A Critical Look at Rescattering Effects on $γ$ from $B^+\to Kπ$

Abstract

Three ways are compared of dealing with rescattering effects in $B^{\pm}\to K^0π^{\pm}$, in order to determine the weak phase $γ$ from these processes and $B^{\pm}\to K^{\pm}π^0$. We find that neglecting these contributions altogether may involve sizable errors in $γ$, 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 $B^{\pm}\to π^{\pm}η_8$.