b → 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 B^-0 _d → K⁰K^-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 B^-0 _d → K⁰K^-0 that parameterize the position on the SM surface are related to hadronic parameters in the B → πK system. The fact that the branching ratio of B^¯0 _d → K⁰K^-0 is very close to its lower bound yields interesting implications for B → πK even without knowledge of the CP asymmetries of B^¯0 _d → K⁰K^{¯ 0}. The mechanism that produces the lower bound for B^¯0 _d → K⁰K^-0 is actually much more general; we derive lower bounds for various other b → d penguin-induced processes, including B → ργ and B^± → K^{(*) ±}K^(*). Some of these theoretical lower bounds are very close to the current experimental upper bounds.