The photon polarization in B -> X gamma in the standard model

Abstract

The standard model prediction for the $B\to X_{s,d}\gamma$ decay amplitude with a right-handed photon is believed to be tiny, suppressed by $m_{s,d}/m_b$, compared to the amplitude with a left-handed photon. We show that this suppression is fictitious: in inclusive decays, the ratio of these two amplitudes is only suppressed by $g_s/(4\pi )$, and in exclusive decays by ${\Lambda }_{QCD}/m_b$. The suppression is not stronger in $B\to X_d\gamma$ decays than it is in $B\to X_s\gamma$. We estimate that the time dependent CP asymmetries in $B\to K^{\ast }\gamma$, $\rho \gamma$, $K_S{\pi }^0\gamma$, and ${\pi }^{+}{\pi }^{-}\gamma$ are of order 0.1 and that they have significant uncertainties.

Comments: Clarifications in the exclusive section, references added