Precision measurement of the $etatopi^+pi^-pi^0$ Dalitz plot distribution with the KLOE detector

Using $1.6$ fb$^{-1}$ of $e^+ e^-tophitoetagamma$ data collected with the KLOE detector at DA$Phi$NE, the Dalitz plot distribution for the $eta to pi^+ pi^- pi^0$ decay is studied with the worlds largest sample of $sim 4.7 cdot 10^6$ events. The Dalitz plot density is parametrized as a polynomial expansion up to cubic terms in the normalized dimensionless variables $X$ and $Y$. The experiment is sensitive to all charge conjugation conserving terms of the expansion, including a $gX^2Y$ term. The statistical uncertainty of all parameters is improved by a factor two with respect to earlier measurements.