Stokes Vector of Photon in the Decays B⁰ -> rho⁰ gamma and B⁰ -> K^* gamma

We consider a model for the decay Bbar^0 -> rho^0 gamma in which the short-distance amplitude determined by the Hamiltonian describing b -> d gamma is combined with a typical long-distance contribution Bbar^0 -> D^+ D^- -> rho^0 gamma. The latter possesses a significant dynamical phase which induces a CP-violating asymmetry A_CP, as well as an important modification of the Stokes vector of the photon. The components S_1 and S_3 of the Stokes vector S = (S_1, S_2, S_3) can be measured in the decay Bbar^0 -> rho^0 gamma^* -> pi^+ pi^- e^+ e^- where they produce a characteristic effect in the angular distribution d Gamma / d phi, phi being the angle between the pi^+ pi^- and e^+ e^- planes. A similar analysis is carried out for the decays Bbar^0 -> Kbar^* gamma and Bbar^0 -> Kbar^* gamma^* -> pi^+ K^- e^+ e^-