$R_*^{-1}$. Similarly, a lower bound can be derived, which is obtained by changing the sign of $\bar\varepsilon_{3/2}$ in the above inequality. These bounds imply nontrivial constraints on $\cos\gamma$ provided that $R_*$ differs from 1 by a significant amount. In Figure \[fig:SMbound\], we show the resulting lower and upper bounds on the quantity $X_R$ versus $\gamma$, obtained by scanning the input parameters in the intervals $0.15<\bar\varepsilon_{3/2}
<0.27$ and $0.49<\delta_{\rm EW}<0.79$. The latter value is obtained by using $|V_{ub}/V_{cb}|=0.085\pm 0.015$ in (\[delval\]). The dependence on the variation of $\bar\varepsilon_{3/2}$ is so small that it would almost be invisible on the scale of the plot. Note that the extremal values $R_*$ can take in the SM are such that $|X_R|\le(1+\delta_{\rm EW})$ irrespective of the value of $\gamma$. A value exceeding this limit would be a clear signal for New Physics [@me; @Mati]. In view of the present large error on $X_R$, this is still a realistic possibility. Because the upper and lower bounds on $X_R$ are, to

a very good approximation, symmetric around $X_R=0$, we will from now on only show the upper bounds, since $X_R>0$ is the region favored by experiment. Also, since the bounds change little under variation of $\delta_{\rm EW}$ 