Search forτ−→γμ−: A test of lepton number conservation

A search for the lepton mumber violating decay of the τ lepton to the γμ final state has been performed with the CLEO II detector at the Cornell ${\mathit{e}}^{+}$ ${\mathit{e}}^{\mathrm{-}}$ storage ring CESR. In a data sample that corresponds to an integrated luminosity of 1.55 ${\mathrm{fb}}^{\mathrm{-}1}$, we observe no candidates in the signal region. We thus determine an upper limit of B(${\mathrm{\tau }}^{\mathrm{-}}$→γ${\mathrm{\mu }}^{\mathrm{-}}$)<4.2×${10}^{\mathrm{-}6}$ at 90% confidence level.