τdecays and chiral perturbation theory

In a small window of phase space, chiral perturbation theory can be used to make standard model predictions for $\tau$ decays into two and three pions. For $\tau \to 2\pi {\nu }_{\tau }$, we give the analytical result for the relevant form factor $F_V$ up to two loops, then calculate the differential spectrum and compare with available data. For $\tau \to 3\pi {\nu }_{\tau }$, we have calculated the hadronic matrix element to one loop. We discuss the decomposition of the three pion states into partition states and we give detailed predictions for the decay in terms of structure functions. We also compare with low energy predictions of meson dominance models. Overall, we find good agreement, but also some interesting discrepancies, which might have consequences beyond the limit of validity of chiral perturbation theory.