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

• 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 $\exp(-{\cal{O}}(\eta^2))$ rapidity dependence of the solution with the fixed coupling constant is replaced by the $\exp(-{\cal{O}}(\eta^{3/2}))$ 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 $\exp(-{\cal{O}}(\eta))$ 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 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.
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Wenchang Xiang, Mengliang Wang, Yanbing Cai and Daicui Zhou. Solution to the Sudakov suppressed Balitsky-Kovchegov equation and its application to the HERA data[J]. Chinese Physics C. doi: 10.1088/1674-1137/abc0cc
Wenchang Xiang, Mengliang Wang, Yanbing Cai and Daicui Zhou. Solution to the Sudakov suppressed Balitsky-Kovchegov equation and its application to the HERA data[J]. Chinese Physics C.
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沈阳化工大学材料科学与工程学院 沈阳 110142

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

###### Corresponding author: Dai-Cui Zhou, dczhou@mail.ccnu.edu.cn
• 1. Guizhou Key Laboratory in Physics and Related Areas, and Guizhou Key Laboratory of Big Data Statistic Analysis, Guizhou University of Finance and Economics, Guiyang 550025, China
• 2. Department of Physics, Guizhou University, Guiyang 550025, China
• 3. Guizhou Key Laboratory in Physics and Related Areas, Guizhou University of Finance and Economics, Guiyang 550025, China
• 4. Key Laboratory of Quark and Lepton Physics (MOE), and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China

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 $\exp(-{\cal{O}}(\eta^2))$ rapidity dependence of the solution with the fixed coupling constant is replaced by the $\exp(-{\cal{O}}(\eta^{3/2}))$ 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 $\exp(-{\cal{O}}(\eta))$ 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 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.

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