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The final state interaction contribution to $D^+$ decays is computed for the$K^-\pi^+\pi^+$ channel within a light-front relativistic three-body model forthe final state interaction. The rescattering process between the kaon and twopions in the decay channel is considered. The off-shell decay amplitude is asolution of a four-dimensional Bethe-Salpeter equation, which is decomposed ina Faddeev form. The projection onto the light-front of the coupled set ofintegral equations is performed via a quasi-potential approach. The S-wave$K\pi$ interaction is introduced in the resonant isospin $1/2$ and thenon-resonant isospin $3/2$ channels. The numerical solution of the light-fronttridimensional inhomogeneous integral equations for the Faddeev components ofthe decay amplitude is performed perturbatively. The loop-expansion convergesfast, and the three-loop contribution can be neglected in respect to thetwo-loop results for the practical application. The dependence on the modelparameters in respect to the input amplitude at the partonic level is exploitedand the phase found in the experimental analysis, is fitted with an appropriatechoice of the real weights of the isospin components of the partonic amplitude.The data suggests a small mixture of total isospin $5/2$ to the dominant $3/2$one. The modulus of the unsymmetrized decay amplitude, which presents a deepvalley and a following increase for $K\pi$ masses above $1.5$ GeV, is fairlyreproduced. This suggests the assignment of the quantum numbers $0^+$ to theisospin 1/2 $K^*(1630)$ resonance.

Final state interaction in $D^+\to K^-\pi^+\pi^+$ with $K\pi$ I=1/2 and 3/2 channels