Numerical upper bounds on theCPnonconservation of neutral-heavy-meson systems in the standard six-quark model

Using recently obtained bounds on the mixing angles in the standard six-quark model and our own calculations of $\frac{\mathrm{Im}{\Gamma }_{12}}{\mathrm{Re}{\Gamma }_{12}}$ as well as the standard expressions of $\frac{\mathrm{Im}{M}_{12}}{\mathrm{Re}{M}_{12}}$ for the heavy-meson systems $D^0-{\overline{D}}^0$, $B^0-{\overline{B}}^0$, and $B_s^0-{\overline{B}}_s^0$, we find upper limits of 4×${10}^{-3\mathrm{}}$, 5×${10}^{-4\mathrm{}}$, and 7×${10}^{-4\mathrm{}}$ for the magnitude of the phase-convention-independent quantity $\frac{2\mathrm{Re}\epsilon }{(1+{\left|\epsilon \right|}^2)}$ as a measure of the size of $\mathrm{CP}$ nonconservation in these respective systems. Although our numerical results depend crucially on the specific values for the mixing angles taken from the work of others, our method is of general application and can be used to set upper limits on $\frac{2\mathrm{Re}\epsilon }{(1+{\left|\epsilon \right|}^2)}$, whatever values these angles might take.