Abstract
In this paper we discuss the effect of the complete leading-order QED corrections to the DGLAP equations in the perturbative evolution of parton distribution functions (PDFs). This requires the extension of the purely QCD DGLAP evolution, including a PDF for the photons and, consistently, also for the charged leptons $e^{\pm}$, $\mu^\pm$ and $\tau^\pm$. We present the implementation of the QED-corrected DGLAP evolution in the presence of photon and lepton PDFs in the APFEL program and, by means of different assumptions for the initial scale PDFs, we produce for the first time PDF sets containing charged lepton distributions. We also present phenomenological studies that aim to assess the impact of the presence of lepton PDFs in the proton for some relevant SM (and BSM) processes at the LHC at 13 TeV and the FCC-hh at 100 TeV. The impact of the photon PDF is also outlined for those processes.
Highlights
JHEP11(2015)194 are never included at the level of parton distribution functions (PDFs), this level of accuracy cannot be formally claimed at the level of the hadronic cross section
We present the implementation of the QED-corrected DGLAP evolution in the presence of photon and lepton PDFs in the APFEL program and, by means of different assumptions for the initial scale PDFs, we produce for the first time PDF sets containing charged lepton distributions
We quote total rates for qq → W +W +qq → + +ν ν qq and for + + → + + in table 2. For the former, we include all coupling combinations entering at leading order (LO), i.e. we evaluate this process at the orders |αsα2 + α3|2.2 As usual, we consider the case of the LHC and of the FCC-hh, requiring the two charged leptons to satisfy the cuts of eqs. (3.9) and (3.10), respectively
Summary
We will show how to extend the DGLAP equations in order to include the evolution of photon and lepton PDFs at leading order (LO) in QED. Combining the system of differential equations in eq (2.1) with the pure-QCD DGLAP equations that govern the evolution of gluons and quarks, we obtain the full (N)NLO QCD plus LO QED evolution in the presence of photons and leptons. The solution of this system is implemented in version 2.4.0, or later, of the APFEL evolution library [13]. It is worth stressing that, contrary to the approach described in the original reference of APFEL [13], in the new implementation of the coupled QCD+QED DGLAP equations the QCD and the QED evolutions are no longer treated separately and combined a posteriori.
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