Abstract
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.
Highlights
Interesting and still not fully resolved aspects of Quantum Chromodynamics (QCD) at high energies
The simplest two-point correlator of Wilson lines, the dipole, i.e. U U †, is directly related to the gluon distribution function unintegrated over the transverse momentum, often called unintegrated dipole gluon density or transverse momentum dependent (TMD) gluon density1 probed in inclusive processes such as deep inelastic scattering
Correlators of four and more Wilson lines can be related to these non-universal TMD gluon distributions – the relation has been first shown at leading power [13,14,15] and recently beyond leading twist [16,17,18]
Summary
In the saturation domain, the occupation number of gluons inside a hadron is so large that they start to overlap. The BK equation is the mean field approximation to an infinite tower of entangled equations, describing the evolution in x of correlators of Wilson line operators U (xT ), stretching on the light-cone from minus to plus infinity, but positioned at a fixed transverse point xT (with respect to the light-cone directions). Intermediate or additional steps, such as the computation of correlation function of Wilson lines, can be implemented both in position and momentum spaces. The recent phenomenological fit to the F2 HERA data provided first estimates of these parameters They are, dependent on different implementation choices of the numerical framework used to solve the JIMWLK evolution equation. General information about the code can be found in Ref. [42]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
