Low-virtuality photon transitions ${\gamma }^{\ast }\to f\bar{f}$ and the photon-to-jet conversion function

Abstract

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 ${\gamma }^{\ast }\to q\bar{q}$. 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 ${\gamma }^{\ast }\to q\bar{q}$ conversion contribution to an integral over the imaginary part of the hadronic vacuum polarization and thus to the experimentally known quantity $\Delta {\alpha }_{\mathrm{had}}^{(5)}(M_{\mathrm{Z}}^2)$. 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 ${\gamma }^{\ast }\to q\bar{q}$ 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 ${\alpha }^2/{\alpha }_{\mathrm{s}}$ relative to the leading-order cross section.

Comments: 13 pages, 7 pdf-figures. Matches the journal version