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arXiv 1107.1232hep-ph
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K，D_（s）和B_（s）衰变中的三重乘积不对称性

Triple product asymmetries in K, D_(s) and B_(s) decays

Michael Gronau, Jonathan L. Rosner

备注：
minor corrections, submitted to Phys. Rev. D
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摘要：

一个区分“真”CP违反三重积（TP）不对称，不需要强相位和“假”不对称，这是由于强相位，但不需要CP违反。到目前为止，在$K_L\to π^+π^- e^+e^-$中测量到了一个单一的真实TP不对称性。本文对四体衰变中的T奇TP不对称性进行了一般性讨论。结果表明，TP不对称消失的两个相同的和运动学上无法区分的粒子在最终状态。两个例子是$D^0\to K^-π^+π^-π^+$和$D^+\to K^-π^+π^+π^0$。当存在非平凡的运动学相关性时，可以预期非零TP不对称性，如在衰变$K_L \to e^+ e^- e^+ e^-$中。在粲粒子衰变中测得的三重产物不对称性表明了一种有趣的末态相互作用模式。我们重申讨论的TP不对称性$B$介子衰变到两个矢量介子每个衰变到一个赝标对，扩展结果的衰变，其中一个矢量介子衰变成轻子对。我们推导出的中性$B$质量差$Δm$和宽度差$ΔΓ$的中性B衰变到无味状态的时间相关TP不对称性的表达式。时间积分的真正CP违反不对称性，测量未标记的$B_s$衰变，被证明是抑制既不$Γ_s/Δm_s$也不$ΔΓ_s/Γ_s$，如果CP偶和CP奇状态的横向振幅涉及不同的弱相位。与此相反，假的不对称性需要风味标记，并抑制前一个比例时，时间积分。我们将我们的结果应用于$B\to K^*ϕ$和$B_s\toϕϕ$数据，并提出了$B_s\to J/ψϕ$的应用。

英文摘要：

One distinguishes between "true" CP violating triple product (TP) asymmetries which require no strong phases and "fake" asymmetries which are due to strong phases but require no CP violation. So far a single true TP asymmetry has been measured in $K_L\to π^+π^- e^+e^-$. A general discussion is presented for T-odd TP asymmetries in four-body decays. It is shown that TP asymmetries vanish for two identical and kinematically indistinguishable particles in the final state. Two examples are $D^0\to K^-π^+π^-π^+$ and $D^+\to K^-π^+π^+π^0$. A non-zero TP asymmetry can be expected when non-trivial kinematic correlations exist, as in the decay $K_L \to e^+ e^- e^+ e^-$. Triple product asymmetries measured in charmed particle decays indicate an interesting pattern of final-state interactions. We reiterate a discussion of TP asymmetries in $B$ meson decays to two vector mesons each decaying to a pseudoscalar pair, extending results to decays where one vector meson decays into a lepton pair. We derive expressions for time-dependent TP asymmetries for neutral B decays to flavorless states in terms of the neutral $B$ mass difference $Δm$ and the width-difference $ΔΓ$. Time-integrated true CP violating asymmetries, measurable for untagged $B_s$ decays, are shown to be suppressed by neither $Γ_s/Δm_s$ nor $ΔΓ_s/Γ_s$ if transversity amplitudes for CP-even and CP-odd states involve different weak phases. In contrast, fake asymmetries require flavor tagging and are suppressed by the former ratio when time-integrated. We apply our results to $B\to K^*ϕ$ and $B_s\toϕϕ$ data and suggest an application for $B_s\to J/ψϕ$.

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