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

Measuring the tau-lepton ($\tau$) anomalous magnetic moment $a_\tau = (g_\tau -2)/2$ in photon fusion production ($\gamma\gamma\to\tau\tau$) tests foundational Standard Model principles. However, $\gamma\gamma\to\tau\tau$ 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 $\text{pp} \to \text{p}(\gamma\gamma\to\tau\tau)\text{p}$ 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 $-0.0092 < a_\tau < 0.011$ 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.