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

TL;DR

This work uses a chiral-unitary approach to PV scattering with the Weinberg–Tomozawa interaction, unitarized via the Bethe–Salpeter equation in coupled channels, to study the low-lying axial-vector meson spectrum. Poles in the T-matrix are searched across Riemann sheets, revealing isovector virtual poles around 1.3–1.4 GeV that can explain the a_1(1420) and a related b_1(1400) signals as dynamical states generated by K^*ar{K} and ρπ couplings, rather than solely TS effects. In the isoscalar sector, f_1(1420) and h_1(1415) acquire substantial K^*ar{K} components or arise from coupled-channel dynamics, while f_1(1285) remains likely non-molecular; the strange sector exhibits a two-pole structure for K_1(1270) and a muted K^*ar{K} isoscalar interaction, with no clear T_ss pole. Overall, the findings support a spectrum where many axial-vector states have significant meson-meson molecular components, offering concrete, testable implications for COMPASS, BESIII, OBELIX, and BES data and contributing to the interpretation of light hadron resonances beyond quark-model pictures.

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 $f_0(980)π$ and $φπ^0$ mass spectra reported by the COMPASS and BESIII collaborations, respectively, in the $πN \to πππN$ and $J/ψ\to ηφπ$ 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 $ρπ$ 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 $χ_{cJ} \to φK^*\bar{K}$ decay, where the \(h_1(1415)\) is observed in the BESIII data.

Figures (14)

• Figure 1: The real parts of the poles on $RS_{--}$ corresponding to the subtractions matched to $q_{max}=800\,\rm{MeV}$.
• Figure 2: The imaginary parts of the poles on $RS_{--}$ corresponding to the subtractions matched to $q_{max}=800\,\rm{MeV}$ .
• Figure 3: Modulus squared of $T$-matrix elements. The dashed and solid lines correspond to the solutions of Eq. \ref{['Eq:BS']}, considering the vector meson width as zero and finite, respectively. The orange and blue lines are $|T_{11}|^2$ and $|T_{22}|^2$ determined by choosing a subtraction constant for the loops involved, matching Eqs. \ref{['Eq:Gl_cut']} and \ref{['eq:Gdr']} at threshold with $q_{\text{max}} = 1000\, \text{MeV}$, while the magenta lines are $\vert T_{22}\vert^2$ determined with $q_{\text{max}} = 800\, \text{MeV}$.
• Figure 4: The $K^{\ast}\bar{K}$ transition to $f_0(980)\pi$ via final state interaction. The black dot and rectangle represent the $K^{\ast}\bar{K}$ production rate and the unitarized scattering amplitude, respectively. The bold, solid, and dashed lines represent the vector mesons, kaon, and pion, respectively. The solid dot and rectangle indicate the production vertex of $K^{\ast}\bar{K}$ and the coupled channel scattering amplitude. The blue vertices represent the effective $K^{\ast}\bar{K} \rightarrow f_0(980)\pi$ transition, including the $K^{\ast}\bar{K} \rightarrow \rho\pi$ coupled channel scattering.
• Figure 5: Numerical results for Eq. \ref{['Eq:xsec']} corresponding to the $f_0(980)\pi$ invariant mass distribution compared to the data from COMPASS COMPASS:2020yhb. The subtraction constant regularizing the loop associated with the production is $\alpha(\mu=1000~{\rm MeV})=-0.70$.