Reevaluating the $a_1(1420)$ enhancement and its molecular partners in the low-lying axial-vector meson spectrum

Abstract

We assess possible axial-vector states with $G$-parity $\left(G=\pm 1\right)$ dynamically generated by pseudoscalar-vector interactions in coupled channels, driven by the Weinberg-Tomozawa term at leading order in chiral perturbation theory. The $S$-wave amplitudes are unitarized via the Bethe-Salpeter equation, and poles of the unitarized amplitudes are searched for in the complex energy plane. In the isovector sector with $I^G(J^{PC})=1^{\pm}(1^{+\mp})$, we identify two poles around 1400 MeV in the second Riemann sheet below the $K^*\bar{K}$ mass threshold. The $G=+1$ and $G=-1$ poles can be one of the origins of the peaks in the $f_0(980)\pi$ and $\phi\pi^0$ mass spectra reported by the COMPASS and BESIII collaborations, respectively, in the $\pi N \to \pi\pi\pi N$ and $J/\psi \to \eta \phi\pi$ processes, in addition to triangle singularity effects discussed in the literature. Additionally, the poles in the isoscalar sector may explain the nontrivial behavior of the $K^*\bar{K}$ spectra line shapes measured by several experiments in different reactions. Specifically, for the $0^+(1^{++})$ case, we find a sizeable $K^*\bar{K}$ component for the $f_1(1420)$. In the $0^-(1^{+-})$ scenario, the pole strongly coupled to $\rho\pi$ can be associated with the $h_1(1170)$ resonance. Lastly, in this same sector, we identify a higher pole that dominates the $K^*\bar{K}$ invariant mass in the $\chi_{cJ} \to \phi K^*\bar{K}$ decay, where the \(h_1(1415)\) is observed in the BESIII data.