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 $r\equiv |T^{\prime }|/|\tilde{P}|$ 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.

Comments: 16 pages, LaTeX, 5 figures. The complete paper is also available via anonymous ftp at ftp://www-ttp.physik.uni-karlsruhe.de/ , or via www at http://www-ttp.physik.uni-karlsruhe.de/cgi-bin/preprints/