Resonance Chiral Lagrangian Currents and Experimental Data for $\tau^-\to\pi^{-}\pi^{-}\pi^{+}\nu_{\tau}$

In this paper we document the modifications introduced to the previous version of the Resonance Chiral Lagrangian current ({\it Phys.Rev.} {\bf D86} (2012) 113008) of the $\tau^\pm \to \pi^\pm \pi^\pm \pi^\mp \nu_\tau$ decay which enable the one dimensional distributions measured by the BaBar collaboration to be well modeled. The main change required to model the data is the addition of the $\sigma$ resonance. Systematic errors, theoretical and experimental ones, limitations due to fits of one dimensional distributions only, and resulting difficulties and statistical/systematic errors for fitted parameters are addressed. The current and fitting environment is ready for comparisons with the fully exclusive experimental data. The present result for $\tau^\pm \to \pi^\pm \pi^\pm \pi^\mp \nu_\tau$ is encouraging for work on other $\tau$ decay modes and Resonance Chiral Lagrangian based currents.