Long-range two-body final-state interactions and directCPasymmetry inB+→π+K0decay

Abstract

We present a calculation of the direct $\mathrm{CP}$ asymmetry ${A}_{\mathrm{CP}}^{\mathrm{dir}}$ for the process ${B}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{K}^{0}$ including the effects of long-range two-body inelastic final-state interactions (FSI). We admit four two-body channels in our calculation: ${B}^{+}\ensuremath{\rightarrow}({\ensuremath{\pi}}^{+}{K}^{0}),(\ensuremath{\eta}{K}^{+}),$ ${(D}_{s}^{+}{D}^{0})$ and the charge-exchange channel ${\ensuremath{\pi}}^{0}{K}^{+}.$ The strong scattering is described in terms of Pomeron and Regge exchanges. We find that the direct $\mathrm{CP}$ asymmetry is enhanced by a factor of $\ensuremath{\sim}3$ as a result of FSI, but remains well short of the claims of (10--20)% in recent literature. A critical assessment of papers claiming large $\mathrm{CP}$ asymmetries is also presented. Many-body decay channels could play an important role in direct $\mathrm{CP}$ asymmetry; however, their contribution is hard to estimate.