Analytic study of FL with the new combined data from color glass condensate

We perform a global analysis of the new combined data on inclusive structure functions in electron-proton scattering at small value of Bjorken x (x <= 0.01) in the framework of the color glass condensate. The new combined HERA data at small-x are studied by an analytic proton structure function. It is shown that the theoretical results of the analytic proton structure function are in agreement with the new combined experimental data. The longitudinal proton structure function is investigated with the analytic expression. It is demonstrated that our approach shows a very good description of the longitudinal structure function experimental data, which is evidence showing the saturation effect is a domination mechanism during the rapidity evolution of the gluon density at high energy.