Size of Penguin Pollution of the CKM CP Violating Phase in B-bar_s -> rho K_s

Abstract

We use the perturbative QCD methods of Lepage and Brodsky to calculate the rate for B-bar_s -> rho K_s, with an eye toward the CP violating unitarity triangle angle gamma. We show that, although the penguins are large, there are regions of the allowed parameter space of the Cabibbo-Kobayashi-Maskawa mixing matrix wherein gamma is measurable in the sense that penguins change the value of sin(2gamma) one would extract from the attendant time dependent asymmetry measurement by less than 29 per cent, so that a 3sigma measurement of sin(2gamma) as being different from 0 is allowed by the corresponding theoretical uncertainty. This would establish CP violation in B_s decays. The rates which we find tend to favor the type of luminosities now envisioned for hadron-based B-factories.