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

We report on a time-dependent Dalitz-plot analysis of the decay $B^0 \to K_S \pi^+ \pi^-$ performed by the {\sl B{\scriptsize A}B {\scriptsize AR}} experiment. An isobar model including scalar, vector and tensor components is fitted to the data and the Unitarity Triangle (UT) angle $\beta_{eff}$ is extracted for the modes $B^0 \to f_0 K_S$ and $B^0 \to \rho^0 K_S$. In addition, the phase difference between $B^0 \to K^{*+}\pi^-$ and $\overline{B^0} \to K^{*-}\pi^+$ is determined. This phase difference is a critical input for a recently developed method for extracting the UT angle $\gamma$.