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Abstract
We study the strong and radiative decays of the anti-quark-quark ground state $J^{PC} = 3^{--}$ ($n^{2 S + 1} L_J = 1^3 D_3$) nonet {$\rho_{3} (1690)$, $K_{3}^{\ast} (1780)$, $\phi_{3} (1850)$, $\omega_{3} (1670)$} in the framework of an effective quantum field theory approach, based on the $SU_\mathrm{V}(3)$-flavor-symmetry. The effective model is fitted to experimental data listed by the Particle Data Group. We predict numerous experimentally unknown decay widths and branching ratios. An overall agreement of theory (fit and predictions) with experimental data confirms the $\bar{q} q$ nature of the states and qualitatively validates the effective approach. Naturally, experimental clarification as well as advanced theoretical description is needed for trustworthy quantitative predictions, which is observed from some of the decay channels. Besides conventional spin-$3$ mesons, theoretical predictions for ratios of strong and radiative decays of a hypothetical glueball state $G_3 (4200)$ with $J^{PC} = 3^{--}$ are also presented.
Highlights
The spectroscopy and the phenomenological description of conventional mesons is important for many reasons
We present the glueball decays into vectors and axial vectors by considering the Lagrangian in which G3 couples to V 1 A1
The extended linear sigma model (ELSM) is built under the assumption of chiral symmetry, where gw3 pp has dimension E−2, and the W 3 A1 P
Summary
The spectroscopy and the phenomenological description of conventional mesons is important for many reasons It allows to test quantum chromodynamics (QCD) in the nonperturbative regime. It aims to the correct and systematic understanding and assignment of experimentally measured states, resonances, and mesons [1]. It is fundamental for the search of mesons that go beyond the antiquark-quark (qq) picture, such as glueballs, hybrids, and multiquark states. Both in the light-quark and heavyquark sectors, it is possible to search for “exotics” only, if the conventional qq mesons are fully under control [2].
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