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.

arXiv commentwill be appear in Phys.Lett.B

References in corpus (59)

• New parton distribution functions from a global analysis of quantum chromodynamics
• The Three-Loop Splitting Functions in QCD: The Singlet Case
• New CTEQ global analysis of quantum chromodynamics with high-precision data from the LHC
• A Large Hadron Electron Collider at CERN: Report on the Physics and Design Concepts for Machine and Detector
• High-Energy Factorization and Small-X Deep Inelastic Scattering Beyond Leading Order
• Measurement of the neutral current cross section and F2 structure function for deep inelastic e+p scattering at HERA
• Parton Distributions of the Proton
• Physical Gluons and High $E_T$ Jets
• Small x: Two Pomerons!
• The Longitudinal Structure Function at the Third Order
• Measurement of the Proton Structure Function F_2 at Very Low Q^2 at HERA
• Measurement of the Proton Structure Function F_2 and σ_{tot}^{γ^* p} at Low Q^2 and Very Low x at HERA
• Measurement of the Inclusive e{\pm}p Scattering Cross Section at High Inelasticity y and of the Structure Function FL
• Measurement of the Inclusive ep Scattering Cross Section at Low Q^2 and x at HERA
• Measurement of the Proton Structure Function F_L at Low x
• On the Rise of the Proton Structure Function F_2 Towards Low x
• Double Asymptotic Scaling at HERA
• Improved Approximations for the Three-Loop Splitting Functions in QCD
• Measurement of the Longitudinal Proton Structure Function at HERA
• The asymptotic behaviour of parton distributions at small and large $x$
• Connection of the virtual ${\gamma }^{\ast }p$ cross section of $ep$ deep inelastic scattering to real $\gamma p$ scattering, and the implications for $\nu N$ and $ep$ total cross sections
• A Direct Test of Perturbative QCD at Small x
• Evidence for the saturation of the Froissart bound
• Experimental Confirmation that the Proton is Asymptotically a Black Disk
• Perturbative Evolution and Regge Behaviour
• The proton's gluon distribution
• Analytic derivation of the next-to-leading order proton structure function $F_2^p(x,Q^2)$ based on the Laplace transformation
• Improved Geometrical Scaling at the LHC
• VHEeP: A very high energy electron-proton collider
• Inclusive diffraction in future electron-proton and electron-ion colliders
• QCD coupling constant at NNLO from DIS data
• The Tensor Pomeron and Low-x Deep Inelastic Scattering
• Evolution of singlet structure functions from DGLAP equation at next-to-next-to-leading order at small-x
• Extracting the longitudinal structure function FL(x,Q2) at small x from a Froissart-bounded parametrization of F2(x,Q2)
• F_L proton structure function from the unified DGLAP/BFKL approach
• The Longitudinal Structure Function F${}_L$ as a Function of F${}_2$ and dF${}_2$/dlnQ${}^2$ at small x. The Next-to-Leading Analysis
• The Color Dipole Picture of low-x DIS: Model-Independent and Model-Dependent Results
• Longitudinal structure function from logarithmic slopes of $F_2$ at low $x$
• The Color Dipole Picture and the ratio of R(W, Q) = sigma L/sigma T
• Probing Proton Structure at the Large Hadron electron Collider
• Longitudinal structure function FL at small x extracted from the Berger-Block-Tan parametrization of F2
• The energy dependence of the saturation scale in DIS at low x
• Absorptive effects and power corrections in low $x$ DGLAP evolution
• The behavior of the structure function by using the effective exponent at low-x
• Effects of next-to-leading order DGLAP evolution on generalized parton distributions of the proton and deeply virtual Compton scattering at high energy
• Color Dipole picture at Low-x DIS: The Mass Range of Active Photon Fluctuations
• A Phenomenological Solution Small $x$ to the Longitudinal Structure Function Dynamical Behavior
• The Color Dipole Picture and extracting the ratio of structure functions at small $x$
• Working Group Report on the Structure of the Proton
• Longitudinal structure function from the parton parameterization
• Analytical solution of the longitudinal structure function $F_L$ in the leading and next-to-leading-order analysis at low x with respect to Laguerre polynomials method
• Ratio of the structure functions and the color dipole model bound
• The exponent of the longitudinal structure function $F_L$ at low $x$
• Study of HERA data at Low Q^2 and Low x
• The approximation method for calculation of the exponent of the gluon distribution-${\lambda }_g$ and the structure function-${\lambda }_S$ at low $x$
• Future Deep Inelastic Scattering with the LHeC
• The study of the gluon distribution function and reduced cross section behavior using the proton structure function
• Combining the small-x evolution and DGLAP for description of inclusive photon induced processes
• The "DIS and Related Subjects" Strategy Document: Fundamental Science from Lepton-Hadron Scattering

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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
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• 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
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