Size of Penguin Pollution of the CKM CP Violating Phase in B̄ s → ρK s ∗

We use the perturbative QCD methods of Lepage and Brodsky, together with the current field identity, to calculate the rate for ¯ B s → ρK s , with an eye toward the CP violating unitarity triangle angle γ. We show that , although the penguins are large, there are regions of the allowed parameter space of the Cabibbo-Kobayashi-Maskawa mixing matrix wherein γ is measurable in the sense that penguins change the value of sin(2γ) one would extract from the attendant time dependent asymmetry measurement by less than 29%. The rates which we find tend to favor the type of luminosities now envisioned for hadron-based B-factories. Now that there are two asymmetric e + e − colliding beam B-Factories, the SLAC-LBL-LLNL and KEK Asymmetric B-Factories, as well as several other B-Factory type machines, such as HERA-B, the CESAR upgrade, and the Tevatron upgrade, for example, under construction, the systematic exploitation of these machines for CP violation studies is not far away. To realize the true potential of these studies, it is important that the complete set of Standard Model CP violation parameters for the B-system be explored, if it is at all possible. In particular, this means that all CP violating angles α, β and γ of the unitarity triangle should be measured ,where we use the notation of [1] for these angles. The angle β is the " gold plated " angle of the triangle, as it will be the presumably the most readily measurable of the three angles, via the modes B → Ψ/JK s , Ψ/JK * + , and is in fact used to specify the minimal requirements for the B-Factory machine and detector system to be successful. (Here, K * + denotes the CP + neutral K * meson.) Accordingly, the B decay modes needed for measurement of the angles α and γ must also be identified and assessed. In this connection, the mode ¯ B 0 s → ρ + K s is worthy of some attention; for, were it not for the possible contamination from penguins, this mode would be a candidate mode for the measurement of γ [1]. Indeed, the potential contamination from penguins is just as substantial as it is for the mode ¯ B → π 0 π 0 in connection with the measurement of α, for which the authors [2] have devised isospin methods to combine the measurements of …