Motivated by recent CLEO measurements of $\overrightarrow{B}\pi K$ modes, we investigate their implications for the CKM angle $\gamma$ and a consistent description of these decays within the standard model. Interestingly it turns out that already the measurement of the combined branching ratios $B^{\pm }\to {\pi }^{\pm }K$ and $B_d\to {\pi }^{\mp }{K}^{\pm }$ allows us to derive stringent constraints on $\gamma$ which are complementary to the presently allowed range for that angle. This range, arising from the usual fits of the unitarity triangle, is typically symmetric around $\gamma =90\mathrm{}°$, while our method can in principle exclude a range of this kind. Consistency within the standard model implies furthermore bounds on the ratio $r\equiv |T^{\prime }|/|\tilde{P}|$ of the current-current and penguin operator contributions to $B_d\to {\pi }^{\mp }{K}^{\pm }$, and upper limits for the $\mathrm{CP}$-violating asymmetry arising in that decay. Commonly accepted means to estimate $r$ yield values at the edge of compatibility with the present CLEO measurements.

• Received 5 May 1997

DOI:https://doi.org/10.1103/PhysRevD.57.2752