arXiv subjects
Publications and source records attributed to Zhi-zhong Xing.
Within the standard electroweak model we point out that the $3\times 3$ matrix of quark mixing is characterized by three universal (rephasing-invariant) quantities: one of them for $CP$ violation and the other two for off-diagonal asymmetries. Unitarity of the quark mixing matrix can in principle be tested through a variety of measurements which are irrelevant to the existence of $CP$-violating effects.
Within the standard electroweak model we carry out an instructive analysis of the effect of $K^{0}-\bar{K}^{0}$ mixing on $CP$ asymmetries in some weak decay modes of $D^{\pm}$ and $\stackrel{(-)}{B}$$^{0}_{d}$ mesons. We point out that a clean signal of $CP$ violation with magnitude of 2Re($ε$) $\approx 3.3\times 10^{-3}$ can manifest in the semileptonic decays $D^{+}\rightarrow l^{+}ν^{~}_{l}K_{S}$ ($K_{L}$) vs $D^{-}\rightarrow l^{-}\barν^{~}_{l}K_{S}$ ($K_{L}$). The $CP$ asymmetries are also dominated by 2Re($ε$) in the two-body nonleptonic decays $D^{\pm} \rightarrow (π^{\pm}, ρ^{\pm}, a^{\pm}_{1})+ (K_{S}, K_{L})$ and in the multi-body processes $D^{\pm}\rightarrow π^{\pm}+n_{0}π^{0}+n_{\pm} (π^{\pm}π^{\mp})+ (K_{S}, K_{L})$, where $n_{0}$ and $n_{\pm}$ are integers. It is possible to observe such $CP$-violating signals with about $10^{7}$ $D^{\pm}$ events at $τ$-charm factories or hadron machines. Finally we show that the $CP$ asymmetry induced by Re($ε$) may compete with those from $B^{0}_{d}-\bar{B}^{0}_{d}$ mixing and final-state interactions in the semi-inclusive and exclusive decays $B_{d}\rightarrow X(c\bar{c})+(K_{S}, K_{L})$ on the $Υ(4S)$ resonance.
To lowest-order weak interactions in the standard model, we point out that a complete graph description of two-body mesonic $B$ (or $D$) decays needs ten topologically different quark diagrams. The two-body baryonic $B$ decays can be illustrated in terms of five diagrams. We remark a variety of features of the graph language. Some pure channels of mesonic $B$ decays, which can be used to test the quark-diagram scheme, are discussed in some detail.
The space-like penguin contributions were ignored on little ground in many previous studies of nonleptonic B decays and CP violation. Taking the penguin-dominated channels $B^{-} _{u}\rightarrow \bar{K}^{0}π$ and $B^{-}_{u}\rightarrow K^{0} K^{-}$ for example, we illustrate the non-negligible effects of the space-like penguin diagrams on CP asymmetries. Some quali- tative remarks are given on the gluonic penguin picture and the direct CP violation in exclusive two-body decays of B mesons.
A generic formalism is presented for the time-dependent or time-integrated decays of any coherent $P^{0}\bar{P}^{0}$ system ($P^{0} = K^{0}, D^{0}, B^{0}_{d}$, or $B^{0}_{s}$). To meet various possible measurements at asymmetric $B$ factories, we reanalyze some typical signals of CP violation in the coherent $B^{0}_{d}\bar{B}^ {0}_{d}$ transitions. The advantage of proper time cuts is illustrated for measuring mixing parameters and CP violation. We show that the direct and indirect CP asymmetries are distinguishable in neutral B decays to CP eigenstates. The possibility to detect the CP- forbidden processes at the $Υ(4S)$ resonance is explored in some detail.
The Wolfenstein parametrization of the $3\times 3$ Kobayashi-Maskawa (KM) matrix $V$ is modified by keeping its unitarity up to the accuracy of $O(λ^{6})$. This modification can self-consistently lead to the off-diagonal asymmetry of $V$: $|V_{ij}|^{2}-|V_{ji}|^{2}$ = $Z\displaystyle\sum_{k}ε^{~}_{ijk}$ with $Z=\approx A^{2}λ^{6} (1-2ρ)$, which is comparable in magnitude with the Jarlskog parameter of $CP$ violation $J\approx A^{2}λ^{6}η$. We constrain the ranges of $J$ and $Z$ by using the current experimental data, and point out that the possibility of a symmetric KM matrix has almost been ruled out.
A reliable prediction for $CP$ violation in $B^{0}_{d}$ vs $\bar{B}^{0}_{d}\rightarrow π^{+}π^{-}$ suffers from the penguin-diagram induced uncertainty. With the help of SU(3) relations, we show that both the magnitude and strong phase shift of the penguin amplitude can be approximately determined only from the branching ratios of $B^{0}_{d}\rightarrow π^{+}π^{-}$, $B^{0}_{d}\rightarrow K^{+}π^{-}$, and $B^{+}_{u}\rightarrow K^{0}π^{+}$.
Considering that the existing experimental limit for $CPT$ violation is still poor, we explore various possible ways to test $CPT$ symmetry in $CP$-violating $B$ decays at $e^{+}e^{-}$ $B$ factories and hadron machines. We find that it is difficult to distinguish between the effect of direct $CP$ violation and that of $CPT$ violation in the time-integrated measurements of neutral $B$ decays to $CP$ eigenstates such as $ψK_{S}$ and $π^{+}π^{-}$. Instead, a cleaner signal of small $CPT$ violation may appear in the time-integrated $CP$ asymmetries for a few non-$CP$-eigenstate channels, e.g., $B^{0}_{d}/\bar{B}^{0}_{d}\rightarrow D^{\pm}π^{\mp}$ and $\stackrel{(-)}{D}$$^{(*)0}K_{S}$. The time-dependent measurements of $CP$ asymmetries are available, in principle, to limit the size of $CPT$-violating effects in neutral $B$-meson decays.
A careful quark-diagram analysis shows that a number of two-body nonleptonic $B$ decays can occur through the so-called hairpin diagram, a QCD loop-induced graph different from penguin in final-state hadronization of valence quarks. Using the two-loop renormalization-group-improved effective Hamiltonian and the naive factorization approximation, we demonstrate the effect of the hairpin diagram on decay rates and $CP$ asymmetries for a few interesting channels such as $B^{0}_{d},\bar{B}^{0}_{d} \rightarrow ψK_{S}$ and $B^{\pm}_{u}\rightarrow ϕK^{\pm}$. Branching ratios of some pure hairpin decay modes, e.g., $B^{-}_{u}\rightarrow ϕπ^{-},ϕρ^{-}$ and $\bar{B}^{0}_{d}\rightarrow ϕπ^{0},ϕρ^{0}, ϕω, ϕη,$ etc., are estimated to be on the order of $10^{-7}$.