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Decoupling the NLO-coupled QED $\otimes$ QCD, DGLAP evolution equations, using Laplace transform method

Marzieh Mottaghizadeh

Department of Physics, Ferdowsi University of Mashhad, Mashhad, Iran

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Parvin Eslami

Department of Physics, Ferdowsi University of Mashhad, Mashhad, Iran

E-mail Address: eslami@um.ac.ir

Corresponding author.

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, and

Fatemeh Taghavi-Shahri

Department of Physics, Ferdowsi University of Mashhad, Mashhad, Iran

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https://doi.org/10.1142/S0217751X17500658Cited by:8 (Source: Crossref)

Abstract

We analytically solved the QED $\otimes$ QCD-coupled DGLAP evolution equations at leading order (LO) quantum electrodynamics (QED) and next-to-leading order (NLO) quantum chromodynamics (QCD) approximations, using the Laplace transform method and then computed the proton structure function in terms of the unpolarized parton distribution functions. Our analytical solutions for parton densities are in good agreement with those from CT14QED $(1.29 5^{2} < Q^{2} < 1 0^{10})$ (Ref. 6) global parametrizations and APFEL (A PDF Evolution Library) $(2 < Q^{2} < 1 0^{8})$ (Ref. 4). We also compared the proton structure function, $F_{2}^{p} (x, Q^{2})$ , with the experimental data released by the ZEUS and H1 collaborations at HERA. There is a nice agreement between them in the range of low and high $x$ and $Q^{2}$ .

Keywords:

PACS: 12.38.-t, 12.20.-m, 12.38.Bx, 12.39.-x

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