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

Abstract

As we pointed out recently, the neutral decays $B_d\to {\pi }^{\mp }{K}^{\pm }$ and $B_d\to {\pi }^{0}K$ 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 $\cos {\delta }_c$.

Comments: 5 pages, LaTeX, 2 figures. Talk given by R. Fleischer at ICHEP 2000, Osaka, Japan, 27 July - 2 August 2000. To appear in the Proceedings