Linearly Polarized Photon Fusion as a Precision Probe of the Tau Lepton Dipole Moments at Lepton Colliders

We present a comprehensive investigation into the anomalous magnetic dipole moment ($a_{\tau }$) and electric dipole moment ($d_{\tau }$) of the $\tau$ lepton using the $\gamma \gamma \to {\tau }^{+}{\tau }^{-}$ process at future lepton colliders, with the Super Tau-Charm Facility serving as a benchmark. By employing transverse-momentum-dependent factorization, we introduce novel observables derived from $\cos 2\phi$, $\sin 2\phi$, and $\cos 4\phi$ azimuthal asymmetries to precisely probe the $\tau$ lepton’s electromagnetic structure. Our analysis significantly enhances the precision of $a_{\tau }$ constraints within the photon-photon fusion process, yielding $\mathrm{R}\mathrm{e}(a_{\tau })\in [-4.6,7.0]\times {10}^{-3}$ at the $2\sigma$ confidence level, which approaches the precision of the Standard Model prediction. These findings highlight the considerable potential of azimuthal asymmetry measurements for high-precision determinations of fundamental particle properties at future lepton colliders.