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To help the difficult determination of the angle $\gamma$ of the unitaritytriangle, Aleksan, Dunietz and Kayser have proposed the modes of the type$K^-D^+_s$, common to $B_s$ and $\bar{B}_s$. We point out that it is possibleto gain in statistics by a sum over all modes with ground state mesons in thefinal state, i.e. $K^-D^+_s$, $K^{*-}D_+^s$, $K^-D^{*+}_s$, $K^{*-}D^{*+}_s$.The delicate point is the relative phase of these different contributions tothe dilution factor $D$ of the time-dependent asymmetry. Each contribution to$D$ is proportional to a product $F^{cb}$ $F^{ub}$ $f_{D_s}$ $f_K$ where $F$denotes form factors and $f$ decay constants. Within a definite phaseconvention, lattice calculations do not show any change in sign whenextrapolating to light quarks the form factors and decay constants. Then, wecan show that all modes contribute constructively to the dilution factor,except the $P$-wave $K^{*-}D^{*+}_s$, which is small. Quark model argumentsbased on wave function overlaps also confirm this stability in sign. By summingover all these modes we find a gain of a factor 6 in statistics relatively to$K^-D^+_s$. The dilution factor for the sum $D_{tot}$ is remarkably stable fortheoretical schemes that are not in very strong conflict with data on $B \to\psi K(K^*)$ or extrapolated from semileptonic charm form factors, giving$D_{tot} \geq 0.6$, always close to $D(K^- D^+_s)$.Comment: 22 pages, LPTHE Orsay 94/03, DAPNIA/SPP/94-2

Determination of the CP violating phase γ by a sum over common decay modes toB s and $$\bar B_s $$