Precision measurements of τ lepton properties, its mass, lifetime, and leptonic branching fractions, provide interesting tests of lepton universality.
With the very large statistics, an important improvement of the τ mass measurement may be possible via the so-called pseudomass method pioneered by ARGUS and later exploited by OPAL at LEP and by BaBar and Belle at the b-factories. In three-prong τ decays, the pseudomass variable depends on the measured mass and momentum of the 3π system and on the beam-energy. At FCC-ee, the beam energy is controlled to 1e−6 via resonant spin depolarisation, and only the measurement of the 3π system contributes to the uncertainty on the pseudomass. As a reference process, in order to control the mass and momentum scale, it is suggested to exploit the very large sample of J/ψs from Z decays (B(Z → J/ψX) = 3.5e−3), and the fact that the J/ψ mass is known to the ppm level due a very precise measurement from KEDR at the VEPP-4M collider likewise based on resonant spin depolarisation. It could be also considered to make use of τ decays with higher charged-particle multiplicities that will provide a larger fraction of events close to the end-point of the pseudomass distribution. An excellent measurement of tracks in collimated multi-track final states is a key experimental requirement.