Amplitude analysis of the D ⁺ → π ⁻ π ⁺ π ⁺ decay and measurement of the π ⁻ π ⁺ S-wave amplitude

An amplitude analysis of the D ⁺ → π ⁻ π ⁺ π ⁺ decay is performed with a sample corresponding to 1.5 fb ⁻¹ of integrated luminosity of pp collisions at a centre-of-mass energy s = 8 TeV collected by the LHCb detector in 2012. The sample contains approximately six hundred thousand candidates with a signal purity of 95%. The resonant structure is studied through a fit to the Dalitz plot where the π ⁻ π ⁺ S-wave amplitude is extracted as a function of π ⁻ π ⁺ mass, and spin-1 and spin-2 resonances are included coherently through an isobar model. The S-wave component is found to be dominant, followed by the ρ(770)⁰ π ⁺ and f ₂(1270)π ⁺ components. A small contribution from the ω(782) → π ⁻ π ⁺ decay is seen for the first time in the D ⁺ → π ⁻ π ⁺ π ⁺ decay.