Constraining the CKM angle $\gamma$ and penguin contributions through combined $B \to \pi K$ branching ratios

Abstract

Motivated by recent CLEO measurements of $B\to\pi K$ 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 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 $\gamma = 90^\circ$, 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 $B_d\to\pi^\mp K^\pm$, 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.