Branching Ratios and Spectral Functions of $\tau$ Decays: final ALEPH measurements and physics implications

The full LEP-1 data set collected with the ALEPH detector at the $Z$ pole during 1991-1995 is analysed in order to measure the $\tau$ decay branching fractions. Extensive systematic studies are performed, in order to match the large statistics of the data sample corresponding to over 300 000 measured and identified $\tau$ decays. Branching fractions are obtained for the two leptonic channels and eleven hadronic channels defined by their respective numbers of charged particles and $\pi^0$'s. Using previously published ALEPH results on final states with charged and neutral kaons, corrections are applied to the hadronic channels to derive branching ratios for exclusive final states without kao…