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.

Will be appear in Phys.Rev.D

References in corpus (10)

• MRST partons generated in a fixed-flavour scheme
• 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
• Extracting the longitudinal structure function FL(x,Q2) at small x from a Froissart-bounded parametrization of F2(x,Q2)
• Longitudinal structure function from logarithmic slopes of $F_2$ at low $x$
• Application of the rescaling model at small Bjorken $x$ values
• A Phenomenological Solution Small $x$ to the Longitudinal Structure Function Dynamical Behavior
• Effect of the parameterization of the distribution functions on the longitudinal structure function at small $x$
• A determination of the longitudinal structure function $F_L$ from the parametrization of $F_2$ based on the Laplace transformation
• Dynamical next-to-next-to-leading order parton distributions and the perturbative stability of F_L(x,Q^2)
• Analytical perturbation theory and Nucleon structure function in infrared region

Cited by in corpus (8)

• The unintegrated gluon distribution from the GBW and BGK models
• Decoupling of the structure functions in momentum space based on the Laplace transformation
• Color dipole cross section in the DGLAP improved saturation model
• An analysis of the fragmentation function of gluon at next-to-leading order approximation
• Nonlinear corrections for the nuclear gluon distribution in $eA$ processes
• Top cross section in the LHeC and FCC-he energy range
• Reduced cross-section in Electron-Ion Colliders at small $x$
• Color dipole cross-section from unifying the color dipole picture and improved saturation models