We investigate the prospects of the search for a nonzero $\tau$ EDM form factor $d_{\tau }(s)$ in $\tau$-pair production by $e^{+}{e}^{-}$ collisions at BEPC-II collider energies. We compute the expectation values and covariances of simple and optimal $CP$-odd observables for $\tau$-pair production at $\sqrt{s}=4.18$ and 4.95 GeV with subsequent decays of ${\tau }^{\pm }$ into major leptonic or semihadronic modes. For the $\tau$ decays to two pions and three charged pions, we take the full kinematic information of the hadronic system into account. Applying cuts and using realistic assumptions on the eventually attainable integrated luminosities at these energies, $\mathcal{L}(4.18)=3\times {10}^4{\mathrm{pb}}^{-1}$ and $\mathcal{L}(4.95)={10}^4{\mathrm{pb}}^{-1}$, respectively, we find the following. By taking into account purely semihadronic and semihadronic-leptonic ${\tau }^{+}{\tau }^{-}$ decays one can achieve with optimal $CP$-odd observables the 1 s.d. sensitivities $\delta \mathrm{Re}{d}_{\tau }=4.5\times {10}^{-18}e\mathrm{cm}$ $(5.3\times {10}^{-18}e\mathrm{cm})$ and $\delta \mathrm{Im}{d}_{\tau }=2.2\times {10}^{-18}e\mathrm{cm}$ $(2.7\times {10}^{-18}e\mathrm{cm})$ at $\sqrt{s}=4.18\mathrm{GeV}$ (4.95 GeV).

中文翻译：

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在 BEPC-II 对撞机上探测 tau 电偶极矩

我们调查了寻找非零的前景 $\tau$ EDM 外形尺寸 $d_{\tau }(秒)$ 在 $\tau$-对生产 ${\mathrm{电子}}^{+}{\mathrm{电子}}^{-}$BEPC-II 对撞机能量下的碰撞。我们计算简单和最优的期望值和协方差$C磷$- 奇数观察 $\tau$-对生产在 $\sqrt{秒}=4.18$ 和 4.95 GeV，随后衰减为 ${\tau }^{\pm }$进入主要的轻子或半强子模式。为了$\tau$衰变为两个介子和三个带电介子，我们考虑了强子系统的完整运动学信息。对这些能量下最终可达到的积分光度应用切割并使用现实假设，$\mathcal{升}(4.18)=3\times {10}^4{铅}^{-1}$ 和 $\mathcal{升}(4.95)={10}^4{铅}^{-1}$，分别，我们发现以下。通过考虑纯半强子和半强子轻子${\tau }^{+}{\tau }^{-}$ 衰减一个可以达到最佳 $C磷$-odd observables 1 sd 敏感性 $\delta \mathrm{关于}{d}_{\tau }=4.5\times {10}^{-18}\mathrm{电子}\mathrm{厘米}$ $(5.3\times {10}^{-18}\mathrm{电子}\mathrm{厘米})$ 和 $\delta \mathrm{我是}{d}_{\tau }=2.2\times {10}^{-18}\mathrm{电子}\mathrm{厘米}$ $(2.7\times {10}^{-18}\mathrm{电子}\mathrm{厘米})$ 在 $\sqrt{秒}=4.18\mathrm{电子伏特}$ (4.95 GeV)。