Spin-flavor entanglement in ${\Lambda }_b\to \Lambda D$ and weak phase extraction

Abstract

We identify a new spin-flavor entanglement structure in ${\Lambda }_b\to \Lambda D$ decays, formed by the correlation between the $\Lambda$ spin and the $D$ flavor states ($D=D^0,{\overline{D}}^0,D_1,D_2$). The entanglement information is encoded in the decay rates and Lee-Yang parameters of the four neutral-$D$ modes. We then show that the same spin-flavor structure provides a new method to determine the weak phase $\gamma$, a key angle of the Cabibbo-Kobayashi-Maskawa unitarity triangle. We find that the experimental uncertainty scales as ${\sigma }_{\gamma }\propto 1/\mathcal{C}$, where $\mathcal{C}$ is the Wootters concurrence, thereby quantitatively relating the precision of the weak-phase extraction to the amount of spin-flavor entanglement.

Comments: 5 pages, 3 figures