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

Abstract

The standard model prediction for the $B\to X_{s,d}{\hat{I}}^3$ 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 $g_s/(4\ddot{I}€)$, and in exclusive decays by $\hat{I}{›}_{QCD}/m_b$. The suppression is not stronger in $B\to X_d{\hat{I}}^3$ decays than it is in $B\to X_s{\hat{I}}^3$. We estimate that the time dependent CP asymmetries in $B\to K^{\ast }{\hat{I}}^3$, $\ddot{I}{\hat{I}}^3$, $K_S\ddot{I}{€}^0{\hat{I}}^3$, and $\ddot{I}{€}^{+}\ddot{I}{€}^{-}{\hat{I}}^3$ are of order 0.1 and that they have significant uncertainties.

Clarifications in the exclusive section, references added