Analysis of the gluon distribution with next-to-leading order splitting function at small-x* *Supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB34030301), the National Natural Science Foundation of China (12375073), the Major Project of Basic and Applied Basic Research in Guangdong Province (2020B0301030008), the Basic Research Program (Natural Science) of Guizhou Province, China(QKHJC-ZK[2023]YB027), and the Education

Abstract

An approximated solution for the gluon distribution from DGLAP evolution equations with the NLO splitting function in the small-x limit is presented. We first obtain simplified forms of the LO and NLO splitting functions in the small-x limit. With these approximated splitting functions, we obtain the analytical gluon distribution using the Mellin transform. The free parameters in the boundary conditions are obtained by fitting the CJ15 gluon distribution data. We find that the asymptotic behavior of the gluon distribution is consistent with the CJ15 data; however, the NLO results considering the "ladder" structure of gluon emission are slightly better than the LO results. These results indicate that the corrections from NLO have a significant influence on the behavior of the gluon distribution in the small-x region. In addition, we investigate the DGLAP evolution of the proton structure function using the analytical solution of the gluon distribution. The differential structure function reveals that our results have a similar tendency to the CJ15 data at small-x.