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 RK3π=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.