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

Comments: 6 pages, 1 figure