Towards orderαs4accuracy inτdecays

Abstract

Recently computed terms of order $\mathcal{O}\left({\alpha }_s^4{n}_f^2\right)$ in the perturbative series for the $\tau$ decay rate, and similar (new) strange quark mass corrections, are used to discuss the validity of various optimization schemes. The results are then employed to arrive at improved predictions for the complete terms of order $\mathcal{O}\left({\alpha }_s^4\right)$ and $\mathcal{O}\left({\alpha }_s^5\right)$ in the massless limit as well as for terms due to the strange quark mass. The phenomenological implications are presented.