The behavior of the structure function by using the effective exponent at low-x

Abstract

An analytical solution of the QCD evolution equations for the singlet and gluon distribution is presented. We decouple DGLAP evolution equations into the initial conditions by using a Laplace transform method at $N^{n}LO$ analysis. The relationship between the nonlinear behavior and color dipole model is considered based on an effective exponent behavior at low-$x$ values. We obtain the effective exponent at NLO analysis from the decoupled behavior of the distribution functions. The proton structure function compared with H1 data from the inclusive structure function $F_2(x,Q^2)$ for $x\le 10^{-2}$ and $5\le Q^2\le 250Ge{V}^2$.

arXiv comment18pages, 13 figurs

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Cited by in corpus (10)

• An Evaluation of The Proton Structure Functions $F_2$ and $F_L$ at Small $x$
• The Color Dipole Picture and extracting the ratio of structure functions at small $x$
• Longitudinal structure function from the parton parameterization
• Ratio of the structure functions and the color dipole model bound
• Nonlinear corrections on the parameterization methods
• The exponent of the longitudinal structure function $F_L$ at low $x$
• The study of the gluon distribution function and reduced cross section behavior using the proton structure function
• Importance of the heavy-quarks longitudinal structure function measurements at future circular collider energies
• Proton structure functions at low $x$: the Fractal distributions
• Geometrical scaling of heavy-quark contributions in the low $x$ region