Current-Algebra Calculation of the Decayτ→3πν

A fit to the integrated rate and $3\pi$ mass distribution of the decay mode ${\tau }^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}{\overline{\nu }}_{\tau }$ has been performed using hard-pion current algebra, including the approximate imposition of unitarity. We find that the existence of an $A_1$ with low mass ($m_A=1.1\mathrm{}$ GeV) and narrow width [${{\Gamma }_A}^{\mathrm{tot}}=150\mathrm{}$ MeV, $\Gamma (A_1\to \rho \pi )=100\mathrm{}$ MeV] is consistent with the data if there is an appreciable non-$\rho \pi$ contribution to the matrix element $〈3\pi \left|A_{\mu }\right|0\mathrm{}〉$. Such a contact term is predicted to exist by current algebra.