Low-virtuality photon transitions gamma* -> f(f)over-bar and the photon-to-jet conversion fundtion [Low-virtuality photon transitions γ⁎→ff¯ and the photon-to-jet conversion function]

The calculation of electroweak corrections to processes with jets in the final state involves contributions of low-virtuality photons leading to jets in the final state via the singular splitting γ⁎→qq¯. These singularities can be absorbed into a photon-to-jet “fragmentation function”, better called “conversion function”, since the physical final state is any hadronic activity rather than an identified hadron. Using unitarity and a dispersion relation, we relate this γ⁎→qq¯ conversion contribution to an integral over the imaginary part of the hadronic vacuum polarization and thus to the experimentally known quantity Δαhad(5)(MZ2). Therefore no unknown non-perturbative contribution remains that has to be taken from experiment. We also describe practical procedures following subtraction and phase-space-slicing approaches for isolating and cancelling the γ⁎→qq¯ singularities against the photon-to-jet conversion function. The production of Z+jet at the LHC is considered as an example, where the photon-to-jet conversion is part of a correction of the order α2/αs relative to the leading-order cross section.