Higher order approximations to the longitudinal structure function $F_L$ from the parametrization of $F_2$ based on the Laplace transformation

Abstract

We describe the determination of the longitudinal structure function $F_L$ at NLO and NNLO approximations, using Laplace transform techniques, into the parametrization of $F_2(x,Q^2)$ and its derivative with respect to $\ln Q^2$ at low values of the Bjorken variable $x$. The obtained results are comparable with others by considering the effect of the charm quark mass to the longitudinal structure function, which leads to rescaling variable for $n_f=4$. Numerical calculations and comparison with H1 data demonstrate that the suggested method provides reliable $F_L(x,Q^2)$ at small $x$ in a wide range of $Q^2$ values and can be applied as well in analyses of ultra-high energy processes with cosmic neutrinos. The obtained longitudinal structure functions with and without the LHeC simulated uncertainties [CERN-ACC-Note-2020-0002, LHeC Collaboration and FCC-he Study Group, P. Agostini et al., J. Phys. G: Nucl. Part. Phys. {\bf48}, 110501(2021).] are compared with the H1 Collaboration data [Eur.Phys.J.C{\bf74}, 2814(2014) and Eur.Phys.J.C{\bf71}, 1579 (2011)] and with the results from CT18 [Phys.Rev.D{\bf103}, 014013(2021)] parametrization model at NLO and NNLO approximations.

arXiv commentWill be appear in Phys.Rev.D

References in corpus (35)

• The Three-Loop Splitting Functions in QCD: The Singlet Case
• New CTEQ global analysis of quantum chromodynamics with high-precision data from the LHC
• Leptoproduction of Heavy Quarks II -- A Unified QCD Formulation of Charged and Neutral Current Processes from Fixed-target to Collider Energies
• High-Energy Factorization and Small-X Deep Inelastic Scattering Beyond Leading Order
• The Large Hadron-Electron Collider at the HL-LHC
• The Longitudinal Structure Function at the Third Order
• Measurement of the Inclusive e{\pm}p Scattering Cross Section at High Inelasticity y and of the Structure Function FL
• MRST partons generated in a fixed-flavour scheme
• Improved Approximations for the Three-Loop Splitting Functions in QCD
• On the Drell-Levy-Yan Relation to $O({\alpha }_s^2)$
• 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
• Analytic derivation of the next-to-leading order proton structure function $F_2^p(x,Q^2)$ based on the Laplace transformation
• A new numerical method for obtaining gluon distribution functions $G(x,Q^2)=xg(x,Q^2)$, from the proton structure function $F_2^{\gamma p}(x,Q^2)$
• Analytic treatment of leading-order parton evolution equations: theory and tests
• The role of F_L(x,Q^2) in parton analyses
• The Tensor Pomeron and Low-x Deep Inelastic Scattering
• Extracting the longitudinal structure function FL(x,Q2) at small x from a Froissart-bounded parametrization of F2(x,Q2)
• Measurements of the Separated Longitudinal Structure Function F_L from Hydrogen and Deuterium Targets at Low Q^2
• 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
• Dynamical NNLO parton distributions and the perturbative stability of F_L(x,Q^2)
• Longitudinal structure function from logarithmic slopes of $F_2$ at low $x$
• Application of the rescaling model at small Bjorken $x$ values
• An Evaluation of The Proton Structure Functions $F_2$ and $F_L$ at Small $x$
• Longitudinal structure function FL at small x extracted from the Berger-Block-Tan parametrization of F2
• Phenomenology of leading nucleon production in $ep$ collisions at HERA in the framework of fracture functions
• On the longitudinal structure function in the dipole model
• Comparison of NNLO DIS scheme splitting functions with results from exact gluon kinematics at small x
• A Phenomenological Solution Small $x$ to the Longitudinal Structure Function Dynamical Behavior
• Longitudinal structure function from the parton parameterization
• Effect of the parameterization of the distribution functions on the longitudinal structure function at small $x$
• The exponent of the longitudinal structure function $F_L$ at low $x$
• Future Deep Inelastic Scattering with the LHeC
• A determination of the longitudinal structure function $F_L$ from the parametrization of $F_2$ based on the Laplace transformation
• Analytical perturbation theory and Nucleon structure function in infrared region
• Dynamical next-to-next-to-leading order parton distributions and the perturbative stability of F_L(x,Q^2)

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