Alex Kovner

Wilson renormalization group for low {bold {ital x}} physics: Towards the high density regime

We continue the study of the effective action for low {ital x} physics based on a Wilson renormalization group approach. We express the full nonlinear renormalization group equation in terms of the average value and the average fluctuation of extra color charge density generated by integrating out gluons with intermediate values of x. This form clearly exhibits the nature of the phenomena driving the evolution and should serve as the basis of the analysis of saturation effects at high gluon density at small x. {copyright} {ital 1998} {ital The American Physical Society}

The BFKL equation from the Wilson renormalization group

Abstract We discuss the Wilson renormalization group approach to the effective action for low x physics. It is shown that in the linearized, weak field regime the RG equation reduces to the BFKL equation for the evolution of the unintegrated gluon density. We discuss the relation of this approach with that of Lipatov.

Intrinsic glue distribution at very small x

We compute the distribution functions for gluons at very small x and not too large values of transverse momenta. We extend the McLerran-Venugopalan model by using renormalization group methods to integrate out effects due to those gluons which generate an effective classical charge density for Weizs{umlt a}cker-Williams fields. We argue that this model can be extended from the description of nuclei at small x to the description of hadrons at yet smaller values of x. This generates a Lipatov-like enhancement for the intrinsic gluon distribution function and a nontrivial transverse momentum dependence as well. We estimate the transverse momentum dependence for the distribution functions, and show how the issue of unitarity is resolved in lepton-nucleus interactions. {copyright} {ital 1997} {ital The American Physical Society}

The Wilson renormalization group for low x physics: Gluon evolution at finite parton density

In this paper we derive the complete Wilson renormalization group equation which governs the evolution of the gluon distribution and other gluonic observables at low {ital x} and arbitrary density. {copyright} {ital 1998} {ital The American Physical Society}

Relating different approaches to nonlinear QCD evolution at finite gluon density

We analyze the relation between evolution equations at low x that have been derived in different approaches in the last several years. We show that the equation derived by Balitsky and Kovchegov is obtained from the Jalilian-Marian–Kovner–Leonidov–Weigert (JKLW) equation in the limit of small induced charge density. We argue that the higher nonlinearities resummed by the JKLW equation correspond, in physical terms, to the breakdown of the eikonal approximation when the gluon fields in the target are large.

Gluon production from non-Abelian Weizsäcker-Williams fields in nucleus-nucleus collisions.

We consider the collisions of large nuclei using the theory of McLerran and Venugopalan. The two nuclei are ultrarelativistic and sources of non-Abelian Weizs\ifmmode\ddot\else\textasciidieresis\fi{}acker-Williams fields. These sources are in the end averaged over all color orientations locally with a Gaussian weight. We show that there is a solution of the equations of motion for the two nucleus scattering problem where the fields are time and rapidity independent before the collision. After the collision the solution depends on proper time, but is independent of rapidity. We show how to extract the produced gluons from the classical evolution of the fields.

Gluon production at high transverse momentum in the McLerran-Venugopalan model of nuclear structure functions.

We consider the production of high transverse momentum gluons in the McLerran-Venugopalan model of nuclear structure functions. We explicitly compute the high momentum component in this model. We compute the nuclear target size {ital A} dependence of the distribution of produced gluons.

In pursuit of Pomeron loops: The Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner equation and the Wess-Zumino term

We derive corrections to the JIMWLK equation in the regime where the charge density in the hadronic wave function is small. We show that the framework of the JIMWLK equation has to be significantly modified at small densities in order to properly account for the noncommutativity of the charge density operators. In particular the weight function for the calculation of averages can not be real, but is shown to contain the Wess-Zumino term. The corrections to the kernel of the JIMWLK evolution which are leading at small density are resummed into a path ordered exponential of the functional derivative with respect to the charge density operator, thus hinting at intriguing duality between the high and the low density regimes.

Vector potential versus color charge density in low- x evolution

We reconsider the evolution equations for multigluon correlators derived by Jalilian-Marian, Kovner, and Weigert. We show how to derive these equations directly in terms of vector potentials (or color field strength) avoiding the introduction of the concept of color charge density in the intermediate steps. The two step procedure of deriving the evolution of the charge density correlators followed by the solution of classical equations for the vector potentials is shown to be consistent with direct derivation of evolution for vector potentials. In the process we correct some computational errors of Jalilian-Marian, Kovner, and Weigert and present the corrected evolution equations which have a somewhat simpler appearance.

Angular correlations in gluon production at high energy

We present a general, model independent argument demonstrating that gluons produced in high energy hadronic collision are necessarily correlated in rapidity and also in the emission angle. The strength of the correlation depends on the process and on the structure/model of the colliding particles. In particular we argue that it is strongly affected (and underestimated) by factorized approximations frequently used to quantify the effect.