Anomalous electromagnetic moments of $\tau$ lepton in $\gamma \gamma \to \tau^+ \tau^-$ reaction in Pb+Pb collisions at the LHC

We discuss the sensitivity of the $\gamma \gamma \to \tau^+ \tau^-$ process in ultraperipheral Pb+Pb collisions on the anomalous magnetic ($a_{\tau}$) and electric ($d_{\tau}$) moments of $\tau$ lepton at LHC energies. We derive the corresponding cross sections by folding the elementary cross section with the heavy-ion photon fluxes and considering semi-leptonic decays of both $\tau$ leptons in the fiducial volume of ATLAS and CMS detectors. We present predictions for total and differential cross sections, and for the ratios to $\gamma \gamma \to e^+ e^- (\mu^+ \mu^-$) process. These ratios allow to cancel theoretical and experimental uncertainties when performing precision measurement of $a_{\tau}$ at the LHC. The expected limits on $a_{\tau}$ with existing Pb+Pb dataset are found to be better by a factor of two comparing to current best experimental limits and can be further improved by another factor of two at High Luminosity LHC.