Probing optimal measurements of the electromagnetic dipole moments of the $\tau$ lepton

Precise measurements of the electromagnetic dipole moments of charged leptons are powerful probes of physics beyond the Standard Model of particle physics. It is essential to study avenues for optimizing the measurement strategies for the anomalous magnetic dipole moment (AMDM) and the electric dipole moment (EDM) of the $\tau$-lepton which have recently become accessible at the Large Hadron Collider (LHC). In this work, we study the prospects of employing optimal observables for measuring the AMDM of the $\tau$-lepton in PbPb collisions at the LHC. The performance of optimal observables is investigated in a statistical analysis, assuming an integrated luminosity of 2.0 nb$^{-1}$, approximately corresponding to the amount of data collected during PbPb collisions in Run 2 of the LHC. Improvements of sensitivity to the $\tau$ AMDM with optimal observables are obtained only for a larger phase space than studied so far, more integrated luminosity or including the determination of the helicities of the $\tau$-leptons. Both, chances and limitations, of optimal observables for the $\tau$ AMDM determination will be important to consider in future experiments.