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

Abstract

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.

16 pages, 2 figures

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