decays is the ratio of the CP-averaged branching ratios for the decays $B^\pm\to\pi^\pm K^0$ and $B^\pm\to\pi^0 K^\pm$, given by $$\label{Rstexp}
   R_* =
   \frac{\mbox{B}(B^+\to\pi^+ K^0)+\mbox{B}(B^-\to\pi^-\bar K^0)}
        {2[\mbox{B}(B^+\to\pi^0 K^+)+\mbox{B}(B^-\to\pi^0 K^-)]}
   = 0.75\pm 0.28 \,,$$ where the quoted experimental value is derived from data reported by the CLEO Collaboration [@CLEO]. It will often be convenient to consider a related quantity defined as $$\label{XRval}
   X_R = \frac{\sqrt{R_*^{-1}}-1}{\bar\varepsilon_{3/2}} 
   = 0.72\pm 0.98_{\rm exp}\pm 0.03_{\rm th} \,.$$ Because of the theoretical factor $R_{\rm SU(3)}$ entering the definition of $\bar\varepsilon_{3/2}$ in (\[eps\]) this is, strictly speaking, not an observable. However, the irreducible theoretical uncertainty in $X_R$ is so much smaller than the present experimental error that it is justified to treat this quantity as an observable. The advantage of presenting our results in terms of $X_R$ rather than $R_*$ is that the leading dependence on $\bar\varepsilon_{3/2}$ cancels out (see below). Also, some experimental errors cancel in the ratio in (\[XRval\]) [@Frank].

When writing theoretical expressions for the quantities $R_*$ and $X_R$ we eliminate the two parameters $\varepsilon_{3/2}$ and $\rho$ in favor of the measurable parameter $\bar\varepsilon_{3/2}$ and a “weak phase” $\varphi\in[-90^\circ,90^\circ]$ defined by $$\sin\varphi = \frac{\rho}{\sqrt{1+\rho^2}} \,, \qquad
   \cos\varphi = \frac{1}{\sqrt{1+\rho^2}} \,.$$ The most direct way of probing 