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_τ) and electric dipole moment (d_τ) of the $τ$ lepton using the γγ→ τ⁺τ⁻ 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 cos2ϕ, sin2ϕ, and cos4ϕ azimuthal asymmetries to precisely probe the $τ$ lepton's electromagnetic structure. Our analysis significantly enhances the precision of a_τ constraints, yielding Re(a_τ) ∈ [-4.5, 6.9] × 10⁻³ at $2σ$ confidence level. This represents an order-of-magnitude improvement over existing experimental limits and 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.