The a1(1420) in a unitary coupled-channel three-body approach

A bstract An enhancement in the three-pion energy at around √s s ≈ 1.42 GeV with a 1 quantum numbers was observed at the COMPASS experiment. This was later attributed to the triangle singularity mechanism involving an on-shell K ∗ (892), K and K̄ K ¯ intermediate states. The alignment of the decay K with the spectator K̄ K ¯ produces an f 0 (980), resulting in a kinematic enhancement, which is classically explained by the Landau equations. However, this one-loop process forms only part of a non-diagonal transition in a much larger coupled-channel framework. This study demonstrates the feasibility of embedding one-loop triangle-singularity calculations into a unitary three-body amplitude allowing one to consistently incorporate final-state interactions and their potentially substantial effect. For this, up to P -wave isobars and all sub-channel isospins are combined in a nine-channel production amplitude that is fitted to COMPASS lineshapes at different momentum transfers. The fitted amplitude reproduces the narrow enhancement in the ( πf 0 ) P channel near √s s ≈ 1 . 42 GeV. This implies that the triangle singularity mechanism sufficiently explains the observed enhancement, and an additional genuine a 1 (1420) pole is not required. Incidentally, the parameters of the ground state axial vector resonance (the a 1 (1260)) are also extracted from that data.