High Parton Density Research Articles

Probing the color glass condensate in an electron-ion collider

Perturbative Quantum Chromodynamics (pQCD) predicts that the small-$x$ gluons in a hadron wavefunction should form a Color Glass Condensate (CGC), characterized by a saturation scale $Q_s (x, A)$ which is energy and atomic number dependent. In this paper we study the predictions of CGC physics for electron - ion collisions at high energies. We consider that the nucleus at high energies acts as an amplifier of the physics of high parton densities and estimate the nuclear structure function $F_2^A(x,Q^2)$, as well as the longitudinal and charm contributions, using a generalization for nuclear targets of the Iancu-Itakura-Munier model which describes the $ep$ HERA data quite well. Moreover, we investigate the behavior of the logarithmic slopes of the total and longitudinal structure functions in the kinematical region of the future electron - ion collider eRHIC.

The PHENIX forward spectrometer upgrade

The forward spectrometer upgrade of the PHENIX detector aims to add capabilities at forward rapidities to: probe nucleon structure through W production and promptphotons in polarized p + p, study nucleon structure in nuclei at high parton densities in p + A collisions through the measurement of γ and π0 in the forward region, greatly extend the acceptance for high p T γ-jet measurements (jet tomography) in A + A, and increase our capabilities to measure the production quarkonium states by giving sensitivity to the χ c through the J/ψ + γ channel.

Impact Parameter Dependence of the Balitsky-Kovchegov Equation

A numerical solution, including the impact parameter dependence of the non-linear equation that governs the dynamics of high parton density QCD, is presented, for restricted size of the interacting dipole. The power-like tail in b → which violates the Proissart bound is eliminated. Comparison is made with results obtained assuming factorized b → dependence.

Charged particle distributions and transverse dynamics in Au+Au and d+Au collisions at √SNN = 200 GeV from STAR

Results of directed and elliptic flow measurements of charged hadrons at midrapidity and forward rapidities from Au+Au collisions at √SNN = 200 GeV will be presented. The pseudorapidity dependence of anistropic flow and mean transverse momentum will be discussed in connenction with the available particle density created in a heavy-ion collision. The measurements of the centrality dependence of dN/dη and transverse momentum spectra from mid-rapidity to forward rapidity in d+Au collisions at 200 GeV are shown to provide a sensitive tool for understanding the dynamics of multi-particle production in the high parton density regime. In particular an explanantion of the observed centrality and pseudorapidty dependence of RCP (and RdAu) at forward rapidities due to the initial asymmetry in particle production in d+Au collisions compared to the symmetric p+p collisions will be presented.

QCD at high parton density

The high parton density regime of Quantum Chromodynamics (QCD) is briefly discussed. Some phenomenological aspects of saturation are described, mainly focusing on possible signatures of the non-linear QCD dynamics in electron-proton/nucleus collisions. Implications of these effects in central and ultraperipheral heavy-ion collisions are also presented.

PARTON SATURATION APPROACH IN HEAVY QUARK PRODUCTION AT HIGH ENERGIES

The high parton density regime of the quantum chromodynamics (QCD), where the physics of parton saturation is expected to be dominant, is briefly discussed. Some phenomenological aspects of saturation are described, mainly focusing on possible signatures of the nonlinear QCD dynamics in the heavy quark production in electron–proton/nucleus collisions. Implications of these effects in the heavy quark production in ultraperipheral heavy-ion collisions are also presented.

Towards a new global QCD analysis: solution to the Balitsky–Kovchegov nonlinear equation at arbitrary impact parameter

A numerical solution of the nonlinear evolution equation that governs the dynamics of high parton density QCD, is presented. A solution is obtained by restricting the kinematical region in which the equation is valid. It is shown that the angle-integrated solution at large values of the impact parameter b falls off exponentially, i.e., as e − m b . In impact parameter distributions the power-like tail of the amplitude appears only after the inclusion of dipoles of size larger than the target, a configuration for which the nonlinear equation is not valid. The value, energy and impact parameter of the saturation momentum Q s ( y = ln ( 1 / x ) , b ) are calculated both for fixed and running QCD coupling cases. It is shown that the solution exhibits geometrical scaling behavior. The radius of interaction increases with rapidity in accordance with the Froissart theorem. The solution we obtain differs from previous treatments, where an ansatz for the b behavior was made. For the particular case of large fixed α s , the behavior of the solution obtained is similar to that found for running α s . However, in general the solutions for running and small fixed α s differ: for running α s , we obtain a larger radius of interaction, a steeper rapidity dependence, and a larger value of the saturation momentum.

PROTON NUCLEUS COLLISIONS AND THE COLOR GLASS CONDENSATE

We review the high parton density limit of QCD and show how the Color Glass Condensate arises at small xbj. We discuss the applications of the Color Glass Condensate formalism to proton (deuteron) nucleus collisions at high energy colliders, such as RHIC and LHC.

Additional $J/\Psi$ suppression from high density effects

At high energies the saturation effects associated to the high parton density should modify the behavior of the observables in proton-nucleus and nucleus-nucleus scattering. In this paper we investigate the saturation effects in the nuclear $J/\Psi$ production and estimate the modifications in the energy dependence of the cross section as well as in the length of the nuclear medium. In particular, we calculate the ratio of $J/\Psi$ to Drell-Yan cross sections and show that it is strongly modified if the high density effects are included. Moreover, our results are compared with the data from the NA50 Collaboration and predictions for the RHIC and LHC kinematic regions are presented. We predict an additional $J/\Psi$ suppression associated to the high density effects.

