Studies of the resonance structure in D^0→ K^∓π ^±π ^±π ^∓ decays

mplitude models are constructed to describe the resonance structure of D^0→ K^-π ^+π ^+π ^- and D^0→ 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 D^0→ a_1(1260)^+ K^- and D^0→ K_1(1270/1400)^+π ^- being prominent in D^0→ K^-π ^+π ^+π ^- and D^0→ K^+π ^-π ^-π ^+ , respectively. Precise measurements of the lineshape parameters and couplings of the a_1(1260)^+ , K_1(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.