Search for the decay ${\mathrm{D}}^{+}$→${\mathrm{\mu }}^{+}$${\nu }_{\mathrm{\mu }}$ and an upper limit on the pseudoscalar decay constant

We report the results of a search for the leptonic decay ${\mathrm{D}}^{+}$→${\mathrm{\mu }}^{+}$ ${\nu }_{\mathrm{\mu }}$ using the Mark III detector at the SLAC ${\mathrm{e}}^{+}$ ${\mathrm{e}}^{\mathrm{-}}$ storage ring SPEAR. A data sample of 9.3 ${\mathrm{pb}}^{\mathrm{-}1}$ collected at the ψ(3770) resonance yields no signal events, corresponding to a 90%-confidence-level upper limit of 7.2×${10}^{\mathrm{-}4}$ on the branching ratio B(${\mathrm{D}}^{+}$→${\mathrm{\mu }}^{+}$ ${\nu }_{\mathrm{\mu }}$). This represents an upper limit on the pseudoscalar decay constant ${\mathrm{f}}_{\mathrm{D}}$ of 290 MeV/${\mathrm{c}}^2$.