Strategy to measure tau $g-2$ via photon fusion in LHC proton collisions

Measuring the tau-lepton (τ) anomalous magnetic moment a_τ=(g_τ-2)/2 in photon fusion production (γγ→ττ) tests foundational Standard Model principles. However, γγ→ττ eludes observation in LHC proton collisions (pp) despite enhanced new physics sensitivity from higher-mass reach than existing probes. We propose a novel strategy to measure pp(γγ→ττ)p by introducing the overlooked electron-muon signature with vertex isolation for signal extraction. Applying the effective field theory of dipole moments, we estimate 95% CL sensitivity of -0.0092<aτ<0.011 assuming 300 fb⁻¹ luminosity and 5% systematics. This fourfold improvement beyond existing constraints opens a crucial path to unveiling new physics imprinted in tau-lepton dipoles.