$B^0-\bar B^0$ entanglement for an ideal experiment on the direct CP violation $\phi_3/\gamma$ phase

Abstract

$B^0$--$\bar B^0$ Entanglement offers a conceptual alternative to the single charged B-decay asymmetry for the measurement of the direct CP violating $\gamma/\phi_3$ phase. With $f=J/\Psi K_L,J/\Psi K_S$ 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.