<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>CP</mml:mi></mml:math>violation in inclusive and exclusive charmless<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi></mml:math>decays

Abstract

Absorptive parts in penguin amplitudes lead to CP-violating partial rate asymmetries in 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 VubVcb, (2) the fact that s(mb) is not too small, and (3) the kinematic suppression of cc absorptive contribution, O(s2) effects have to be kept consistently. We find a strong correlation between the CP rate asymmetries of the b'suu mode and the purely loop-induced b sdd and sss modes, which is a consequence of the constraints of CPT invariance. The semi-inclusive charmless b'suu decay rate asymmetry is therefore negligibly small. With the (semi-)inclusive result as a guide, we estimate the rates and CP asymmetries for several exclusive modes. Keeping only the perturbative, penguin-induced absorptive part, one finds that the modes due to b'suu (e.g., B-'K-0) could have CP rate asymmetries opposite in sign with respect to pure penguin modes (such as B-'K-), contrary to naive expectations. Charmless b'd transitions are also discussed. We emphasize that exclusive b'd modes (such as B-'K-KS) may be more promising for CP studies within the standard model. Many uncertainties and problems related to penguin processes are discussed and assessed in detail.