Towards three-body unitarity in $D^+ \to K^- \pi^+ \pi^+$

We assess the importance of final state interactions in D+ -> K-pi(+)pi(+) , stressing the consistency between two-and three-body interactions. The basic building block in the calculation is a K pi amplitude based on unitarized chiral perturbation theory and with parameters determined by a fit to elastic LASS data. Its analytic extension to the second sheet allows the determination of two poles, associated with the kappa and the K*(1430), and a representation of the amplitude based on them is constructed. The problem of unitarity in the three-body system is formulated in terms of an integral equation, inspired in the Faddeev formalism, which implements a convolution between the weak vertex and the final state hadronic interaction. Three different topologies are considered for the former and, subsequently, the decay amplitude is expressed as a perturbation series. Each term in this series is systematically related to the previous one and a resummation was performed. Remaining effects owing to single and double rescattering processes were then added and results compared to FOCUS data. We found that proper three-body effects are important at threshold and fade away rapidly at higher energies. Our model, based on a vector-weak vertex, can describe qualitative features of the modulus of the decay amplitude and agrees well with its phase in the elastic region.