ar X iv : h ep - p h / 03 09 16 6 v 1 1 5 Se p 20 03 Strong Phases in the Decays B to Dπ

The observed strong phase difference of 30 o between I = 3 2 and I = 1 2 final states for the decay B → Dπ is analyzed in terms of rescattering like D * π → Dπ, etc. It is concluded that for the decay B o → D + π − the strong phase is only about 10 o. Implications for the determination of sin (2β + γ) are discussed. The weak decay amplitude to a specific final state can be written as Ae iδ where A is the decay amplitude, in general complex, and δ is the " strong phase ". For a final eigenstate δ is simply the elastic scattering phase in accordance with the Watson theorem. For the case of B decays the final scattering is primarily inelastic; δ arises from the absorptive part of the decay amplitude corresponding to a weak decay to intermediate states followed by a strong scattering to the final state. Many papers have discussed the expected size of δ [1]. Recently data has suggested a significant non-zero phase for the decays B to Dπ [2]. These decays can be analyzed in terms of two amplitudes A 3 e iδ3 and A 1 e iδ1 corresponding to the final isospin states 3 2 and 1 2. The amplitudes for the three decays of interest are the following: