Analytic derivation of the next-to-leading order proton structure function F2p(x,Q2) based on the Laplace transformation

Abstract

An analytical solution based on the Laplace transformation technique for the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi 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 p 2 (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 GJR08 [Eur. Phys. J C 53 (2008) 355-366] and KKT12 [J. Phys. G 40 (2013) 045002] parametrization models as well as the x-space results using 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 JR14, MMHT14, NNPDF and 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.

Global analysis on determination of fracture functions considering sea quark asymmetries in the nucleon

“…The uncertainties of nucleon FFs as well as the leadingnucleon structure functions have been obtained using the Hessian method [21,22,23,24,25,26,27,28].…”

QCD analysis of nucleon structure functions in deep-inelastic neutrino-nucleon scattering: Laplace transform and Jacobi polynomials approach

“…In recent years, using the Laplace transform technique, some analytical solutions of the DGLAP evolution equations have been reported [21][22][23][24][25][26][27][28] which reached considerable phenomenological success. There is also some progress to extract the analytical solutions of the proton spin-independent structure function F p 2 (x, Q 2 ) [16] and the spin-dependent one xg…”

“…criteria for the value of χ 2 in the goodness-of-fit test [64][65][66][67][68][69] which comes from the quality of the experimental data sets they used in their fits. In the results presented in our recent spin-dependant PDFs analysis [59] as well as in our nuclear PDFs analysis [16], we followed the standard parameter-fitting criterion and considered a 68% (1σ) confidence level (C.L.) limit by the choice of tolerance T = (∆χ 2 ) 1/2 = 1.…”

“…In our earlier work [16], we have made an extensive comparative study on the applicability of the Laplace transform technique to obtain the analytical solution for the proton structure function, F p 2 (x, Q 2 ). In the following manuscript, we present a detailed QCD analysis of charged-current structure functions xF 3 (x, Q 2 ) measured in neutrino-nucleon scattering at CCFR, NuTeV and CHORUS experiments.…”

EMC effect in the next-to-leading order approximation based on the Laplace transformation

“…To access the PDFs and then nPDFs, it is required to get the solution of Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations [6][7][8][9].DGLAP using the Laplace transform technique, some analytical solutions of these equations have been reported in recent * J.Sheibani@stu.yazd.ac.ir † A.Mirjalili@yazd.ac.ir (Corresponding Author) ‡ Atashbart@gmail.com years [10][11][12][13][14][15][16][17][18] ,which have resulted in noticeable success from the phenomenological point of view. There has also been some progress toward extracting the analytical solutions of the proton spin-independent structure function F p 2 (x, Q 2 ) [19], charged-current structure functions xF 3 (x, Q 2 ) [20], and also the spin-dependent one, i.e., xg p 1 (x, Q 2 ), at the next-to-leading order (NLO) and next-to-NLO (NNLO) approximations [21,22], using the Laplace transform technique.…”