QCD saturation in the semi-classical approach

In this paper the semi-classical approach to the solution of non-linear evolution equation is developed. We found the solution in the entire kinematic region to the non-linear evolution equation that governs the dynamics in the high parton density QCD. The large impact parameter ( b t ) behaviour of the solution is discussed as well as the way how to include the non-perturbative QCD corrections in this region of b t . The geometrical scaling behaviour and other properties of the solution in the saturation (colour glass condensate) kinematic domain are analyzed. We obtain the asymptotic behaviour for the physical observables and found the unitarity bounds for them.

What are we learning from RHIC?

This talk is an attempt to summarize some of the first results obtained at RHIC. I discuss the significance of these measurements for establishing the properties of hot and dense QCD matter and for understanding the dynamics of the theory at the high parton density, strong color field frontier.

Important experimental observables at RHIC

In this talk I discuss the significance of the first RHIC measurements for establishing the properties of hot and dense QCD matter and for understanding the dynamics of the theory at the high parton density, strong color field frontier. Hopes and expectations for the future are discussed as well.

Polarized hyperons from pA scattering in the gluon saturation regime

We study the production of transversely polarized Λ hyperons in high-energy collisions of protons with large nuclei. The large gluon density of the target at saturation provides an intrinsic semi-hard scale which should naturally allow for a weak-coupling QCD description of the process in terms of a convolution of the quark distribution of the proton with the elementary quark–nucleus scattering cross section (resummed to all twists) and a fragmentation function. In this case of transversely polarized Λ production we employ a so-called polarizing fragmentation function, which is an odd function of the transverse momentum of the Λ relative to the fragmenting quark. Due to this kt-odd nature, the resulting Λ polarization is essentially proportional to the derivative of the quark–nucleus cross section with respect to transverse momentum, which peaks near the saturation momentum scale. Such processes might therefore provide generic signatures for high parton density effects and for the approach to the “black-body” (unitarity) limit of hadronic scattering.

Does parton saturation at high density explain hadron multiplicities at RHIC?

We discuss the recent claim that hadron multiplicities measured at RHIC energies are directly described in terms of gluon degrees of freedom fixed from the initial conditions of central heavy ion collisions. The argument is based on the parton saturation scenario expected to be valid at high parton densities and on the assumption of conserved gluon number. Alternatively we conjecture that “bottom-up” equilibration before hadronization modifies this picture, due to nonconservation of the number of gluons.

Inclusive gluon production in deep inelastic scattering at high parton density

We calculate the cross section of single inclusive gluon production in deep inelastic scattering at very high energies in the saturation regime, where the parton densities inside hadrons and nuclei are large and the evolution of structure functions with energy is nonlinear. The expression we obtain for the inclusive gluon production cross section is generated by this nonlinear evolution. We analyze the rapidity distribution of the produced gluons as well as their transverse momentum spectrum given by the derived expression for the inclusive cross section. We propose an ansatz for the multiplicity distribution of gluons produced in nuclear collisions which includes the effects of nonlinear evolution in both colliding nuclei.

Small x physics and the initial conditions in heavy ion collisions

At very high energies, the high parton densities (characterized by a semi-hard saturation scale \Lambda_s) ensure that parton distributions can be described by a classical effective field theory with remarkable properties analogous to those of spin glass systems. This color glass condensate (CGC) of gluons also provides the initial conditions for multi-particle production in high energy nuclear collisions. In this talk, we briefly summarize recent theoretical and phenomenological progress in the CGC approach to small x physics. In particular, we discuss recent numerical work on the real time gluodynamics of partons after a nuclear collision. The implications of this work for the theoretical study of thermalization in nuclear collisions and on the phenomenological interpretation of results of the recent RHIC experiments are also discussed.

Higher twist corrections and maxima for DIS on a proton in the high density QCD region

We show that the ratio of different structure functions have a maximum which depends on energy. We argue, using the Golec-Biernat and Wusthoff model as well as the eikonal approach, that these maxima are functions of the saturation scale. We analyze leading and higher twist contributions for different observables to check whether a kinematic region exists where high parton density effects can be detected experimentally.

Reggeization in High Energy QCD

We study QCD in the regime of high parton density arising in hadronic collisions at large center-of-mass energy. The n-gluon amplitudes of the generalized leading logarithmic approximation are investigated. We find identities relating amplitudes with different numbers of gluons in the t-channel. These identities constrain the reggeization of the gluon in high energy QCD. The tensors describing the reggeization of a gluon in color space are identified.

The description of F2 at very high parton densities

The behavior of the structure function at high energies (high densities) is directly associated to the gluon distribution. In this Letter we analyze the asymptotic behavior of the structure function at very high densities considering a leading and a higher twist relation between these two quantities. We verify that (a) if the leading twist relation between the structure function and the gluon distribution is used, we recover the black disc limit, and (b) a softer behavior is predicted if a higher twist relation between F 2 and xG is considered. While the first behavior is well-established by the current high density approaches, the higher twist behavior is a new result. In both cases, the F 2 structure function unitarizes and the Froissart boundary is not violated in the asymptotic regime of high density QCD.

Higher twists and maxima for DIS on nuclei in high density QCD region

We show that the ratio of different structure functions have a maximum which depends on xB and A. We argue that these maxima are proportional to the saturation scale. The analysis of leading and higher twist contributions for different observables is given with the aim of determining the kinematic region where high parton density effects could be seen experimentally.