In our previous paper we applied U-spin symmetry to charmless hadronic $B^{\pm }\to M^0{M}^{\pm }$ decays for the purpose of precise extraction of the unitarity angle $\gamma$. In this paper we extend our approach to neutral $B^0$ and $B_s\to M_1{M}_2$ decays. A very important feature of this method is that no assumptions regarding relative sizes of topological decay amplitudes need to be made. As a result, this method avoids an uncontrollable theoretical uncertainty that is often related to the neglect of some topological diagrams (e.g., exchange and annihilation graphs) in quark-diagrammatic approaches. In charged $B^{\pm }$ decays, each of the four data sets, $P^0{P}^{\pm }$, $P^0{V}^{\pm }$, $V^0{P}^{\pm }$ and $V^0{V}^{\pm }$, with $P\equiv \mathrm{\text{pseudoscalar}}$ and $V\equiv \mathrm{\text{vector}}$, can be used to obtain a value of $\gamma$. Among neutral decays, only experimental data in the $B^0$, $B_s\to P^{-}{P}^{+}$ subsector is sufficient for a U-spin fit. Application of the U-spin approach to the current charged and neutral $B$ decay data yields: $\gamma =({80}_{-8}^{+6})°$. In this method, which is completely data driven, in a few years we should be able to obtain a model-independent determination of $\gamma$ with an accuracy of O(few degrees).

• Received 18 September 2006

DOI:https://doi.org/10.1103/PhysRevD.75.054006