Pomeron loop and running coupling effects in high energy QCD evolution

TL;DR

This paper investigates how running coupling affects high-energy QCD evolution with Pomeron loops using a simplified (1+1)D model. It demonstrates analytically and numerically that running coupling strongly suppresses fluctuation-driven Pomeron-loop effects, slowing front formation and diffusion so that the evolution remains effectively mean-field-like up to $Y \,\approx\,200$. The results attribute this suppression to the slow diffusion and delayed front formation rather than a mere reduction of the coupling, leading to approximate geometric scaling in the averaged amplitude. The findings support using BK-like mean-field approaches with running coupling for DIS and forward production and offer a potential explanation for the successful phenomenology at HERA, while outlining limitations and avenues for future universality studies.

Abstract

Within the framework of a (1+1)-dimensional model which mimics evolution and scattering in QCD at high energy, we study the influence of the running of the coupling on the high-energy dynamics with Pomeron loops. We find that the particle number fluctuations are strongly suppressed by the running of the coupling, by at least one order of magnitude as compared to the case of a fixed coupling, for all the rapidities that we have investigated, up to Y=200. This reflects the slowing down of the evolution by running coupling effects, in particular, the large rapidity evolution which is required for the formation of the saturation front via diffusion. We conclude that, for all energies of interest, processes like deep inelastic scattering or forward particle production can be reliably studied within the framework of a mean-field approximation (like the Balitsky-Kovchegov equation) which includes running coupling effects.

Figures (8)

• Figure 1: The (average) saturation scale and the corresponding velocity in the evolution at fixed coupling, as obtained via the numerical study of the one--dimensional model, for 3 values of $\alpha$. The results of the full evolution (thin lines) are compared to the respective predictions of the MFA (thick lines).
• Figure 2: The front dispersion in the fixed--coupling evolution for 3 values of $\alpha$; the respective values of the diffusion coefficient $D$ can be read off the figure on the right. Note the 'formation time' $Y_{\rm form}$ (which increases when decreasing $\alpha$) during which the dispersion remains negligible.
• Figure 3: The front dispersion in the evolution with running coupling, for $Y\le 200$ and 3 values of $\beta$.
• Figure 4: Left: A comparison between FC and RC results for the dispersion. Right: The front diffusion coefficient with running coupling, as extracted from a fit to the numerical results.
• Figure 5: The 3rd cumulant $C_3$ in the evolution with running coupling, for $Y\le 100$ and 3 values of $\beta$. For comparison, the fixed coupling result corresponding to $\alpha=0.1$ is also shown; note that, in order to fit inside this plot, the FC result has been divided by a factor of 20.