Combining CP Asymmetries in B → Kπ Decays

We prove an approximate equality, to leading order in dominant terms, between CP-violating rate differences in B/B 0 → Kπ and B → Kπ. We propose several versions of averaged asymmetry measurements in these two processes, for which present data are already capable of yielding a statistically significant nonzero result in the most favorable case of weak and strong phases. PACS codes: 12.15.Hh, 12.15.Ji, 13.25.Hw, 14.40.Nd Up to now, CP violation has only been observed in the mixing of neutral K meson states [1]. Thus, it remains to be confirmed that CP violation in the kaon system arises from phases in the Cabibbo-Kobayashi-Maskawa matrix [2] describing weak charge-changing transitions of quarks. Such evidence can be provided by B meson decays, in which the standard model predicts sizable CP asymmetries between partial rates of B mesons and their corresponding antiparticles [3]. Model-dependent calculations of CP asymmetries in B decays to a pair of charmless pseudoscalar mesons have been carried out by a large number of authors [4]. In the present Letter we study relations between direct CP asymmetries in B → Kπ decays. Observation of three of these decays, B → Kπ, B → Kπ and B → Kπ, combining processes with their charge conjugates, was reported recently by CLEO [5, 6]. The number of events in these modes is 43, 38, and 12, respectively. Permanent Address: Physics Department, Technion – Israel Institute of Technology, 32000 Haifa, Israel.