The study of the gluon distribution function and reduced cross section behavior using the proton structure function

Abstract

We present a set of formulas to extract the gluon distribution function and the reduced cross section from the proton structure function and its derivatives with respect to lnQ 2 in the next-tonext-to-leading order of the perturbative theory at low x based on a hard poemron exchange. The behavior of the DIS reduced cross section studied and compared with the experimental data, also these behaviors controlled by the nonlinear and higer twist corrections at low Q 2 . These results were augmented by including an additional higher-twist term in the description of the nonlinear correction. This additional term, modified nonlinear correction, improves the description of the reduced cross sections significantly at low values of Q 2 . Our calculations show a good agreement with the DIS experimental data throughout the low values of x. We discuss, furthermore, how this behavior can be determine the reduced cross section with respect to the proton parameterization at high-y values. These results within the next-to-next-to-leading order approximation at very low x can be applied in the LHeC and FCC-eh regions for analyses of ultra-high energy processes. The resulting predictions for σr suggest that further corrections are required for Q 2 less than about 3 GeV 2 .