Updated Measurement of {cal B}(B_s to D_s^((*)+)D_s^((*)-)) and Determination of Delta Gamma_(s)

Using fully reconstructed $B_{s}$ mesons, we measure exclusive branching fractions for the decays $B_s \to D_s^{(*)+}D_s^{(*)-}$. The results are ${\cal B}(B^0_s\ra D^+_s D^-_s)=(0.58\,^{+0.11}_{-0.09}\,\pm 0.13)%$, ${\cal B}(B^0_s\ra D^{*\pm}_s D^{\mp}_s)=(1.8\, \pm 0.2\,\pm 0.4)%$, and ${\cal B}(B^0_s\ra D^{*+}_s D^{*-}_s)=(2.0\,\pm 0.3\,\pm 0.5)%$; the sum is ${\cal B}(B^0_s\ra D^{(*)+}_s D^{(*)-}_s)=(4.3\,\pm 0.4\,\pm 1.0)%$. Assuming these decay modes saturate decays to CP-even final states, the branching fraction determines the relative width difference between the $B_s$ CP-odd and CP-even eigenstates. Taking \cp\ violation to be negligibly small, we obtain $\dgs/\gs = 0.090\,\pm 0.009\,{\rm(stat.)}\,\pm 0.022 \,{\rm (syst.)}$, where $\gs$ is the mean decay width. The results are based on a data sample collected with the Belle detector at the KEKB $e^+ e^-$ collider running at the $\Upsilon(5S)$ resonance with an integrated luminosity of 121.4 fb$^{-1}$.