Measurables of $CP$ Violation in $B_d\to D^0_{CP}K_S$ at a $B$-meson Factory

TL;DR

This paper explores how $B_d ightarrow D^0_{CP}K_S$ decays can be used to measure $CP$ violation and test the CKM unitarity triangle at $B$-meson factories, highlighting the measurability of phases despite final-state interactions.

Contribution

It demonstrates that $B_d ightarrow D^0_{CP}K_S$ decays are competitive with other methods for studying $CP$ violation and shows how to determine weak and strong phases experimentally.

Findings

Both direct and indirect $CP$ asymmetries are measurable.

Weak and strong phases can be determined despite unknown final-state interactions.

The method is feasible at asymmetric $B$-meson factories on the $A9(4S)$ resonance.

Abstract

In the context of the standard electroweak model, we emphasize that $B_d\rightarrow D^0_{CP}K_S$ ($D^0_{CP}$ denotes a $CP$ eigenstate of $D^0$ or $\bar{D}^0$) can compete with $B_d\rightarrow \pi^+\pi^-$ in studying $CP$ violation and probing the Cabibbo-Kobayashi-Maskawa unitarity triangle. We discuss the measurables of direct and indirect $CP$ asymmetries in $B^0_d$ vs $\bar{B}^0_d\rightarrow D^0_{CP}K_S$ under the circumstance of an asymmetric $B$-meson factory running on the $\Upsilon(4S)$ resonance, and show that both the weak and strong phases are experimentally determinable even in the presence of unknown final-state interactions.