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The $\tau$ lepton anomalous magnetic moment: $a_\tau = \frac{g_{\tau}-2}{2}$was measured, so far, with a precision of only several percents despite itshighly sensitivity to physics beyond the Standard Model such as compositenessor Supersymmetry. A new study is presented to improve the sensitivity of the$a_\tau $ measurement with photon-photon interactions from ultra-peripherallead-lead collisions at LHC. The theoretical approach used in this work isbased on an effective Lagrangian and on a photon flux implemented in theMadGraph5 Monte Carlo simulation. Using a multivariate analysis to discriminatethe signal from the background processes, a sensitivity to the anomalousmagnetic moment $\rm{a_{\tau}}$ = 0 $_{+0.011} ^{-0.019}$ is obtained at 95\%CL with a dataset corresponding to an integrated luminosity of 2 nb$^{-1}$ oflead-lead collisions and assuming a conservative 10\% systematic uncertainty.The present results are compared with previous calculations and availablemeasurements.

A study of the measurement of the $\tau$ lepton anomalous magnetic moment in high energy lead-lead collisions at LHC