Solution to the Sudakov suppressed Balitsky-Kovchegov equation and its application to the HERA data

TL;DR

This paper analytically solves the Sudakov suppressed Balitsky-Kovchegov equation in the saturation region, revealing modified rapidity dependence due to sub-leading logarithmic corrections, and demonstrates its good fit to HERA data.

Contribution

The paper provides the first analytic solution to the Sudakov suppressed BK equation with fixed and running coupling, highlighting the importance of sub-leading logarithms in evolution.

Findings

Analytic solution shows modified rapidity dependence in the saturation region.

Numerical solutions confirm the analytic results.

The evolution equation fits HERA data well.

Abstract

We analytically solve the Sudakov suppressed Balitsky-Kovchegov evolution equation with the fixed and running coupling constants in the saturation region. The analytic solution of the $S$-matrix shows the $\exp(\mathcal{O}(\eta^2))$ rapidity dependence of the solution with the fixed coupling constant is replaced by $\exp(\mathcal{O}(\eta^{3/2}))$ dependence in the smallest dipole running coupling case rather than obeying the law found in our previous publication, in which all the solutions of the next-to-leading order evolution equations comply with $\exp(\mathcal{O}(\eta))$ rapidity dependence once the QCD coupling is switched from the fixed coupling to the smallest dipole running coupling prescription. This finding indicates that the corrections of the sub-leading double logarithms in the Sudakov suppressed evolution equation are significant, which compensate part of the evolution decrease of the dipole amplitude made by running coupling effect. To test the analytic findings, we calculate the numerical solutions of the Sudakov suppressed evolution equation, the numerical results confirm the analytic outcomes. Moreover, we use the numerical solutions of the evolution equation to fit the HERA data. It shows that the Sudakove suppressed evolution equation can give good quality fit to the data.