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

Abstract

Abstract We analytically solve the Sudakov suppressed Balitsky-Kovchegov evolution equation with fixed and running coupling constants in the saturation region. The analytic solution of the S-matrix shows that the rapidity dependence of the solution with the fixed coupling constant is replaced by the dependence in the smallest dipole running coupling case, as opposed to obeying the law found in our previous publication, where all the solutions of the next-to-leading order evolution equations comply with 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 for a part of the evolution decrease of the dipole amplitude introduced by the running coupling effect. To test the analytic findings, we calculate the numerical solutions of the Sudakov suppressed evolution equation, and the numerical results confirm the analytic outcomes. Moreover, we use the numerical solutions of the evolution equationto fit the HERA data. This demonstrates that the Sudakov suppressed evolution equation can achieve a good quality fit to the data.