A study of the decay width difference in the $B^{0}_{s}-\overline{B}^{0}_{s}$ system using $\phi\phi$ correlations

In a data sample of about four million hadronic Z decays recorded with the ALEPH detector from 1991 to 1995, the $B^{0}_{s} \to D^{(*)+}_{s}D^{(*)-}_{s}$ decay is observed, based on tagging the nal state with two $\phi$ mesons in the same hemisphere. The $D^{(*)+}_{s}D^{(*)-} _{s}$ final state is mostly CP even and corresponds to the short-lived $B^0$ mass eigenstate. The branching ratio of this decay is measured to be BR$(B^{0}_{s}(short) \to D^{(*)+}_{s}D^{(*)-}_{s}) = (23\pm 10^{+19}_{-9})%$. A measurement of the lifetime of the $B^0$(short) gives 1.27$\pm$ 0.33$\pm$ 0.07 ps. The lifetime and branching ratio measurements allow two essentially independent estimates to be made of the relative decay width difference $\Delta\Gamma/\Gamma$ in the $B^{0}_{s}-\overline{B}^{0}_{s}$ system, corresponding to an average value $\Delta\Gamma/\Gamma = (25^{+21}_{-14})%.