Constraints on $\gamma$ and Strong Phases from $B\to\pi K$ Decays

As we pointed out recently, the neutral decays $B_d\to\pi^\mp K^\pm$ and $B_d\to\pi^0K$ may provide non-trivial bounds on the CKM angle $\gamma$. Here we reconsider this approach in the light of recent CLEO data, which look 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 $B\to\pi K$ 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 $\cos\delta_c$.