An Evaluation of The Proton Structure Functions $F_2$ and $F_L$ at Small $x$

Abstract

We describe the determination of the DIS structure functions $F_2$ and $F_L$ by using the singlet Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) and Altarelli-Martinelli equations at small values of $x$. The determination of the longitudinal structure function is presented as a parameterization of $F_2(x,Q^2)$ and its derivative. Analytical expressions for ${\sigma }_r(x,Q^2)$ in terms of the effective parameters of the parameterization of $F_2(x,Q^2)$ and $F_L(x,Q^2)$ are presented. This analysis is enriched by including the higher-twist effects in calculation of the reduced cross sections which is important at low-$x$ and low-$Q^2$ regions. Numerical calculations and comparison with H1 data demonstrate that the suggested method provides reliable $F_L(x,Q^2)$ and ${\sigma }_r(x,Q^2)$ at low $x$ in a wide range of the low absolute four-momentum transfers squared ($1.5{\mathrm{GeV}}^2<Q^2<120{\mathrm{GeV}}^2$) at moderate and high inelasticity. Expanding the method to low and ultra low values of $x$ can be considered in the process analysis of new colliders. We compare the obtained longitudinal structure function with respect to the LHeC simulated uncertainties [CERN-ACC-Note-2020-0002, arXiv:2007.14491 [hep-ex] (2020)] with the results from CT18 [Phys.Rev.D{\bf103}, 014013(2021)] parametrization model.

will be appear in Phys.Lett.B

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Cited by in corpus (15)

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• The color dipole model bounds with the gluon-gluon recombination correction
• Higher order approximations to the longitudinal structure function $F_L$ from the parametrization of $F_2$ based on the Laplace transformation
• Effect of the parameterization of the distribution functions on the longitudinal structure function at small $x$
• Physical limits in the Color Dipole Model Bounds
• Heavy quark structure functions from unifying the color dipole picture and double asymptotic scaling approaches
• A determination of the longitudinal structure function $F_L$ from the parametrization of $F_2$ based on the Laplace transformation
• Reduced cross section and gluon distribution in a momentum-space approach
• Geometrical scaling of heavy-quark contributions in the low $x$ region
• Proton structure functions at low $x$: the Fractal distributions
• Color dipole cross-section from unifying the color dipole picture and improved saturation models
• Reduced cross-section in Electron-Ion Colliders at small $x$
• Investigation of proton structure function $F_2^p$ at HERA in light of an analytical solution to Balitsky-Kovchegov equation
• Longitudinal Structure Function at the Limit $x=Q^2/s$
• Investigation of the ratio $\frac{{\sigma }_r}{F_2}(Q^2/s,Q^2)$ in the momentum-space approach