$b \to d$ Penguins: CP Violation, General Lower Bounds on the Branching Ratios and Standard Model Tests

With the wealth of new data from the B-factories, b -> d penguin decays become available for study, in addition to their b -> s counterparts that have proven an indespensable tool for the exploration of new-physics effects in flavour physics. A prominent example of the b -> d penguin transitions is $\bar B^0_d \to K^0 \bar K^0$. We show that this decay can be charaterized in the Standard Model by a surface in the observable space of the direct and mixing-induced CP asymmetries and the branching ratio. The form of this surface, which is theoretically clean, implies a lower bound for the branching ratio that has recently been confirmed experimentally. If future measurements of the CP asymmetries yield a point away from the SM surface, this would be an interesting signal of new physics. We point out that the hadronic parameters in $\bar B^0_d \to K^0 \bar K^0$ that parameterize the position on the SM surface are related to hadronic parameters in the B -> pi K system. The fact that the branching ratio of $\bar B^0_d \to K^0 \bar K^0$ is very close to its lower bound yields interesting implications for B -> pi K even without knowledge of the CP asymmetries of $\bar B^0_d \to K^0 \bar K^0$. The mechanism that produces the lower bound for $\bar B^0_d \to K^0 \bar K^0$ is actually much more general; we derive lower bounds for various other b -> d penguin-induced processes, including B -> rho gamma and $B^\pm \to K^{(\ast)\pm} K^{(\ast)}$. Some of these theoretical lower bounds are very close to the current experimental upper bounds.