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

We present a calculation of the direct $\mathrm{CP}$ asymmetry $A_{\mathrm{CP}}^{\mathrm{dir}}$ for the process $B^{+}\to {\pi }^{+}{K}^0$ including the effects of long-range two-body inelastic final-state interactions (FSI). We admit four two-body channels in our calculation: $B^{+}\to \left({\pi }^{+}{K}^0\right),\left(\eta K^{+}\right),$ ${(D}_s^{+}{D}^0)$ and the charge-exchange channel ${\pi }^0{K}^{+}.$ 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 $\sim 3$ 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.