Abstract

The decay $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\nu}$ is analyzed using different methods to account for the resonance structure, which is usually ascribed to the ${a}_{1}$. One scenario is based on the recently developed techniques to generate axial-vector resonances dynamically, whereas in a second calculation the ${a}_{1}$ is introduced as an explicit resonance. We investigate the influence of different assumptions on the result. In the molecule scenario the spectral function is described surprisingly well by adjusting only one free parameter. This result can be systematically improved by adding higher-order corrections to the iterated Weinberg-Tomozawa interaction. Treating the ${a}_{1}$ as an explicit resonance on the other hand leads to peculiar properties.

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