Studies of the resonance structure in decays

Amplitude models are constructed to describe the resonance structure of $$ and $$ 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  $$ . The largest contributions to both decay amplitudes are found to come from axial resonances, with decay modes $$ and $$ being prominent in $$ and $$ , respectively. Precise measurements of the lineshape parameters and couplings of the $$ , $$ and $$ resonances are made, and a quasi model-independent study of the $$ resonance is performed. The coherence factor of the decays is calculated from the amplitude models to be $$ , which is consistent with direct measurements. These models will be useful in future measurements of the unitary-triangle angle $$ and studies of charm mixing and $$ violation.