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Raju Venugopalan

Publications and source records attributed to Raju Venugopalan.

At least 181 records · Page 10Linked to original sources
arXiv1999

Minding one's P's and Q's : from the one loop effective action in quantum field theory to classical transport theory

The one loop effective action in quantum field theory can be expressed as a quantum mechanical path integral over world lines, with internal symmetries represented by Grassmanian variables. In this paper, we develop a real time, many body, world line formalism for the one loop effective action. In particular, we study hot QCD and obtain the classical transport equations which, as Litim and Manuel have shown, reduce in the appropriate limit to the non-Abelian Boltzmann-Langevin equation first obtained by Bödeker. In the Vlasov limit, the classical kinetic equations are those that correspond to the hard thermal loop effective action. We also discuss the imaginary time world line formalism for a hot $ϕ^4$ theory, and elucidate its relation to classical transport theory.

hep-ph↗
arXiv1999

The first fermi in a high energy nuclear collision

At very high energies, weak coupling, non-perturbative methods can be used to study classical gluon production in nuclear collisions. One observes in numerical simulations that after an initial ``formation'' time, the produced partons are on shell, and their subsequent evolution can be studied using transport theory. At the initial formation time, a simple non-perturbative relation exists between the energy and number densities of the produced partons, and a scale determined by the saturated parton density in the nucleus.

hep-ph↗
arXiv1999

The initial energy density of gluons produced in very high energy nuclear collisions

In very high energy nuclear collisions, the initial energy of produced gluons per unit area per unit rapidity, $dE/L^2/dη$, is equal to $f(g^2μL) (g^2μ)^3/g^2$, where $μ^2$ is proportional to the gluon density per unit area of the colliding nuclei. For an SU(2) gauge theory, we perform a non--perturbative numerical computation of the function $f(g^2μL)$. It decreases rapidly for small $g^2μL$ but varies only by $\sim 25$%, from $0.208\pm 0.004$ to $0.257\pm 0.005$, for a wide range 35.36--296.98 in $g^2μL$, including the range relevant for collisions at RHIC and LHC. Extrapolating to SU(3), we estimate the initial energy per unit rapidity for Au-Au collisions in the central region at RHIC and LHC.

hep-ph↗
arXiv1999

Non-perturbative computation of gluon mini-jet production in nuclear collisions at very high energies

At very high energies, in the infinite momentum frame and in light cone gauge, a hard scale proportional to the high parton density arises in QCD. In an effective theory of QCD at small $x$, this scale is of order $α_Sμ$, where $μ$ is simply related to the gluon density at higher rapidities. The ab initio real time evolution of small $x$ modes in a nuclear collision can be described consistently in the classical effective theory and various features of interest can be studied non-perturbatively. In this paper, we discuss results from a real time lattice computation of the production of gluon jets at very high energies. At very large transverse momenta, $k_t\geq μ$, our results match the predictions from pQCD based mini-jet calculations. Novel non-perturbative behaviour of the small $x$ modes is seen at smaller momenta $k_t\sim α_Sμ$. Gauge invariant energy-energy correlators are used to estimate energy distributions evolving in proper time.

hep-ph↗
arXiv1999

Fock Space Distributions, Structure Functions, Higher Twists and Small x

We compute quark structure functions and the intrinsic Fock space distribution of sea quarks in a hadron wavefunction at small x. The computation is performed in an effective theory at small x where the gluon field is treated classically. At $Q^2$ large compared to an intrinsic scale associated with the density of gluons $μ^2$, large compared to the QCD scale $Λ^2_{QCD}$, and large compared to the quark mass squared $M^2$, the Fock space distribution of quarks is identical to the distribution function measured in deep inelastic scattering. For $Q^2 \le M^2$ but $Q^2 >> μ^2$, the quark distribution is computed in terms of the gluon distribution function and explicit expressions are obtained. For $Q^2 \le μ^2$ but $Q^2 >> Λ_{QCD}^2$ we obtain formal expressions for the quark distribution functions in terms of the glue. An evaluation of these requires a renormalization group analysis of the gluon distribution function in the regime of high parton density. For light quarks at high $Q^2$, the DGLAP flavor singlet evolution equations for the parton distributions are recovered. Explicit expressions are given for heavy quark structure functions at small x.

hep-ph↗
arXiv1998

Real time simulations of high energy nuclear collisions

We discuss real time simulations of high energy nuclear collisions in a classical effective theory of QCD at small x. At high transverse momenta, our results match the lowest order predictions of pQCD based mini-jet calculations. We discuss novel non-perturbative behaviour of the small x modes seen at small transverse momenta.

hep-ph↗
arXiv1998

On colliding ultrarelativistic nuclei on a transverse lattice

We argue that the classical evolution of small x modes in the collision of two ultrarelativistic nuclei is described on a transverse lattice by the Kogut--Susskind Hamiltonian in 2+1-dimensions coupled to an adjoint scalar field. The initial conditions for the evolution are provided by the non--Abelian Weizsäcker--Williams fields which constitute the classical parton distributions in each of the nuclei. We outline how lattice techniques developed for real time simulations of field theories in thermal equilibrium can be used to study non--perturbatively, thermalization and classical gluon radiation in ultrarelativistic nuclear collisions.

hep-ph↗
arXiv1997

Boost covariant gluon distributions in large nuclei

It has been shown recently that there exist analytical solutions of the Yang-Mills equations for non-Abelian Weizsäcker-Williams fields which describe the distribution of gluons in large nuclei at small x. These solutions however depend on the color charge distribution at large rapidities. We here construct a model of the color charge distribution of partons in the fragmentation region and use it to compute the boost covariant momentum distributions of wee gluons. The phenomenological applications of our results are discussed.

