The longitudinal structure function in the presence of QED effects

Abstract

The highest precision for theoretical predictions at the high LHC energy requires the calculation of parton distribution function (PDFs) and the structure functions which include heavy quarks that include perturbative QCD and QED corrections. In this paper, the first, we review calculation of PDFs with QED corrections that we obtain them from the QCD⊗QED DGLAP evolution equations in Mellin space in NLO QCD and NLO QED approximations. We give a detailed explanation of the approach that we follow to determine the longitudinal structure functions up to O(αs2) in QCD, O(ααs) and O(α2) in QED approximations. We show how our method gives an exact representation for the total longitudinal structure functions, FL(x,Q2), including the heavy quark structure functions in terms of the PDFs based on the Mellin transform techniques, valid to all orders in QED and QCD. In this work, we investigate the effects of the O(ααs) and O(α2) corrections to PDFs on the longitudinal structure functions. We compare our results with APFEL and experimental data in the different values of Q2. The results are shown that the QED corrections have a small but non-negligible impact on the structure functions.