Dalitz plots and lineshape of $a_1(1260)$ from a relativistic three-body unitary approach

We formulate the final-state interaction of the a1(1260) resonance decay in a manifestly three-body unitary parametrization and fit it to the a1(1260) line shape measured by the ALEPH experiment. Dalitz plots calculated from this fit are presented. The work demonstrates the feasibility to numerically solve a previously derived amplitude and its generalization to isobars with spin and coupled channels. The model can also be applied to other meson decays and modified for the finite-volume problem as it arises in lattice QCD due to its manifest unitarity.