Heribert Weigert

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.

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}

Unitarity at small Bjorken x

Abstract This paper presents a solution to the nonlinear small- x “projectile side” evolution equations as derived by Balitskii in 1996. The solution is based on functional Fokker–Planck methods. The fixed point at small x is explicitly calculated and all correlation functions in this limit are determined. They show clear saturation and unitarization properties. Scaling laws that hold during the saturation phase and throughout the whole course of the evolution are established. The corresponding Langevin equations are given as a basis for numerical simulations opening the field for future studies of dynamical issues of the evolution not analytically accessible. The methods used may be extended to the “target side” equations of Jalilian-Marian, Kovner, Leonidov and Weigert.

Universal features of JIMWLK and BK evolution at small x

Abstract In this paper we present the results of numerical studies of the JIMWLK and BK equations with a particular emphasis on the universal scaling properties and phase space structure involved. The results are valid for near zero impact parameter in DIS. We demonstrate IR safety due to the occurrence of a rapidity-dependent saturation scale Q s ( τ ). Within the set of initial conditions chosen, both JIMWLK and BK equations show remarkable agreement. We point out the crucial importance of running coupling corrections to obtain consistency in the UV for both equations. Explicit studies of this have been performed with BK. Despite the scale breaking induced by the running coupling we find that evolution drives correlators towards an asymptotic form with near scaling properties. We discuss asymptotic features of the evolution, such as the τ - and A -dependence of Q s away from the initial condition.

Non linear gluon evolution in path-integral form

We explore and clarify the connections between two different forms of the renormalization group equations describing the quantum evolution of hadronic structure functions at small x. This connection is established via a Langevin formulation and associated path integral solutions that highlight the statistical nature of the quantum evolution, pictured here as a random walk in the space of Wilson lines. The results confirm known approximations, form the basis for numerical simulations and widen the scope for further analytical studies.

Intrinsic glue at very small x

Resummation of small x logarithms in deep inelastic scattering needs to take into account high density corrections in order to go beyond the region of validity of the BFKL equation. I describe an approach that allows to do this using classical color fields as resummation tool for the density effects within a Wilsonian renormalization group framework to resum the small x logarithms.