K(k)x: Decay Distributions, Branching Ratios and Cp Asymmetries

The semi-inclusive charmless hadronic decays B → K(K)X , where X is a hadronic recoil system containing no charmed and strange particles, are useful for studying direct CP violation and determining the weak phase γ . Direct CP violation can also be studied with exclusive or inclusive charmless hadronic B decays. Although theoretical uncertainties in inclusive decays may be small, it is experimentally hard to identify final states inclusively, while exclusive decays have a clear experimental signature, but the theoretical calculation is not as clean. Semiinclusive hadronic decays, which lie somewhere between inclusive and exclusive hadronic decays, have a small theoretical uncertainty and a clear experimental signature, thereby providing an interesting channel for studying direct CP violation. Here we report on a recent study 2 of B → K(K)X decays. Charmless hadronic B → K(K)X decays involve two types of amplitudes: b → u tree amplitudes and b → s penguin amplitudes. Direct CP violation arises due to the interference between two or more participating amplitudes with different weak and strong phases for a single decay mode. The effective Hamiltonian for charmless hadronic B decays with ∆S = 1 is given by