A Critical Look at Rescattering Effects on $\gamma$ from $B^{+}\to K\pi$

Abstract

Three ways are compared of dealing with rescattering effects in $B^{\pm }\to K^0{\pi }^{\pm }$, in order to determine the weak phase $\gamma$ from these processes and $B^{\pm }\to K^{\pm }{\pi }^0$. We find that neglecting these contributions altogether may involve sizable errors in $\gamma$, depending on the rescattering amplitude and on the value of a certain measurable strong phase. We show that an attempt to eliminate these effects by using the charge-averaged rate of $B^{\pm }\to K^{\pm }{K}^0$ suffers from a large theoretical error due to SU(3) breaking, which may be resolved when using also the processes $B^{\pm }\to {\pi }^{\pm }{\eta }_8$.

Comments: 10 pages with 6 figures