In studies of electron‑positron collisions, physicists treat the incoming lepton as a composite object. The probability of finding an electron, a positron or a photon inside the incoming particle is encoded in parton‑density functions (PDFs). These PDFs obey evolution equations that were originally developed for strongly interacting quarks and gluons but have been adapted to the electromagnetic theory of QED.

Using this framework, researchers calculated how much the cross section for final‑state radiation changes when photons or lepton pairs are emitted from the initial state. At the mass of the Z boson (√s≈91.2 GeV) with no invariant‑mass cut, the leading photonic correction is –32.75 %. When a cut on the minimal invariant mass is applied (zmin=0.8) the correction reduces to –19.71 %. In both cases the leading pair correction remains essentially zero. A more detailed table shows the full set of coefficients for different cuts and energies.