arXiv subjects
Publications and source records attributed to Larry McLerran.
We discuss forward-backward correlations in the mutliplicity of produced particles in heavy ion collisions. We find the Color Glass Condensate generates distinctive predictions for the long range component of this correlation. In particular, we predict the growth of the long range correlation with the centrality of the collision. We argue that the correlation for mesons is stronger than that for baryons.
We discuss two special limiting forms of QCD matter which may be produced at RHIC. We conclude from the available empirical evidence that an equilibrated, but strongly coupled Quark Gluon Plasma has been made in such collisions. We also discuss the growing body of evidence that its source is a Color Glass Condensate.
We consider the influence of parton saturation in the Color Glass Condensate on the back-to-back azimuthal correlations of high $p_T$ hadrons in $pA$ (or $dA$) collisions. When both near--side and away--side hadrons are detected at mid-rapidity at RHIC energy, the effects of parton saturation are constrained to transverse momenta below the saturation scale $p_T \leq Q_s$; in this case the back-to-back correlations do not disappear but exhibit broadening. However when near-side and away-side hadrons are separated by several units of rapidity, quantum evolution effects lead to the depletion of back-to-back correlations as a function of rapidity interval between the detected hadrons (at fixed $p_T$). This applies to both $pp$ and $pA$ (or $dA$) collisions; however, due to the initial conditions provided by the Color Glass Condensate, the depletion of the back-to-back correlations is significantly stronger in the $pA$ case. An experimental study of this effect would thus help to clarify the origin of the high $p_T$ hadron suppression at forward rapidities observed recently at RHIC.
I introduce the concept of the Color Glass Condensate. I review data from HERA and RHIC which suggest that such a universal form of matter has been found.
The purpose of these lectures is to provide an introduction to the physics issues which are being studied in the RHIC heavy ion program. These center around the production of new states of matter. The Quark Gluon Plasma is thermal matter which once existed in the big bang which may be made at RHIC. The Color Glass Condensate is a universal form of matter which controls the high energy limit of strong interactions. Both such forms of matter might be produced and probed at RHIC.
We argue that the amount of baryon stopping observed in the central rapidity region of heavy ion collisions at RHIC is proportional to the nuclear valence quark distributions at small x. By generalizing Mueller's dipole model to describe Reggeons we construct a non-linear evolution equation for the valence quark distributions at small x in the leading double-logarithmic approximation. The equation includes the effects of gluon saturation in it. The solution of the evolution equation gives a valence quark distribution function $dn_{val}/dy \sim e^{-(0.4\div0.5) y}$. We show that this y-dependence as well as the predictions of Regge theory are consistent with the net-proton rapidity distribution reported by BRAHMS.
We construct a Gaussian approximation to the effective theory for the Colour Glass Condensate which describes correctly the gluon distribution both in the low density regime at high transverse momenta (above the saturation scale $Q_s$), and in the high density regime below $Q_s$, and provides a simple interpolation between these two regimes. At high momenta, the effective theory reproduces the BFKL dynamics, while at low momenta, it exhibits gluon saturation and, related to it, colour neutrality over the short distance scale $1/Q_s \ll 1/Λ_{QCD}$. Gauge--invariant quantities computed within this approximation are automatically infrared finite.
One of the most dramatic results from the first RHIC run are the STAR results for pi+- pi+- interferometry. They showed that the ratio of the so-called R_{out} and R_{sid} radii seem to decrease below unity for increasing transverse momentum of the pair (K_T). This was subsequently confirmed by PHENIX, which also extended the K_T range of the measurements. We consider here the effects of opacity of the nuclei on this ratio, and find that such a small value is consistent with surface emission from an opaque source.
In these lectures, we develop the theory of the Colour Glass Condensate. This is the matter made of gluons in the high density environment characteristic of deep inelastic scattering or hadron-hadron collisions at very high energy. The lectures are self contained and comprehensive. They start with a phenomenological introduction, develop the theory of classical gluon fields appropriate for the Colour Glass, and end with a derivation and discussion of the renormalization group equations which determine this effective theory.
Motivated from the formation of an initial state of gluon-saturated matter, we discuss scaling relations for the transverse mass spectra at BNL's Relativistic Heavy-Ion Collider (RHIC). We show on linear plots, that the transverse mass spectra for various hadrons can be described by an universal function. The transverse mass spectra for different centralities can be rescaled into each other. Finally, we demonstrate that scaling is also present in proton-antiproton collider data and compare it to scaling at RHIC.
