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.

The Color Glass Condensate

I briefly review the physical picture of the saturated gluons at small-x as a Colour Glass Condensate, and the effective theory which forms the basis of this picture.

The Colour Glass Condensate

We present a global analysis of available data on inclusive structure functions and reduced cross sections measured in electron–proton scattering at small values of Bjorken-x, x<0.01, including the latest data from HERA on reduced cross sections. Our approach relies on the dipole formulation of DIS together with the use of the non-linear running coupling Balitsky–Kovchegov equation for the description of the small-x dynamics. We improve our previous studies by including the heavy quark (charm and beauty) contribution to the reduced cross sections, and also by considering a variable flavor scheme for the running of the coupling. We obtain a good description of the data, with the fit parameters remaining stable with respect to our previous analyses where only light quarks were considered. The inclusion of the heavy quark contributions resulted in a good description of available experimental data for the charm component of the structure function and reduced cross section provided the initial transverse distribution of heavy quarks was allowed to differ from (more specifically, to have a smaller radius than) that of the light flavors.

AAMQS: A non-linear QCD analysis of new HERA data at small-x including heavy quarks

We perform a global fit to the structure function F{sub 2} measured in lepton-proton experiments at small values of Bjorken-x, x{<=}0.01, for all experimentally available values of Q{sup 2}, 0.045 GeV{sup 2}{<=}Q{sup 2}{<=}800 GeV{sup 2}. We show that the recent improvements resulting from the inclusion of running coupling corrections allow for a description of data in terms of nonlinear QCD evolution equations. In this approach F{sub 2} is calculated within the dipole model with all Bjorken-x dependence described by the running coupling Balitsky-Kovchegov equation. Two different initial conditions for the evolution are used, both yielding good fits to data with {chi}{sup 2}/d.o.f.<1.1. The proton longitudinal structure function F{sub L}, not included in the fits, is also well described. Our analysis allows to perform a first principle extrapolation of the proton-dipole scattering amplitude once the initial condition has been fitted to presently available data. We provide predictions for F{sub 2} and F{sub L} in the kinematical regions of interest for future colliders and ultra-high energy cosmic rays. A numerical implementation of our results down to x=10{sup -12} is released as a computer code for public use.

Nonlinear QCD meets data: A global analysis of lepton-proton scattering with running coupling Balitsky-Kovchegov evolution

We study the solution of the nonlinear Balitsky-Kovchegov evolution equation with the recently calculated running coupling corrections [I. I. Balitsky, Phys. Rev. D 75, 014001 (2007). and Y. Kovchegov and H. Weigert, Nucl. Phys. A784, 188 (2007).]. Performing a numerical solution we confirm the earlier result of Albacete et al. [Phys. Rev. D 71, 014003 (2005).] (obtained by exploring several possible scales for the running coupling) that the high energy evolution with the running coupling leads to a universal scaling behavior for the dipole-nucleus scattering amplitude, which is independent of the initial conditions. It is important to stress that the running coupling corrections calculated recently significantly change the shape of the scaling function as compared to the fixed coupling case, in particular, leading to a considerable increase in the anomalous dimension and to a slow-down of the evolution with rapidity. We then concentrate on elucidating the differences between the two recent calculations of the running coupling corrections. We explain that the difference is due to an extra contribution to the evolution kernel, referred to as the subtraction term, which arises when running coupling corrections are included. These subtraction terms were neglected in both recent calculations. We evaluate numerically the subtractionmore » terms for both calculations, and demonstrate that when the subtraction terms are added back to the evolution kernels obtained in the two works the resulting dipole amplitudes agree with each other. We then use the complete running coupling kernel including the subtraction term to find the numerical solution of the resulting full nonlinear evolution equation with the running coupling corrections. Again the scaling regime is recovered at very large rapidity with the scaling function unaltered by the subtraction term.« less

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Solving The High Energy Evolution Equation Including Running Coupling Corrections

Saturation physics at HERA and RHIC: An unified description

In this paper, we investigate the saturation physics in diffractive deep inelastic electron-ion scattering. We estimate the energy and nuclear dependence of the ratio σdiff/σtot and predict the xℙ and β behavior of the nuclear diffractive structure function F2,AD(3)(Q2,β,xℙ). Moreover, we analyze the ratio RdiffA1,A2(Q2,β,xℙ)=F2,A1D(3)/F2,A2D(3), which probes the nuclear dependence of the structure of the pomeron. We show that saturation physics predicts that approximately 37% of the events observed at eRHIC should be diffractive.

Saturation in diffractive deep inelastic eA scattering

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 Qs(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 F2A(x,Q2), as well as the longitudinal and charm contributions, using a generalization for nuclear targets of the Iancu–Itakura–Munier model that 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.

Probing the color glass condensate in an electron-ion collider

Perturbative quantum chromodynamics predicts that the small-x gluons in a hadron wavefunction should form a color glass condensate (CGC), which has universal properties, which are the same for all hadrons or nuclei. Assuming this property, in this paper we cross-relate the current CGC descriptions of the ep HERA data and dAu RHIC data. In particular, we use the quark dipole scattering amplitude recently proposed by Kharzeev, Kovchegov and Tuchin (KKT) to explain the high pT particle suppression observed in dAu collisions at RHIC in our calculations of the proton and longitudinal structure functions. We present a detailed comparison between this parameterization and those proposed to describe the ep HERA data. We find that, due to its peculiar dependence on the energy and dipole separation, the KKT parameterization is able to describe the experimental ep data only in a limited kinematical range of photon virtualities.

Testing universality of the color glass condensate descriptions

In this paper we investigate the saturation physics in diffractive deep inelastic electron-ion scattering. We estimate the energy and nuclear dependence of the ratio $\sigma^{diff}/\sigma^{tot}$ and predict the $x_{\pom}$ and $\beta$ behavior of the nuclear diffractive structure function $F_{2,A}^{D(3)}(Q^2, \beta, x_{IP})$. Moreover, we analyze the ratio $R^{diff}_{A1,A2}(Q^2, \beta, x_{IP}) = F_{2,A1} ^{D(3)}/F_{2,A2} ^{D(3)}$, which probes the nuclear dependence of the structure of the Pomeron. We show that saturation physics predicts that approximately 37 % of the events observed at eRHIC should be diffractive.

M.S. Kugeratski

Papers

Saturation physics at HERA and RHIC: An unified description

Saturation in diffractive deep inelastic eA scattering

Probing the color glass condensate in an electron-ion collider

Testing universality of the color glass condensate descriptions

Saturation in diffractive deep inelastic eA scattering