Measurement of the pseudoscalar decay constant ${f}_{{D}_{s}}$ using ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}\ensuremath{\nu}$, ${\ensuremath{\tau}}^{+}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{+}\overline{\ensuremath{\nu}}$ decays

Measurement of the pseudoscalar decay constant $f_{D_{s}}$ using $D_{s}^{+} \to τ^{+} ν$ , $τ^{+} \to ρ^{+} \bar{ν}$ decays

P. Naik et al. (CLEO Collaboration)

Phys. Rev. D 80, 112004 – Published 28 December 2009

Abstract

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 $B (D_{s}^{+} \to τ^{+} ν) = (5.52 \pm 0.57 \pm 0.21) %$ using the $τ^{+} \to ρ^{+} \bar{ν}$ decay mode. Combining with other CLEO measurements of $B (D_{s}^{+} \to τ^{+} ν)$ we determine the pseudoscalar decay constant $f_{D_{s}} = (259.7 \pm 7.8 \pm 3.4) MeV$ consistent with the value obtained from our $D_{s}^{+} \to μ^{+} ν$ measurement of $(257.6 \pm 10.3 \pm 4.3) MeV$ . Combining these measurements we find a value of $f_{D_{s}} = (259.0 \pm 6.2 \pm 3.0) MeV$ , 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 $B (D_{s}^{+} \to K^{0} π^{+} π^{0}) = (1.00 \pm 0.18 \pm 0.04) %$ , and $B (D_{s}^{+} \to π^{+} π^{0} π^{0}) = (0.65 \pm 0.13 \pm 0.03) %$ , and measure a new value for $B (D_{s}^{+} \to η ρ^{+}) = (8.9 \pm 0.6 \pm 0.5) %$ .