Zhi-zhong XING | Searcharxiv

arXiv1994

On the Unitarity Triangles of the CKM Matrix

The unitarity triangles of the $3\times 3$ Cabibbo-Kobayashi-Maskawa (CKM) matrix are studied in a systematic way. We show that the phases of the nine CKM rephasing invariants are indeed the outer angles of the six unitarity triangles and measurable in the $CP$-violating decay modes of $B_{d}$ and $B_{s}$ mesons. An economical notation system is introduced for describing properties of the unitarity triangles. To test unitarity of the CKM matrix we present some approximate but useful relations among the sides and angles of the unitarity triangles, which can be confronted with the accessible experiments of quark mixing and $CP$ violation.

hep-ph↗

arXiv1994

On Measuring $CP$ Violation in Neutral $B$-meson Decays at the $Υ(4S)$ Resonance

Within the standard model we carry out an analysis of $CP$-violating observables in neutral $B$-meson decays at the $Υ(4S)$ resonance. Both time-dependent and time-integrated $CP$ asymmetries are calculated, without special approximations, to meet various possible measurements at symmetric and asymmetric $e^{+}e^{-}$ $B$ factories. We show two ways to distinguish between direct and indirect $CP$-violating effects in the $CP$-eigenstate channels such as $B^{0}_{d}/\bar{B}^{0}_{d}\rightarrow π^{+}π^{-}$ and $π^{0} K_{S}$. Reliable knowledge of the Cabibbo-Kobayashi-Maskawa phase and angles can in principle be extracted from measurements of some non-$CP$-eigenstate channels, e.g. $B^{0}_{d}/\bar{B}^{0}_{d}\rightarrow D^{\pm}π^{\mp}$ and $\stackrel{(-)}{D}$$^{(*)0}K_{S}$, even in the presence of significant final-state interactions.

hep-ph↗