Pauli blocking and entanglement solve $K\pi$ puzzle. CP violation in $B^o\to K\pi$; not in $B^{\pm }\to K\pi$decays

Abstract

New data analysis with Pauli blocking and entanglement explains CP violation in $B^o\to K\pi$ decays, absence in $B^{\pm }\to K\pi$ decays and predicts unexpected contrast between pure I=1/2 in individual $B^{\pm }$ and $B^o$ final states and I=1/2 violation in relations between them. Analysis of $B\to K\pi$ data predicts these observed isospin relations and explains dependence on spectator quark flavor. $B^{+}\to K\pi$ tree diagram $\bar{b}u\to \bar{s}u\bar{u}u$ has two identical $u$ quarks from weak vertex and spectator. The Pauli principle requires these quarks at short distances to have wave functions antisymmetric in color or spin. The eigenvalues of conserved symmetries remain entangled in a final state of two separated mesons. This Pauli entanglement suppresses tree-penguin interference and CP violation in $B^{+}$ decay but not in $B^o$ decay with spectator $d$ quark. The four-body wave function must have two antiquarks with the same symmetry combining with two u-quarks to fragment into a two-pseudoscalar-meson state even under charge conjugation with angular momentum zero. It is classified in the 27-dimensional representation of flavor SU(3) with isospin I=2 for the $\pi \pi$ state and V spin V=2 for the corresponding strange state which is linear combination of $K\pi$ and $K{\eta }_8$. These symmetries remain entangled in four-body wave function even after separation into two mesons. Strong Pauli suppression in tree transitions to $K\pi$ which has only a small V=2 component and is mainly V=1. No Pauli suppression in transitions to I=2 $\pi \pi$ state with also two $u$ quarks but different color-spin couplings. Standard definition of independent color favored and suppressed tree diagrams in $B^{\pm }\to K\pi$ decays neglects $uu$ Pauli entanglement.

Comments: 14 pages. 3 figures. Revision includes entanglement. arXiv admin note: substantial text overlap with arXiv:1102.4700 and arXiv:1107.1888