Measurement of the Absolute Branching Fractions for $D^-_s\!\rightarrow\!\ell^-\bar{\nu}_{\ell}$ and Extraction of the Decay Constant $f_{D_s}$

TL;DR

This paper measures the absolute branching fractions of $D_s^-$ meson leptonic decays and extracts the decay constant $f_{D_s}$ using a large data sample from the Belle detector, providing precise experimental results.

Contribution

The study provides the first precise measurement of $D_s^-$ leptonic decay branching fractions and determines the decay constant $f_{D_s}$ with improved accuracy.

Findings

Measured $D_s^- ightarrow au^-ar{ u}_ au$, $ ext{e}^-ar{ u}_e$, and $ ext{mu}^-ar{ u}_ ext{mu}$ branching fractions.

Determined $f_{D_s} = (258.6 ext{ MeV})$ with statistical and systematic uncertainties.

Results are consistent with theoretical predictions and previous measurements.

Abstract

The absolute branching fractions for the decays $D^-_s\!\rightarrow\!\ell^-\bar{\nu}_{\ell}$ ($\ell=e$, $\mu$, or $\tau$) are measured using a data sample corresponding to an integrated luminosity of 521 fb$^{-1}$ collected at center of mass energies near 10.58 GeV with the \mbox{\slshape B\kern-0.1em{\smaller A}\kern-0.1em B\kern-0.1em{\smaller A\kern-0.2em R}} detector at the PEP-II $e^+e^-$ collider at SLAC. The number of $D^-_s$ mesons is determined by reconstructing the recoiling system $DKX\gamma$ in events of the type $e^+e^-{\rightarrow}DKXD^{*-}_s$, where $D^{*-}_s\rightarrow D^-_s\gamma$ and $X$ represents additional pions from fragmentation. The $D^-_s\!\rightarrow\!\ell^-\bar{\nu}_{\ell}$ events are detected by full or partial reconstruction of the recoiling system $DKX\gamma\ell$. The branching fraction measurements are combined to determine the $D^-_s$ decay constant $f_{D_s} = (258.6 \pm 6.4 \pm 7.5)$ MeV, where the first uncertainty is statistical and the second is systematic.