Dynamical behavior connection of the gluon distribution and the proton structure function at small $x$

Abstract

We make a critical study of the relationship between the singlet structure function $F_2^S$ and the gluon distribution $G(x,Q^2)$ proposed in the past two decades, which is frequently used to extract the gluon distribution from the proton structure function. We show that a simple relation is not generally valid in the simplest state. We complete this relation by using a Laplace transform method and hard-pomeron behavior at LO and NLO at small $x$. Our study shows that this relation is dependent on the splitting functions and initial conditions at $Q^2=Q_0^2$ and running coupling constant at NLO. The resulting analytic expression allows us to predict the proton structure function with respect to the gluon distributions and to compare the results with H1 data and a QCD analysis fit. Comparisons with other results are made and predictions for the proposed best approach are also provided.

arXiv comment8 pages,5 figures

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Cited by in corpus (4)

• Solution of QCD$\otimes$QED coupled DGLAP equations at NLO
• Ratio of the structure functions and the color dipole model bound
• Nonlinear corrections on the parameterization methods
• The study of the gluon distribution function and reduced cross section behavior using the proton structure function