We argue that the transverse mass spectra of identified hadrons as measured in gold-gold collisions at BNL's Relativistic Heavy-Ion Collider (RHIC) follows a generalized scaling law. Such a scaling behavior is motivated by the idea of a Color Glass Condensate, or more generally, saturation of the gluon density. In particular, we describe the shapes of transverse mass spectra as a function of centrality. This scaling of the transverse mass spectrum is shown to be consistent with previously observed scaling of multiplicity with centrality.
In this talk, I present what I believe we have learned from the recent RHIC heavy ion experiments. The goal of these experiments is to make and study matter at very high energy densities, greater than an order of magnitude larger than that of nuclear matter. Have we made such matter? What have we learned about the properties of this matter? What do we hope and expect to learn in the future?
We consider the implications of the Color Glass Condensate for the central region of p+A collisions. We compute the k_t distribution of radiated gluons and their rapidity distribution dN/dy analytically, both in the perturbative regime and in the region between the two saturation momenta. We find an analytic expression for the number of produced gluons which is valid when the saturation momentum of the proton is much less than that of the nucleus. We discuss the scaling of the produced multiplicity with A. We show that the slope of the rapidity density dN/dy provides an experimental measure for the renormalization-group evolution of the color charge density of the Color Glass Condensate (CGC). We also argue that these results are easily generalized to collisions of nuclei of different A at central rapidity, or with the same A but at a rapidity far from the central region.
We complete the construction of the renormalization group equation (RGE) for the Color Glass Condenstate begun in Paper I. This is the equation which governs the evolution with rapidity of the statistical weight function for the color glass field. The coefficients in this equation --- one-loop real and virtual contributions --- are computed explicitly, to all orders in the color glass field. The resulting RGE can be interpreted as the imaginary-time evolution equation, with rapidity as the ``imaginary time'', for a quantum field theory in two spatial dimensions. In the weak field limit it reduces to the BFKL equation. In the general non-linear case, it is equivalent to an equation by Weigert which summarizes in functional form the evolution equations for Wilson line operators previously derived by Balitsky and Kovchegov.
The mean transverse momentum in high energy nuclear collisions is studied. The formation of a Color Glass Condensate results in an increase of the square of the mean transverse momentum with the charged multiplicity per unit rapidity and unit transverse area. This prediction is in agreement with the presently available data, in particular with the heavy-ion data, lending support to the notion that the transverse momentum spectra in ultrarelativistic collisions of heavy nuclei might be controlled by intrinsic transverse momentum broadening and not by hadronic rescattering, i.e. transverse flow.
The Color Glass Condensate is a state of high density gluonic matter which controls the high energy limit of hadronic matter. These lectures begin with a discussion of general problems of high energy strong interactions. The infinite momentum frame description of a single hadron at very small x is developed, and this picture is applied to the description of ultrarelativistic nuclear collisions. Recent developments in the renormalization group description of the Color Glass Condensate are reviewed.
We find approximate solutions to the renormalization group equation which governs the quantum evolution of the effective theory for the Color Glass Condensate. This is a functional Fokker-Planck equation which generates in particular the non-linear evolution equations previously derived by Balitsky and Kovchegov within perturbative QCD. In the limit where the transverse momentum of the external probe is large compared to the saturation momentum, our approximations yield the Gaussian Ansatz for the effective action of the McLerran-Venugopalan model. In the opposite limit, of a small external momentum, we find that the effective theory is governed by a scale-invariant universal action which has the correct properties to describe gluon saturation.
We consider a nonlinear evolution equation recently proposed to describe the small-$x$ hadronic physics in the regime of very high gluon density. This is a functional Fokker-Planck equation in terms of a classical random color source, which represents the color charge density of the partons with large $x$. In the saturation regime of interest, the coefficients of this equation must be known to all orders in the source strength. In this first paper of a series of two, we carefully derive the evolution equation, via a matching between classical and quantum correlations, and set up the framework for the exact background source calculation of its coefficients. We address and clarify many of the subtleties and ambiguities which have plagued past attempts at an explicit construction of this equation. We also introduce the physical interpretation of the saturation regime at small $x$ as a Color Glass Condensate. In the second paper we shall evaluate the expressions derived here, and compare them to known results in various limits.