Dalitz plots and lineshape of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>a</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>1260</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>from a relativistic three-body unitary approach

Abstract

We formulate the final-state interaction of the ${a}_{1}(1260)$ resonance decay in a manifestly three-body unitary parametrization and fit it to the ${a}_{1}(1260)$ 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.

Topics & Concepts