New physics and tau $g-2$ using LHC heavy ion collisions

The anomalous magnetic moment of the tau lepton $a_τ=(g_τ-2)/2$ strikingly evades measurement but is highly sensitive to new physics such as compositeness or supersymmetry. We propose using ultraperipheral heavy ion collisions at the LHC to probe modified magnetic $δa_τ$ and electric dipole moments $δd_τ$. We design a suite of analyses with signatures comprising one electron/muon plus track(s), leveraging the exceptionally clean photon fusion $γγ→ττ$ events to reconstruct both leptonic and hadronic tau decays sensitive to $δa_τ,δd_τ$. Assuming 10% systematic uncertainties, the current $2 nb^{-1}$ lead-lead dataset could already provide constraints of $-0.0080<a_τ<0.0046$ at 68% C.L. This surpasses 15-year-old lepton collider precision by a factor of 3 while opening novel avenues to new physics.