Studies of the resonance structure in D⁰ → K^-+π^±π^±π^-+ decays

Amplitude models are constructed to describe the resonance structure of D⁰ → K^-π⁺π⁺π^- and D⁰ → K⁺π^-π^-π⁺ decays using pp collision data collected at centre-of-mass energies of 7 and 8 TeV with the LHCb experiment, corresponding to an integrated luminosity of 3.0 fb^-1. The largest contributions to both decay amplitudes are found to come from axial resonances, with decay modes D⁰ → a₁(1260)⁺K^- and D⁰ → K₁(1270/1400)⁺π^- being prominent in D⁰ → K^-π⁺π⁺π^- and D⁰ → K⁺π^-π^-π⁺, respectively. Precise measurements of the lineshape parameters and couplings of the a₁(1260)⁺, K₁(1270)^- and K(1460)^- resonances are made, and a quasi model-independent study of the K(1460)^- resonance is performed. The coherence factor of the decays is calculated from the amplitude models to be R_K3π = 0.459 ± 0.010 (stat) ± 0.012 (syst) ± 0.020 (model), which is consistent with direct measurements. These models will be useful in future measurements of the unitary-triangle angle γ and studies of charm mixing and CP violation. (orig.)