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

Understand

We formulate the final state interaction of the $a_1(1260)$ resonance decay in a manifestly three-body unitary parameterization and fit it to the $a_1(1260)$ lineshape 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.