Measurement of the pseudoscalar decay constant fDs using Ds+→τ+ν, τ+→ρ+ν decays

Analyzing 600 pb(-1) of e(+)e(-) collisions at 4170 MeV center-of-mass energy with the CLEO-c detector, we measure the branching fraction B(D-s(+)->tau(+)nu)=(5.52 +/- 0.57 +/- 0.21)% using the tau(+)->rho(+)nu decay mode. Combining with other CLEO measurements of B(D-s(+)->tau(+)nu) we determine the pseudoscalar decay constant f(Ds)=(259.7 +/- 7.8 +/- 3.4) MeV consistent with the value obtained from our D-s(+)->mu(+)nu measurement of (257.6 +/- 10.3 +/- 4.3) MeV. Combining these measurements we find a value of f(Ds)=(259.0 +/- 6.2 +/- 3.0) MeV, that differs from the most accurate prediction based on unquenched lattice gauge theory of (241 +/- 3) MeV by 2.4 standard deviations. We also present the first measurements of B(D-s(+)-> K-0 pi(+)pi(0))=(1.00 +/- 0.18 +/- 0.04)%, and B(D-s(+)->pi(+)pi(0)pi(0))=(0.65 +/- 0.13 +/- 0.03)%, and measure a new value for B(D-s(+)->eta rho(+))=(8.9 +/- 0.6 +/- 0.5)%.