On the nature of $a_1(1420)$

Abstract

The resonance-like signal with axial-vector quantum numbers $J^{PC}=1^{++}$ at a mass of $1420\,$MeV and a width of $140\,$MeV, recently observed by the COMPASS and VES experiments in the $f_0(980)\pi$ final state and tentatively called $a_1(1420)$, is discussed. Instead of a genuine new meson, we interpret this signal as a dynamical effect due to a singularity (branching point) in the triangle diagram formed by the processes $a_1(1260) \to K^\star \bar{K}$, $K^\star\to K\pi$, and $K \bar{K} \to f_0(980)$ (+ c.c). The amplitude for this diagram is calculated. The result exhibits a peak in the intensity with a sharp phase motion with respect to the dominant $a_1(1260) \to \rho \pi$ $S$-wave decay, in good agreement with the data. The branching ratio of $a_1(1260)\to f_0(980)\pi$ via the triangle diagram is estimated and compared to the dominant decay $a_1(1260)\to\rho\pi$.