Constraints on γ and strong phases from B→πK decays

As we pointed out recently, the neutral decays B-d --> pi K--/+(+/-) and B-d --> pi K-0 may provide non-trivial bounds on the CKM angle gamma. Here we reconsider this approach in the light of recent CLEO data, which took very interesting. In particular, the results for the corresponding CP-averaged branching ratios are in favour of strong constraints on gamma, where the second quadrant is preferred. Such a situation would be in conflict with the standard analysis of the unitarity triangle. Moreover, constraints on a CP-conserving strong phase delta (n) are in favour of a negative value of cos delta (n), which would be in conflict with the factorization expectation. In addition, there seems to be an interesting discrepancy with the bounds that are implied by the charged B --> piK system: whereas these decays favour a range for gamma that is similar to that of the neutral modes, they point towards a positive value of cos delta (c), which would be in conflict with the expectation of equal signs for cos delta (n) and cos delta (c).