CP violation in polarized $b \to d l^+ l^-$: A Detailed Standard Model Analysis

The electroweak CP violating rate asymmetries in the decay $b \to d l^+ l^-$ are reexamined in detail and updated. In particular, the rate asymmetries are studied when one of the final state leptons is polarised. We find an estimate for the asymmetry of (5-15)% in the polarised decay spectrum which is close to known results for the unpolarised case. Interestingly, in the region separating the $\rho-\omega$ and $c \bar c$ resonances, which is also theoretically cleanest, the polarised contribution to the asymmetry is larger than the unpolarised result. A $3\sigma$ signal for direct CP violation, requires about 10^{10} $B \bar B$ pairs at a B factory. In general these results indicate an asymmetric contribution from the individual polarisation states to the unpolarised CP asymmetry; an atribute for any new physics searches.