RadiativeτDecays and theσMeson

The rate for radiative $\tau$ decay ${\tau }^{\pm }\to {\pi }^{\pm }+{\pi }^{+}+{\pi }^{-}+\gamma$ has been calculated using a linearized form of the Brown-Singer $\sigma$-meson model. The corrections to the leading term, which was obtained previously by Dalitz, are of the order of a few percent. The validity of the linear approximation for nonradiative $\tau$ decay is discussed in the Appendix.