Predictions for ${\bar \nu} \nu \gamma$ Production at LEP

We study predictions for the reaction $e^+e^- \to {\bar \nu} \nu (n \gamma)$. The complete one-loop corrections are taken into account and higher order contributions, in particular those for the observed real photons, are added whenever necessary. The event generator \KK MC, a general-purpose Monte Carlo generator for the process $e^+e^- \to \bar f f n\gamma$ based on the method of exclusive exponentiation, is used as the environment. We extend its applicability to the process $e^+e^- \to \bar \nu_l \nu_l n\gamma$, $l=e,\mu,\tau$, where the observation of at least a single $\gamma$ is required. The exponentiation is implemented in much the same way as for the s-channel process alone. In particular, all photonic effects present in the case of W exchange, which {\it cannot} be included in the s-channel exponentiation scheme, are calculated to a finite order only. The real hard photon matrix element is calculated up to ${\cal O} ({\alpha^2})$. Leading logarithmic contributions of the two-loop corrections and one-loop photonic corrections accompanying real single photon emission are included. The electroweak corrections are calculated with the DIZET library of the ZFITTER package. Numerical tests and predictions for typical observables are presented.