Determination of pseudoscalar-charmed-meson decay constants fromB-meson decays

Abstract

Recent progress in understanding form factors for weak $B\to D$ and $B\to D^{*}$ transitions, combined with a factorization hypothesis, allows one to extract the pseudoscalar-meson decay constant $f_{D_s}=259\mathrm{}\pm 74$ MeV, implying that the branching ratios for $D_s\to \tau {\overline{\nu }}_{\tau }$ and $D_s\to \mu {\overline{\nu }}_{\mu }$ are (4.6±2.6)% and (0.5±0.3)%, respectively. A scaling law for nonrelativistic wave functions then implies $f_D=207\mathrm{}\pm 60$ MeV, $f_B=140\mathrm{}\pm 40$ MeV, and $f_{B_s}=175\mathrm{}\pm 50$ MeV. Other consequences of the approach include a prediction that the branching ratio of ${\overline{B}}^0$ to $D^{*+}{D}^{*-}$ is about 0.06%, of which 94% occurs in the $CP=+$ final state.