Abstract
An extended collinearly improved Balitsky-Kovchegov evolution equation in the target rapidity representation is derived by including the running coupling corrections during the expansion of the ``real'' $S$-matrix. We find that the running coupling brings important modifications to the evolution equation, as one can see that there are extra contributions to the evolution kernel once the running coupling is included. To identify the significance of the modifications, we numerically solve the evolution equation with and without the running coupling contributions during the $S$-matrix expansion. The numerical results show that the scattering amplitude is largely suppressed by the running coupling corrections, which indicate that one needs to consider the running coupling contributions during the derivation of the nonlinear evolution equation in the target rapidity representation.
Highlights
The color glass condensate (CGC) effective theory has proven to be a powerful theory to describe the strong interactions associated with high-energy and -density environments
We find that the running coupling brings important modifications to the evolution equation, as one can see that there are extra contributions to the evolution kernel once the running coupling is included
The leading-order (LO) CGC calculations, which refer to the derivation of the nonlinear Balitsky– Jalilian-Marian–Iancu–McLerran–Weigert–Leonidov– Kovner (Balitsky-JIMWLK) equation [1,2,3,4,5] and its mean-field version known as the Balitsky-Kovchegov (BK) equation [1,6], have been able to qualitatively describe many phenomenological results, such as the reduced cross section in deep inelastic scattering (DIS) [7,8] and single and double inclusive particle production in high-energy heavyion collisions [9,10,11,12,13]
Summary
The color glass condensate (CGC) effective theory has proven to be a powerful theory to describe the strong interactions associated with high-energy and -density environments. The main purpose of this paper is to extend the collinearly improved BK equation in the η representation to the full next-to-leadingorder case by including the running coupling corrections during the expansions of the “real” S-matrix. We obtain an extended “canonical” Balitsky-Kovchegov equation (exBK-η) whose evolution kernel is modified by the running coupling corrections as compared to the caBK-η equation. Its analytic solution shows that the exponent of the S-matrix has a linear dependence on rapidity instead of the quadratic rapidity dependence in the caBK-η case, which obeys a similar law as results in the Y representation in that the evolution speed of the dipole amplitude is suppressed. It is easy to find that there are eight extra terms resulting from the running coupling corrections, which indicate that the precision of the expansion of the S-matrix has a significant impact on the evolution equation. The running coupling effect has a large influence on the evolution speed of the front, which largely suppresses the rapidity evolution of the dipole amplitude
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