14 single-spaced pages + 8 ps figure

Schwinger Mechanism for Gluon Pair Production in the Presence of Arbitrary Time Dependent Chromo-Electric Field

We study Schwinger mechanism for gluon pair production in the presence of arbitrary time-dependent chromo-electric background field $E^a(t)$ with arbitrary color index $a$=1,2,...8 in SU(3) by directly evaluating the path integral. We obtain an exact expression for the probability of non-perturbative gluon pair production per unit time per unit volume and per unit transverse momentum $\frac{dW}{d^4x d^2p_T}$ from arbitrary $E^a(t)$. We show that the tadpole (or single gluon) effective action does not contribute to the non-perturbative gluon pair production rate $\frac{dW}{d^4x d^2p_T}$. We find that the exact result for non-perturbative gluon pair production is independent of all the time derivatives $\frac{d^nE^a(t)}{dt^n}$ where $n=1,2,....\infty$ and has the same functional dependence on two casimir invariants $[E^a(t)E^a(t)]$ and $[d_{abc}E^a(t)E^b(t)E^c(t)]^2$ as the constant chromo-electric field $E^a$ result with the replacement: $E^a \to E^a(t)$. This result may be relevant to study the production of a non-perturbative quark-gluon plasma at RHIC and LHC.Comment: 13 pages latex, Published in European Physical Journal

O(4)-Invariant Formulation of the Nodal Liquid

We consider the O(4) symmetric point in the phase diagram of an electron system in which there is a transition between d_{x^2 - y^2} density-wave order and d_{x^2 - y^2} superconductivity. If the pseudospin $SU(2)\subset O(4)$ symmetry is disordered by quantum fluctuations, the Nodal Liquid can result. In this context, we (1) construct a pseudospin $\sigma$-model; (2) discuss its topological excitations; (3) point out the possibility of a {\it pseudospin-Peierls} state and (4) propose a phase diagram for the underdoped cuprate superconductors

Altarelli-Parisi Equation in Non-Equilibrium QCD

The $Q^2$ evolution of fragmentation function in non-equilibrium QCD by using DGLAP evolution equation may be necessary to study hadron formation from quark-gluon plasma at RHIC and LHC. In this paper we study splitting functions in non-equilibrium QCD by using Schwinger-Keldysh closed-time path integral formalism. For quarks and gluons with arbitrary non-equilibrium distribution functions $f_q({\vec p})$ and $f_g({\vec p})$, we derive expressions for quark and gluon splitting functions in non-equilibrium QCD at leading order in $\alpha_s$. We make a comparison of these splitting functions with that obtained by Altarelli and Parisi in vacuum.Comment: QCD Evolution Time vs Non-Equilibrium Relaxation Time Added, 13 pages latex, Final Version to be Published in Phys. Part. Nucl. V.43, N6 (2012). arXiv admin note: text overlap with arXiv:0808.128