Longitudinal structure function from logarithmic slopes of $F_2$ at low $x$

Abstract

Using Laplace transform techniques, I calculate the longitudinal structure function $F_L(x,Q^2)$ from the scaling violations of the proton structure function $F_2(x,Q^2)$, and make a critical study of this relationship between the structure functions at leading order (LO) up to next-to-next-to leading order (NNLO) analysis at small $x$. Furthermore, I consider heavy quark contributions to the relation between the structure functions, which leads to compact formula for $N_f=3+\mathrm{Heavy}$. The nonlinear corrections to the longitudinal structure function at LO up to NNLO analysis are shown in the $N_f=4$ (light quark flavor) based on the nonlinear corrections at $R=2$ and $R=4Ge{V}^{-1}$. The results are compared to experimental data of the longitudinal proton structure function $F_L$ in the range of $6.5\le Q^2\le 800Ge{V}^2$.

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Cited by in corpus (20)

• Extracting the longitudinal structure function FL(x,Q2) at small x from a Froissart-bounded parametrization of F2(x,Q2)
• 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
• 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
• The color dipole model bounds with the gluon-gluon recombination correction
• Decoupling of the structure functions in momentum space based on the Laplace transformation
• Higher order approximations to the longitudinal structure function $F_L$ from the parametrization of $F_2$ based on the Laplace transformation
• Nonlinear corrections on the parameterization methods
• The exponent of the longitudinal structure function $F_L$ at low $x$
• Effect of the parameterization of the distribution functions on the longitudinal structure function at small $x$
• Physical limits in the Color Dipole Model Bounds
• A determination of the longitudinal structure function $F_L$ from the parametrization of $F_2$ based on the Laplace transformation
• Approximation method for the nuclear structure functions at small $x$
• Proton structure functions at low $x$: the Fractal distributions
• Reduced cross-section in Electron-Ion Colliders at small $x$
• Color dipole cross-section from unifying the color dipole picture and improved saturation models
• GRANIITTI: A Monte Carlo Event Generator for High Energy Diffraction
• Longitudinal Structure Function at the Limit $x=Q^2/s$