In general, three-body decays can be described as quasi-two-body decays where intermediate resonances decay into two particles, and then observing a the final state constituted of three particles. To study these processes it is necessary to perform an amplitude analysis to the corresponding Dalitz Plot (the two-dimensional representation of the decay phase space). It is common to use the so-called Isobar Model, in which each resonance is modelled as a relativistic Breit-Wigner function and, together with proper angular distributions and form factors, the total amplitude is written as a coherent sum of the individual resonance amplitudes. However, dealing with broad scalar states - which appear in π π S-wave — the Isobar Model turns out to be inadequate and other approaches, as a model-independent partial wave analysis, are interesting alternatives. The treatment of the ππ scalar amplitude is currently an open problem.
In this work, we show the current status towards the full amplitude analysis of the decay D+ → π- π+ π+ using run I data from the LHCb experiment.