CP violation in inclusive and exclusive charmless B decays.

Abstract

Absorptive parts in penguin amplitudes lead to {ital CP}-violating partial rate asymmetries in {ital B}-meson decays. A careful study of the inclusive process reveals a subtlety in the implementation of this mechanism. Because of (1) the smallness of {ital V}{sub {ital u}{ital b}}/{ital V}{sub {ital c}{ital b}}, (2) the fact that {alpha}{sub {ital s}}({ital m}{sub {ital b}}) is not too small, and (3) the kinematic suppression of {ital c{bar c}} absorptive contribution, {ital O}({alpha}{sub {ital s}}{sup 2}) effects have to be kept consistently. We find a strong correlation between the {ital CP} rate asymmetries of the {ital b}{r arrow}{ital su{bar u}} mode and the purely loop-induced {ital b}{r arrow}{ital sd{bar d}} and {ital ss{bar s}} modes, which is a consequence of the constraints of {ital CPT} invariance. The semi-inclusive charmless {ital b}{r arrow}{ital su{bar u}} decay rate asymmetry is therefore negligibly small. With the (semi-)inclusive result as a guide, we estimate the rates and {ital CP} asymmetries for several exclusive several exclusive modes. Keeping only the perturbative, penguin-induced absorptive part, one finds that the modes due to {ital b}{r arrow}{ital su{bar u}} (e.g., {ital B}{sup {minus}}{r arrow}{ital K}{sup {minus}}{pi}{sup 0}) could have {ital CP} rate asymmetries opposite in sign withmore » respect to pure penguin modes (such as {ital B}{sup {minus}}{r arrow}{ital K}{sup {minus}}{phi}), contrary to naive expectations. Charmless {ital b}{r arrow}{ital d} transitions are also discussed. We emphasize that exclusive {ital b}{r arrow}{ital d} modes (such as {ital B}{sup {minus}}{r arrow}{ital K}{sup {minus}}{ital K}{sub {ital S}}) may be more promising for {ital CP} studies within the standard model. Many uncertainties and problems related to penguin processes are discussed and assessed in detail.« less