Time-dependent Dalitz analysis of $B^0\to K^0\pi^+\pi^-$

We present preliminary results of a maximum-likelihood, time-dependent Dalitz-plot analysis of charmless hadronic $B^0$ decays to the $K^0\pi^+\pi^-$ final state, from data corresponding to an integrated on-resonance luminosity of approximately 350~fb$^{-1}$ recorded by the BaBar experiment at the SLAC PEP-II asymmetric-energy $B$ Factory from 1999 to 2006. We measure decay amplitudes and phases for the intermediate resonance states, and extract time-dependent $CP$ asymmetries for the $\rho^0 K^0$ and $f_0 K^0$ intermediate states, and direct $CP$ asymmetries for $K^{*+}\pi^-$.