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

Abstract

The standard model prediction for the $B\to X_{s,d}γ$ 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 $g_s/(4π)$, and in exclusive decays by $Λ_{QCD}/m_b$. The suppression is not stronger in $B\to X_dγ$ decays than it is in $B\to X_sγ$. We estimate that the time dependent CP asymmetries in $B\to K^*γ$, $ργ$, $K_Sπ^0γ$, and $π^+π^-γ$ are of order 0.1 and that they have significant uncertainties.

Clarifications in the exclusive section, references added