nucl-th↗
arXiv1996

Hydrodynamical Description of 200 A GeV/c S+Au Collisions: Hadron and Electromagnetic Spectra

We study relativistic S+Au collisions at 200 A GeV/c using a hydrodynamical approach. We test various equations of state (EOSs), which are used to describe the strongly interacting matter at densities attainable in the CERN-SPS heavy ion experiments. For each EOS, suitable initial conditions can be determined to reproduce the experimental hadron spectra; this emphasizes the ambiguity between the initial conditions and the EOS in such an approach. Simultaneously, we calculate the resulting thermal photon and dielectron spectra, and compare with experiments. If one allows the excitation of resonance states with increasing temperature, the electro-magnetic signals from scenarios with and without phase transition are very similar and are not resolvable within the current experimental resolution. With regard to the CERES dilepton data, none of the EOSs considered, in conjunction with the standard leading order dilepton rates, succeed in reproducing the observed excess of dileptons below the rho peak. Our work, however, suggests that an improved measurement of the photon and dilepton spectra has the potential to strongly constrain the EOS.

nucl-th↗
arXiv1996

Lattice Computations of Small-x Parton Distributions in a Model of Parton Densities in Very Large Nuclei

Using weak coupling methods McLerran and Venugopalan~\cite{LV1} expressed the parton distributions in large nuclei as correlation functions of a two dimensional Euclidean field theory. The theory has the dimensionful coupling $g^2 μ$, where $μ^2\sim A^{1/3}$ is the valence quark color charge squared per unit area. We use a lattice regularization to investigate these correlation functions both analytically and numerically for the simplified case of $SU(2)$ gauge theory. In weak coupling ($g^2μL<< 5$), where $L$ is the transverse size of the nucleus, the numerical results agree with the {\it analytic} lattice weak coupling results. For $g^2μL>> 5$, no solutions exist at O($a^4$) where $a$ is the lattice spacing. This suggests an ill-defined infrared behavior for the two dimensional theory. A recent proposal of McLerran et al.~\cite{Kovner} for an {\it analytic} solution of the classical problem is discussed briefly.

hep-ph↗
arXiv1996

Small x parton distributions and initial conditions in ultrarelativistic nuclear collisions

At the colliders RHIC and LHC, nuclei at the ultrarelativistic energies of $100$ GeV/A and $2.7$ TeV/A will be smashed together with the hope of creating an elusive and short-lived state of matter called the quark gluon plasma. The initial conditions which determine the dynamical evolution of the quark gluon matter formed in the central region after the collision depend crucially on the small $x$ component of the nuclear wavefunction before the collision. In this comment, we discuss recent work which argues that, for large nuclei, weak coupling techniques in QCD can be used to calculate the distribution of these small $x$, or wee, partons. The ramifications of this approach for the dynamics of heavy ion collisions and the various signatures of a quark gluon phase of matter are discussed.

hep-ph↗
arXiv1995

Wee partons in large nuclei: from virtual dream to hard reality

We construct a weak coupling, many body theory to compute parton distributions in large nuclei for $x\ll A^{-1/3}$. The wee partons are highly coherent, non--Abelian Weizsäcker--Williams fields. Radiative corrections to the classical results are discussed. The parton distributions for a single nucleus provide the initial conditions for the dynamical evolution of matter formed in ultrarelativistic nuclear collisions.

hep-ph↗
arXiv1995

The Gluon Propagator in non-Abelian Weizsäcker-Williams fields

We carefully compute the gluon propagator in the background of a non--Abelian Weizsäcker--Williams field. This background field is generated by the valence quarks in very large nuclei. We find contact terms in the small fluctuation equations of motion which induce corrections to a previously incorrect result for the gluon propagator in such a background field. The well known problem of the Hermiticity of certain operators in Light Cone gauge is resolved for the Weizsäcker--Williams background field. This is achieved by working in a gauge where singular terms in the equations of motion are absent and then gauge transforming the small fluctuation fields to Light Cone gauge.

hep-ph↗
arXiv1994

Green's Functions in the Color Field of a Large Nucleus

We compute the Green's functions for scalars, fermions and vectors in the color field associated with the infinite momentum frame wavefunction of a large nucleus. Expectation values of this wavefunction can be computed by integrating over random orientations of the valence quark charge density. This relates the Green's functions to correlation functions of a two dimensional, ultraviolet finite, field theory. We show how one can compute the sea quark distribution functions, and explictly compute them in the kinematic range of transverse momenta, $α_s^2 μ^2 << k_t^2 << μ^2$, where $μ^2$ is the average color charge squared per unit area. When $m_{quark}^2 << μ^2 \sim A^{1/3}$, the sea quark contribution to the infinite momentum frame wave function saturates at a value that is the same as that for massless sea quarks.

hep-ph↗
arXiv1993

Gluon Distribution Functions for Very Large Nuclei at Small Transverse Momentum

We show that the gluon distribution function for very large nuclei may be computed for small transverse momentum as correlation functions of an ultraviolet finite two dimensional Euclidean field theory. This computation is valid to all orders in the density of partons per unit area, but to lowest order in $α_s$. The gluon distribution function is proportional to $1/x$, and the effect of the finite density of partons is to modify the dependence on transverse momentum for small transverse momentum.

hep-ph↗