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 design a suite of analyses with signatures comprising one electron/muon plus track(s), 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 $2{\mathrm{nb}}^{-1}$ lead-lead dataset could already provide constraints of $-0.0080<a_{\tau }<0.0046$ at 68% C.L. This surpasses 15-year-old lepton collider precision by a factor of 3 while opening novel avenues to new physics.

• Received 1 November 2019
• Revised 5 April 2020
• Accepted 16 November 2020

DOI:https://doi.org/10.1103/PhysRevD.102.113008

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Published by the American Physical Society