Analytic derivation of the next-to-leading order proton structure function $F_2^p(x,Q^2)$ based on the Laplace transformation

Abstract

An analytical solution based on the Laplace transformation technique for the DGLAP evolution equations is presented at next-to-leading order accuracy in perturbative QCD. This technique is also applied to extract the analytical solution for the proton structure function, $F_2^p(x,Q^2)$, in the Laplace $s$-space. We present the results for the separate parton distributions for all parton species, including valence quark densities, the anti-quark and strange sea parton distribution functions (PDFs), and the gluon distribution. We successfully compare the obtained parton distribution functions and the proton structure function with the results from {\tt GJR08} and {\tt KKT12} parametrization models as well as the $x$-space results using {\tt QCDnum} code. Our calculations show a very good agreement with the available theoretical models as well as the deep inelastic scattering (DIS) experimental data throughout the small and large values of $x$. The use of our analytical solution to extract the parton densities and the proton structure function is discussed in detail to justify the analysis method considering the accuracy and speed of calculations. Overall, the accuracy we obtain from the analytical solution using the inverse Laplace transform technique is found to be better than 1 part in 10${}^4$ to 10${}^5$. We also present a detailed QCD analysis of non-singlet structure functions using all available DIS data to perform global QCD fits. In this regard we employ the Jacobi polynomial approach to convert the results from Laplace $s$ space to Bjorken $x$ space. The extracted valence quark densities are also presented and compared to the {\tt JR14}, {\tt MMHT14}, {\tt NNPDF} and {\tt CJ15} PDFs sets. We evaluate the numerical effects of target mass corrections (TMCs) and higher twist (HT) terms on various structure functions, and compare fits to data with and without these corrections.

25 Pages, 11 Figures and 3 Tables

References in corpus (21)

• Parton distributions for the LHC
• LHAPDF6: parton density access in the LHC precision era
• Parton distributions in the LHC era: MMHT 2014 PDFs
• Constraints on large-$x$ parton distributions from new weak boson production and deep-inelastic scattering data
• QCDNUM: Fast QCD Evolution and Convolution
• Measurement of the inclusive jet cross section in $p\bar{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$
• Dynamical parton distributions of the nucleon and very small-x physics
• A Critical Appraisal and Evaluation of Modern PDFs
• Global analysis of nuclear parton distribution functions and their uncertainties at next-to-next-to-leading order
• Impact of CLAS and COMPASS data on Polarized Parton Densities and Higher Twist
• On the role of heavy flavor parton distributions at high energy colliders
• Specialized minimal PDFs for optimized LHC calculations
• Physics at a 100 TeV pp collider: Standard Model processes
• Next-to-next-to-leading order QCD analysis of spin-dependent parton distribution functions and their uncertainties: Jacobi polynomials approach
• Non-singlet QCD analysis of F_2(x,Q^2) up to NNLO
• Study of HERA ep Data at Low Q^2 and Low x_Bj and the Need for Higher-Twist Corrections to Standard pQCD Fits
• The curvature of $F_2^p(x,Q^2)$ as a probe of the range of validity of perturbative QCD evolutions in the small-$x$ region
• Fragmentation functions of the pion, kaon, and proton in the NLO approximation: Laplace transform approach
• Evolving images of the proton: Hadron physics over the past 40 years
• Combined Electroweak and QCD Fit to HERA Data
• $x{F}_3(x,Q^2)$ Structure Function and Gross-Llewellyn Smith Sum Rule with Nuclear Effect and Higher Twist Correction

Cited by in corpus (36)

• Nucleon spin structure functions at NNLO in the presence of target mass corrections and higher twist effects
• First determination of $D^{\ast +}$-meson fragmentation functions and their uncertainties at next-to-next-to-leading order
• Analytical approaches to the determination of spin-dependent parton distribution functions at NNLO approximation
• Study of spin-dependent structure functions of ${}^3\mathrm{He}$ and ${}^3\mathrm{H}$ at NNLO approximation and corresponding nuclear corrections
• Longitudinal structure function from logarithmic slopes of $F_2$ at low $x$
• Analytical solutions of the QCD$\otimes$QED DGLAP evolution equations based on the Mellin transform technique in NLO approximation
• Solution of QCD$\otimes$QED coupled DGLAP equations at NLO
• An Evaluation of The Proton Structure Functions $F_2$ and $F_L$ at Small $x$
• Phenomenology of leading nucleon production in $ep$ collisions at HERA in the framework of fracture functions
• Determination of neutron fracture functions from a global QCD analysis of leading neutron production at HERA
• The behavior of the structure function by using the effective exponent at low-x
• Longitudinal structure function from the parton parameterization
• 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
• The color dipole model bounds with the gluon-gluon recombination correction
• Probing nuclear modifications of parton distribution functions through the isolated prompt photon production at the LHC
• Ratio of the structure functions and the color dipole model bound
• Nuclear longitudinal structure function in eA processes at the LHeC
• EMC effect in the next-to-leading order approximation based on the Laplace transformation
• Decoupling the NLO coupled QED $\otimes$ QCD, DGLAP evolution equations,Using Laplace Transform Method
• On phenomenological study of the solution of nonlinear GLR-MQ evolution equation beyond leading order
• Improved determination of $\bar{d}(x)-\bar{u}(x)$ flavor asymmetry in the proton by BONuS experiment at JLAB and using an approach by Brodsky, Hoyer, Peterson, and Sakai
• Recent data analysis to revisit the spin structure function of nucleon in Laplace space
• Physical limits in the Color Dipole Model Bounds
• Parton distribution functions with QED corrections in the valon model
• The study of the gluon distribution function and reduced cross section behavior using the proton structure function
• Analytic derivation of the non-linear gluon distribution function
• QCD analysis of non-singlet structure functions at NNLO accuracy, based on the Laplace transform
• Study of the $s-\bar{s}$ asymmetry in the proton
• Nuclear parton distribution functions (nPDFs) and their uncertainties in the LHC Era
• A determination of the longitudinal structure function $F_L$ from the parametrization of $F_2$ based on the Laplace transformation
• QCD analysis of leading-neutron production at HERA: Determination of neutron fracture functions
• Global analysis on determination of fracture functions considering sea quark asymmetries in the nucleon
• Evolution of entropy at small $x$
• Investigation of the ratio $\frac{{\sigma }_r}{F_2}(Q^2/s,Q^2)$ in the momentum-space approach
• Nucleon spin structure functions, considering target mass correction and higher twist effects at the NNLO accuracy and their transverse momentum dependence