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

We discuss the sensitivity of the $γγ\to τ^+ τ^-$ process in ultraperipheral Pb+Pb collisions on the anomalous magnetic ($a_τ$) and electric ($d_τ$) moments of $τ$ 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 $τ$ leptons in the fiducial volume of ATLAS and CMS detectors. We present predictions for total and differential cross sections, and for the ratios to $γγ\to e^+ e^- (μ^+ μ^-$) process. These ratios allow to cancel theoretical and experimental uncertainties when performing precision measurement of $a_τ$ at the LHC. The expected limits on $a_τ$ 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.