Analytical solutions of the QCD⊗\otimesQED DGLAP evolution equations based on the Mellin transform technique in NLO approximation

In this paper we present a new and efficient analytical solutions for evolving the QED$\otimes$QCD DGLAP evolution equations in mellin space and obtain the parton distribution functions (PDFs) in perturbative QCD including the QED corrections. The validity of our analytical solutions, which have done in the next to leading order QCD and the leading order QED approximations, are checked with the initial parton distributions from newly released CT14QED global analysis code (Phys. Rev.D93,114015(2016)). The evolved parton distributions are in good agreement with CT14QED code and also with those from APFEL (Computer Physics Communications 185, 1647 (2014)) program

Phenomenological investigation of the parton distribution functions (PDFs) and the partonic luminosities in high energy LHC physics

The phenomenological investigation of parton distribution functions (PDFs) based on the “valon” model presented here from the QCD $$\otimes$$ QED coupled DGLAP evolution equations in the Mellin space. The PDFs are calculated at the next to leading order $${\mathcal {O}}(\alpha _s^2)$$ in QCD, and we consider the QED effects at $${\mathcal {O}}(\alpha )$$; $${\mathcal {O}}(\alpha \alpha _s)$$ and $${\mathcal {O}}(\alpha ^2)$$ approximations. We also investigate in detail the phenomenological implications of these PDFs on the partonic luminosities. We conclude that at the region of the large values for the di-lepton’s invariant mass, the luminosity combinations, quark–quark, quark–antiquark and gluon–gluon, get closer to the luminosity involving photons, suggesting possibly non-negligible phenomenological implications due to the photon channel. We Also done a perfect comparison of our results with those obtained by the NNPDF2.3QED set, NNPDF3.1luxQED set and APFEL and there are a nice agreement between them. We demonstrate the necessity of including QED corrections and photon-induced contributions for a correct determination of the parton distribution functions and partonic luminosities