Constraining the CKM angle $γ$ and penguin contributions through combined $B \to πK$ branching ratios

Motivated by recent CLEO measurements of $B\toπK$ modes, we investigate their implications for the CKM angle $γ$ and a consistent description of these decays within the Standard Model. Interestingly it turns out that already the measurement of the combined branching ratios $B^\pm\toπ^\pm K$ and $B_d\toπ^\mp K^\pm$ allows to derive stringent constraints on $γ$ 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 $γ= 90^\circ$, while our method can in principle exclude a range of this kind. Consistency within the Standard Model implies furthermore bounds on the ratio $r\equiv|T'|/|\tilde P|$ of the current-current and penguin operator contributions to $B_d\toπ^\mp K^\pm$, and upper limits for the 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.

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