  The anomalous magnetic moment of the tau lepton $a_\tau = (g_\tau -2)/2$
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 $\delta a_\tau$ and electric
dipole moments $\delta d_\tau$. We introduce a suite of one electron/muon plus
track(s) analyses, leveraging the exceptionally clean photon fusion
$\gamma\gamma \to \tau\tau$ events to reconstruct both leptonic and hadronic
tau decays sensitive to $\delta a_\tau, \delta d_\tau$. Assuming 10% systematic
uncertainties, the current 2 nb$^{-1}$ lead-lead dataset could already provide
constraints of $-0.0080 < a_\tau < 0.0046$ at 68% CL. This surpasses 15 year
old lepton collider precision by a factor of three while opening novel avenues
to new physics.

High Energy Physics - Phenomenology;High Energy Physics - Experiment