Universality of the saturation scale and the initial eccentricity in heavy ion collisions

Recent estimates that Color Glass Condensate initial conditions may generate a larger initial eccentricity for noncentral relativistic heavy ion collisions (relative to the initial eccentricity assumed in earlier hydrodynamic calculations) have raised the possibility of a higher bound on the viscosity of the Quark Gluon Plasma. We show that this large initial eccentricity results in part from a definition of the saturation scale as proportional to the number of nucleons participating in the collision. A saturation scale proportional to the nuclear thickness function (and therefore independent of the probe) leads to a smaller eccentricity, albeit still larger than the value used in hydrodynamic models. Our results suggest that the early elliptic flow in heavy ion collisions (unlike multiplicity distributions) is sensitive to the universality of the saturation scale in high energy QCD.Comment: 5 pages, 3 figures, RevTE

Anomalous dimensions from rotating open strings in AdS/CFT

We propose a new entry within the dictionary of the AdS/CFT duality at strong coupling: in the limit of a large spin or a large R-charge, the anomalous dimension of the gauge theory operator dual to a semiclassical rotating string is proportional to the string proper length. This conjecture is motivated by a generalization to strings of the rule for computing anomalous dimensions of massive particles and supergravity fields in the anti-de Sitter space. We show that this proportionality holds for a rotating closed string in global AdS space, representing a high spin operator made of fields in the adjoint representation. It is also valid for closed strings rotating in $S^5$ (representing operators with large R-charge), for closed strings with multiple AdS spin, and for giant magnons. Based on this conjecture, we calculate the anomalous dimension $\delta$ of operators made of fields in the fundamental representation, associated with high spin mesons, and which are represented by rotating open strings attached to probe D7-branes. The result is a logarithmic dependence upon the spin, $\delta\sim \sqrt{\lambda}\ln S$, similar to the closed string case. We show that the operator properties --- anomalous dimension and spin --- are obtained from measurements made by a local observer in the anti-de Sitter space. For the open string case, this ensures that these quantities are independent of the mass scale introduced by the D7-branes (the quark mass), as expected on physical grounds. In contrast, properties of the gauge theory states, like the energy, correspond to measurements by a gauge theory observer and depend upon the mass scale --- once again, as expected.Comment: V2: two related references include

The Color Glass Condensate

We provide a broad overview of the theoretical status and phenomenological applications of the Color Glass Condensate effective field theory describing universal properties of saturated gluons in hadron wavefunctions that are extracted from deeply inelastic scattering and hadron-hadron collision experiments at high energies.Comment: 41 pages, 18 figures, submitted to the Annual Review of Nuclear and Particle Science

Violation of kT factorization in quark production from the Color Glass Condensate

We examine the violation of the kT factorization approximation for quark production in high energy proton-nucleus collisions. We comment on its implications for the open charm and quarkonium production in collider experiments.Comment: 4 pages, 6 figures, contribution to proceedings of Quark Matter 2005, Budapest, Aug 4-

Low x saturation at HERA ?

We compare the predictions of two distinct dipole models for inclusive and exclusive diffractive processes. While only one of these dipole models contains perturbative saturation dynamics, we show that the predictions of both models are fully consistent with the available HERA data, indicating no compelling evidence for saturation at present HERA energies.Comment: 8 pages, 4 figures, presented at the 26th Montreal-Rochester-Syracuse-Toronto (MRST) conference held at Concordia University, Montreal, Canada, 12th-14th May 2004. To appear in the proceeding

Infrared instability from nonlinear QCD evolution

Using the Balitsky-Kovchegov (BK) equation as an explicit example, we show that nonlinear QCD evolution leads to an instability in the propagation toward the infrared of the gluon transverse momentum distribution, if one starts with a state with an infrared cut-off. This effect takes the mathematical form of rapidly moving traveling wave solutions of the BK equation, which we investigate by numerical simulations. These traveling wave solutions are different from those governing the transition to saturation, which propagate towards the ultraviolet. The infrared wave speed, formally infinite for the leading order QCD kernel, is determined by higher order corrections. This mechanism could play a role in the rapid decrease of the mean free path in the Color Glass Condensate scenario for heavy ion collisions.Comment: 12 pages, 8 figures. Update to match version in Nuclear Physics

From RHIC to EIC: Nuclear Structure Functions

We study the nuclear structure function $F_2^A$ and its logarithmic derivative in the high energy limit (small $x$ region) using the Color Glass Condensate formalism. In this limit the structure function $F_2$ depends on the quark anti-quark dipole-target scattering cross section $N_F (x_{bj}, r_t, b_t)$. The same dipole cross section appears in single hadron and hadron-photon production cross sections in the forward rapidity region in deuteron (proton)-nucleus collisions at high energy, i.e. at RHIC and LHC. We use a parameterization of the dipole cross section, which has successfully been used to describe the deuteron-gold data at RHIC, to compute the nuclear structure function $F_2^A$ and its log $Q^2$ derivative (which is related to gluon distribution function in the double log limit). We provide a quantitative estimate of the nuclear shadowing of $F_2^A$ and the gluon distribution function in the kinematic region relevant to a future Electron-Ion Collider.Comment: 13 pages, 6 figure

QCD traveling waves at non-asymptotic energies

Using consistent truncations of the BFKL kernel, we derive analytical traveling-wave solutions of the Balitsky-Kovchegov saturation equation for both fixed and running coupling. A universal parametrization of the ``interior'' of the wave front is obtained and compares well with numerical simulations of the original Balitsky-Kovchegov equation, even at non-asymptotic energies. Using this universal parametrization, we find evidence for a traveling-wave pattern of the dipole amplitude determined from the gluon distribution extracted from deep inelastic scattering data.Comment: 10 pages, 5 figures, minor revision, version to appear in PL

Recent Developments in the Nuclear Many-Body Problem

The study of quantum chromodynamics (QCD) over the past quarter century has had relatively little impact on the traditional approach to the low-energy nuclear many-body problem. Recent developments are changing this situation. New experimental capabilities and theoretical approaches are opening windows into the richness of many-body phenomena in QCD. A common theme is the use of effective field theory (EFT) methods, which exploit the separation of scales in physical systems. At low energies, effective field theory can explain how existing phenomenology emerges from QCD and how to refine it systematically. More generally, the application of EFT methods to many-body problems promises insight into the analytic structure of observables, the identification of new expansion parameters, and a consistent organization of many-body corrections, with reliable error estimates.Comment: 15 pages, 10 figures, plenary talk at the 11th Conference on Recent Progress in Many-Body Theories (MB 11), Manchester, England, 9-13 Jul 200

Initial and Final State Interaction Effects in Small-x Quark Distributions

We study the initial and final state interaction effects in the transverse momentum dependent parton distributions in the small-$x$ saturation region. In particular, we discuss the quark distributions in the semi-inclusive deep inelastic scattering, Drell-Yan lepton pair production and dijet-correlation processes in $pA$ collisions. We calculate the quark distributions in the scalar-QED model and then extend to the color glass condensate formalism in QCD. The quark distributions are found universal between the DIS and Drell-Yan processes. On the other hand, the quark distribution from the $qq'\to qq'$ channel contribution to the dijet-correlation process is not universal. However, we find that it can be related to the quark distribution in DIS process by a convolution with the normalized unintegrated gluon distribution in the color glass condensate formalism in the large $N_c$ limit.Comment: 20 pages, 6 figure