$B^0-{\bar{B}}^0$ entanglement for an ideal experiment on the direct CP violation ${\varphi }_3\mathrm{/}\gamma$ phase

$B^0$–${\bar{B}}^0$ Entanglement offers a conceptual alternative to the single charged B-decay asymmetry for the measurement of the direct CP violating $\gamma \mathrm{/}{\varphi }_3$ phase. With $f=J\mathrm{/}\mathrm{\Psi }{K}_L,J\mathrm{/}\mathrm{\Psi }{K}_S$ and $g=(\pi \pi {)}^0,({\rho }_L{\rho }_L{)}^0$ the 16 time-ordered double decay rate Intensities to $(f,g)$ depend on the relative phase between the the $f$- and $g$-decay amplitudes given by $\gamma$ at tree-level. Several constraining consistencies appear. An intrinsic accuracy of the method at the level of $\pm 1^\circ$ could be achievable at Belle-II with an improved determination of the penguin amplitude to $g$-channels from existing facilities.