Systematic study of exotic $1^{-+}$ tetraquark spectroscopy

TL;DR

This work tackles the problem of identifying and characterizing exotic $1^{-+}$ tetraquarks across light, charmonium-like, and fully-charm sectors using a nonrelativistic constituent-quark model with a Cornell-like central potential and Breit-Fermi hyperfine corrections. It constructs a complete diquark–antidiquark basis with appropriate color structures and employs a harmonic-oscillator basis up to $N_{\max}=13$, solving for the spectrum and then incorporating spin–orbit effects perturbatively. The main results include a light-tetraquark ground state near $1.9$ GeV, a candidate $I=1$ $E2$ state around $2$ GeV for $\pi_1(2015)$, and a robust finding that $\eta_1(1855)$ cannot be a compact tetraquark due to vanishing CSF overlap in the $\eta\eta'$ channel; the charmonium-like tetraquark lies near $4.2$ GeV with dominant $\eta\chi_{c1}$ decays, and the fully-charm sector centers near $6.6$ GeV with notable $\eta_c\chi_{c1}$ decays. These predictions guide targeted experimental searches in channels like $\eta\chi_{c1}$, $J/\psi h_c$, and $\eta_c\chi_{c1}$, and help discriminate between tetraquark, hybrid, and molecular interpretations. The work provides a coherent framework to compare with existing and future $XYZ$-sector data and to prioritize channels that reveal the internal structure of exotic $1^{-+}$ states.

Abstract

The masses of exotic quantum-number $1^{-+}$ compact tetraquark states are calculated in a constituent quark model, where a Cornell-like potential is employed as the central potential, spin-spin and spin-orbit coupling derived from the Breit-Fermi interaction are treated as hyperfine corrections, and model parameters are taken from previous works. The ground state $1^{-+}$ P-wave tetraquarks are predicted at 1.9, 4.2, and 6.6~GeV for the light, charmonium-like, and fully-charm sectors, respectively. The decay width ratios of $1^{-+}$ tetraquark states are calculated for two-body strong decay channels within the rearrangement mechanism, including $ωh_1$ and $ηf_1$ for isospin $I=0$ light tetraquarks, $ρh_1$ and $πf_1$ for isospin $I=1$ light tetraquarks, $π/η+χ_{c1}$ and $ρ/ω+ h_c$ for charmonium-like tetraquarks, and $η_c χ_{c1}$ and $J/ψh_c$ for fully-charm tetraquarks. The theoretical results are compared with the observed exotic $1^{-+}$ states, and promising search channels for $1^{-+}$ tetraquarks are discussed. The work suggests that $η_1(1855)$ is unlikely to be a compact tetraquark state.

Figures (1)

• Figure 1: Quark rearranged diagram for $1^{-+}$ tetraquark.