Regular Article - Theoretical Physics
On systematic effects in the numerical solutions of the JIMWLK equation
Institute of Theoretical Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348, Kraków, Poland
2 Center for Theoretical Physics, Massachusetts Institute of Technology, 02139, Cambridge, MA, USA
3 Faculty of Physics, Adam Mickiewicz University, Uniwersytetu Poznańskiego 2, 61-614, Poznan, Poland
4 Institut für Theoretische Physik, Universität Regensburg, 93040, Regensburg, Germany
5 Physics Faculty, AGH University of Science and Technology, ul. Mickiewicza 30, 30-059, Kraków, Poland
6 Institute of Nuclear Physics Polish Academy of Sciences, 31342, Kraków, Poland
7 CPHT, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, 91128, Palaiseau, France
Accepted: 24 June 2021
Published online: 29 July 2021
In the high energy limit of hadron collisions, the evolution of the gluon density in the longitudinal momentum fraction can be deduced from the Balitsky hierarchy of equations or, equivalently, from the nonlinear Jalilian–Marian–Iancu–McLerran–Weigert–Leonidov–Kovner (JIMWLK) equation. The solutions of the latter can be studied numerically by using its reformulation in terms of a Langevin equation. In this paper, we present a comprehensive study of systematic effects associated with the numerical framework, in particular the ones related to the inclusion of the running coupling. We consider three proposed ways in which the running of the coupling constant can be included: “square root” and “noise” prescriptions and the recent proposal by Hatta and Iancu. We implement them both in position and momentum spaces and we investigate and quantify the differences in the resulting evolved gluon distributions. We find that the systematic differences associated with the implementation technicalities can be of a similar magnitude as differences in running coupling prescriptions in some cases, or much smaller in other cases.
© The Author(s) 2021
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