Search for new phenomena using single photon events in the DELPHI detector at LEP

Data are presented on the reaction \epem~\into~\gamma + no other detected particle at center-of-mass energies, \sqs = 89.48 GeV, 91.26 GeV and 93.08 GeV. The cross section for this reaction is related directly to the number of light neutrino generations which couple to the \zz boson, and to several other phenomena such as excited neutrinos, the production of an invisible `X' particle, a possible magnetic moment of the tau neutrino, and neutral monojets. Based on the observed number of single photon events, the number of light neutrinos which couple to the \zz is measured to be N_\nu = 3.15 \pm 0.34. No evidence is found for anomalous production of energetic single photons, and upper limits at the 95\% confidence level are determined for excited neutrino production (BR < 4-9 \times 10^{-6}), production of an invisible `X' particle (\sigma < 0.1 pb), and the magnetic moment of the tau neutrino (< 5.2 \times 10^{-6} \mu_B). No event with the topology of a neutral monojet is found, and this corresponds to the limit \sigma < 0.044/\epsilon pb at the 95\% confidence level, where \epsilon is the unknown overall monojet detection efficiency.