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).

• Received 7 September 2021
• Accepted 11 November 2021

DOI:https://doi.org/10.1103/PhysRevD.104.115002

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Published by the American Physical Society