Branching ratios and CP violations of $B \to\rho (\omega) \gamma$ decays in the modified perturbative QCD approach and the relevant dark photonic decays of $B\to \rho (\omega) \gamma^\prime $

Abstract

In this work we study the radiative decays of $B\to \rho (\omega)\gamma$ processes in the modified perturbative QCD approach, where the transverse momenta of the quark and gluons envolved in the interaction process are kept, and the Sudakov factor is incorporated in the theoretical calculation, which are helpful to suppress the infrared end-point contribution. A critical infrared momentum cutoff scale is introduced, which is used to separate the soft and hard contributions in QCD. Then the form factors envolved in the radiative decays should be separated as hard and soft form factors. The hard form factors can be calculated with the perturbative QCD approach, while the soft form factors should be viewed as soft input parameters. The soft form factors can be obtained by confronting the theoretical calculation of the branching ratios of the radiative decay of $B$ meson with the experimental data. Summing the soft and hard form factors, we find that the total form factors are in fine agreement with that obtained by nonperturbative theoretical method, such as the light-cone sum rules of QCD. We also study $B\to \rho (\omega) \gamma^\prime$ decays by using the form factors obtained in the $B\to \rho (\omega)\gamma$ decay processes, where $\gamma^\prime$ is the dark photon introduced by the extra $U(1)$ symmetry model. The upper limit of the branching ratios of thes decays are estimated.