Amplitude analysis of the $D_s^+ \to \pi^- \pi^+ \pi^+$ decay

A Dalitz plot analysis of the $D_s^+ \to \pi^- \pi^+ \pi^+$ decay is presented. The analysis is based on proton-proton collision data recorded by the LHCb experiment at a centre-of-mass energy of $8$ TeV and corresponding to an integrated luminosity of $1.5 fb^{-1}$. The resonant structure of the decay is obtained using a quasi-model-independent partial-wave analysis, in which the $\pi^+\pi^-$ S-wave amplitude is parameterised as a generic complex function determined by a fit to the data. The S-wave component is found to be dominant, followed by the contribution from spin-2 resonances and a small contribution from spin-1 resonances. The latter includes the first observation of the $D_s^+ \to \omega(782) \pi^+$ channel in the $D_s^+ \to \pi^- \pi^+ \pi^+$ decay. The resonant structures of the $D_s^+ \to \pi^- \pi^+ \pi^+$ and $D^+ \to \pi^- \pi^+ \pi^+$ decays are compared, providing information about the mechanisms for the hadron formation in these decays.