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Measurement of the Pseudoscalar Decay Constant fDs Using Ds+ -> tau+ nu, tau+ -> rho+ anti-nu Decays

Analyzing 600/pb of e+e- collisions at 4170 MeV center-of-mass energy with the CLEO-c detector, we measure the branching fraction B(Ds+ -> tau+ nu)=(5.52\pm 0.57\pm 0.21)% using the tau+ -> rho^+ anti-nu decay mode. Combining with other CLEO measurements of B(Ds+ -> tau+ nu) we determine the pseudoscalar decay constant fDs = (259.7\pm 7.8\pm 3.4) MeV consistent with the value obtained from our Ds+ -> mu+ nu measurement of (257.6\pm 10.3\pm 4.3) MeV. Combining these measurements we find a value of fDs=(259.0 \pm 6.2\pm 3.0) MeV, that differs from the most accurate prediction based on unquenched lattice gauge theory of (241\pm 3) MeV by 2.4 standard deviations. We also present the first measurements of B(Ds+ -> K0 pi+ pi0)=(1.00\pm0.18\pm 0.04)%, and B(Ds+ -> pi+ pi0 pi0)=(0.65\pm0.13\pm 0.03)%, and measure a new value for B(Ds+ -> eta rho+)=(8.9\pm0.6\pm0.5)%.