First Measurement of the Quark-to-Photon Fragmentation Function

Earlier measurements at LEP of isolated hard photons in hadronic $Z$ decays attributed to radiation from primary quark pairs, have been extended in the ALEPH experiment to include hard photon production {\em inside} hadron jets. Events are selected where all particles combine democratically to form hadron jets, one of which contains a photon with a fractional energy $z\geq 0.7$. After statistical subtraction of non-prompt photons, the quark- to-photon fragmentation function, $D(z)$, is extracted directly from the measured prompt production rate. By taking into account the perturbative contributions to $D(z)$ obtained from an $\cal{O}(\alpha \alpha_S)$ QCD calculation, the unknown non-perturbative component of $D(z)$ is determined at high $z$. This measurement is compared with an earlier theoretical parametrisation widely used to determine the level of quark bremsstrahlung present in prompt photon production at the hadron colliders.