Measurement of B(D_s+ -> mu+ nu_mu)/B(D_s+ -> phi mu+ nu_mu) and Determination of the Decay Constant f_{D_s}

We have observed $23.2 pm 6.0_{-0.9}^{+1.0}$ purely-leptonic decays of $D_s^+ -> mu^+ u_mu$ from a sample of muonic one prong decay events detected in the emulsion target of Fermilab experiment E653. Using the $D_s^+ -> phi mu^+ u_mu$ yield measured previously in this experiment, we obtain $B(D_s^+ --> mu^+ u_mu) / B(D_s^+ --> phi mu^+ u_mu) =0.16 pm 0.06 pm 0.03$. In addition, we extract the decay constant $f_{D_s}=194 pm 35 pm 20 pm 14 MeV$.