be obtained by changing the sign of $\bar\varepsilon_{3/2}$. In contrast to the previous case, now the maximal value of $|X_R|$ is given by $1+|a|$ and thus can exceed the SM bound provided that $|a|>\delta_{\rm EW}$. This is illustrated in the right-hand plot in Figure \[fig:case12\], where we show the resulting upper bound on $X_R$ versus $\gamma$ for different values of $|a|$. In contrast with the case of isospin-conserving New Physics, even a moderate enhancement of the coefficient $a$ corresponding to a 10%–20% change in the decay amplitudes can lead to a significant increase of the upper bound on $X_R$.

If both isospin-violating and isospin-conserving New Physics effects are present and involve new CP-violating phases, the analysis becomes more complicated. Still, it is possible to derive from (\[Rstar\]) a series of bounds on $R_*^{-1}$. We find $$\begin{aligned}
   R_*^{-1} &\le& 1 + 2\bar\varepsilon_{3/2} \Big[
    \cos\varphi\,(|a|+|\cos\gamma|)
    + |\sin\varphi|\,(|b|+|\sin\gamma|) \Big] \nonumber\\
   &&\mbox{}+ \bar\varepsilon_{3/2}^2 \Big[
    (|a|+|\cos\gamma|)^2 + (|b|+|\sin\gamma|)^2 \Big] \nonumber\\
   &\le& \left[ 1 + \bar\varepsilon_{3/2}
    \sqrt{(|a|+|\cos\gamma|)^2 + (|b|+|\sin\gamma|)^2} \right]^2 
    \nonumber\\
   &\le& \left[ 1 + \bar\varepsilon_{3/2} \left( 1
   + \sqrt{a^2 + b^2} \right) \right]^2 \,,\end{aligned}$$ where in the second and third steps we have eliminated $\varphi$ and $\gamma$, respectively. As before a series of lower bounds 