Abstract
We use the running coupling Balitsky-Kovchegov (rcBK) equation to study the rapidity dependence of saturation in inclusive HERA data and we discuss the behaviour of its numerical solution. The rcBK equation has been solved using Runge-Kutta methods. The influence of the parameters implicit in the numerical evolution has been studied. They include, among others, the order of the Runge-Kutta evolution, the size of the different grids and the step in the numerical evolution. Some suggestions on the minimum value of these parameters are put forward.
Highlights
One of the open questions in particle physics is particle production in the high-energy limit of QCD
The BFKL evolution equation predicts the emergence of new partons as the energy of the collision increases and in this approach, the gluon density is not bound by unitarity restrictions
An extension of the BFKL equation was found by Balitsky [6] and Kovchegov [7] (BK) resulting in an equation that generates dynamical balance between radiation and recombination processes driven by a saturation scale
Summary
Evolution equations such as BFKL [1,2,3,4,5] are used to describe the gluon density of the hadron in highenergy collisions. The integro-differential BK evolution equation [8,9,10] considered in this work, and denoted by rcBK in the following, includes a running-coupling kernel that takes into account two-loop processes and assumes an impact-parameter independent solution [11] It was derived from the JIMWLK evolution equations in the limit of large number of colors by Kovchegov [7, 12]. Numerical methods used to compute the rcBK solution need to be studied and an optimal setup regarding precision and speed of computation has to be tested in order to estimate the uncertainty coming from the non-analytic solution of rcBK equation
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