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

TL;DR

This paper examines different methods to handle rescattering effects in B meson decays to accurately determine the weak phase gamma, highlighting potential errors and proposing improved approaches involving SU(3) breaking considerations.

Contribution

It compares three approaches to account for rescattering effects in B decays and proposes using additional decay processes to reduce theoretical uncertainties.

Findings

Neglecting rescattering can cause sizable errors in gamma estimation.

Using charge-averaged rates of B to KK decays introduces large SU(3) breaking errors.

Incorporating B to pi eta_8 decays helps mitigate theoretical uncertainties.

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 $B^{\pm}\to \pi^{\pm}\eta_8$.