Finding an Amplitude Model for $D^0 \to \pi^- \pi^+ \pi^+ \pi^-$ using CLEO-c Data

Abstract

Amplitude analyses of four body $D$ decays are of significant interest for multiple reasons, including their potential contribution to CP violation studies in both $B$ and $D$ decays. The resonant substructure of a four body decay has many possible components and combinations. Here, a genetic algorithm for the optimisation of such amplitude models is described. The application to an amplitude analysis of the decay mode $D^0 \to \pi^- \pi^+ \pi^+ \pi^-$ using CLEO-c data is discussed and the performance of the algorithm is verified on simulated data, showing convergence to the original model.