Modern meson spectroscopy: the fundamental role of unitarity

Abstract

The importance of $S$-matrix unitarity in realistic meson spectroscopy is reviewed, both its historical development and more recent applications. First the effects of imposing $S$-matrix unitarity on meson resonances is demonstrated in both the elastic and the inelastic case. Then, the static quark model is revisited and its theoretical as well as phenomenological shortcomings are highlighted. A detailed account is presented of the mesons in the tables of the Particle Data Group that cannot be explained at all or only poorly in models describing mesons as pure quark-antiquark bound states. Next the earliest unitarised and coupled-channel models are revisited, followed by several examples of puzzling meson resonances and their understanding in a modern unitarised framework. Also, recent and fully unquenched lattice descriptions of such mesons are summarised. Finally, attention is paid to production processes, which require an unconventional yet related unitary approach. Proposals for further improvement are discussed.

Invited review paper, 51 pages, 16 figures, 4 tables; to be published in "Progress in Particle and Nuclear Physics" 2021. v2: several typos corrected, in particular in Eqs. (15), (17), (36), and (37) in Section 2; some accompanying remarks rephrased for clarity; Eq. (41) improved. NOTE: v3 is identical to v2; published version (in print and online) largely corresponds to v1; v3 (=v2) is correct

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• Baryons as relativistic three-quark bound states
• A low-lying scalar meson nonet in a unitarized meson model
• Observation of a near-threshold enhancement in the e+e- -->Lambda_c+Lambda_c- cross section using initial-state radiation
• Isoscalar $\pi \pi$ scattering and the $\sigma$ meson resonance from QCD
• The Experimental Status of Glueballs
• $D_s$ mesons with $DK$ and $D^{\ast }K$ scattering near threshold
• Resonances in coupled $\pi K,\eta K$ scattering from lattice QCD
• Hadron Loops: General Theorems and Application to Charmonium
• The nature of $\sigma$, $\kappa$, $a_0(980)$ and $f_0(980)$
• D_{sJ}(2860) as the first radial excitation of the D_{s0}^*(2317)
• Effects of eight-quark interactions on the hadronic vacuum and mass spectra of light mesons
• Remarks on the study of the X(3872) from Effective Field Theory with Pion-Exchange Interaction
• Possible psi(5S), psi(4D), psi(6S) and psi(5D) signals in Lambda(c)-antiLambda(c)
• Tetraquark interpolating fields in a lattice QCD investigation of the $D_{s0}^{\ast }(2317)$ meson
• Unquenched quark-model calculation of X(3872) electromagnetic decays
• Coupling constants and transition potentials for hadronic decay modes of a meson
• Angular momentum coefficients for meson strong decay and unquenched quark models
• The complex relation between production and scattering amplitudes
• Multichannel calculation of the very narrow $D_{s0}^{\ast }(2317)$ and the very broad $D_0^{\ast }(2300-2400)$
• Strong evidence of $\rho (1250)$ from a unitary multichannel reanalysis of elastic scattering data with crossing-symmetry constraints
• Review on dynamically generated resonances

Cited by in corpus (16)

• Heavy tetraquarks in the relativistic quark model
• Study of the $DK$ interaction with femtoscopic correlation functions
• Observation of $e^{+}{e}^{-}\to \omega {\chi }_{bJ}(1P)$ and search for $X_b\to \omega {\rm Y}(1S)$ at $\sqrt{s}$ near 10.75 GeV
• Charmonium spectrum in an unquenched quark model
• Diabatic description of charmoniumlike mesons II: mass corrections and strong decay widths
• Status and Prospects of Exotic Hadrons at Belle II
• ${\chi }_{c1}(2p)$: an overshadowed charmoniumlike resonance
• Second resonance of the Higgs field: motivations, experimental signals, unitarity constraints
• Understanding the $f_0(980)$ and $a_0(980)$ masses as well as their widths
• Unitary model analysis of $f_0(500)$ pole positions by continuously varying $m_{\pi }$: comparison with discrete lattice predictions
• Strangeonium spectrum with the screening effects and interpretation of $h_1(1911)$ and $X(2300)$ observed by BESIII
• A note on the tensor and vector exchange contributions to $K\bar{K}\to K\bar{K},D\bar{D}\to D\bar{D}$ and ${\pi }^{+}{\pi }^{-}\to {\pi }^{+}{\pi }^{-}$ reactions
• Search for $e^{+}{e}^{-}\to \gamma {\chi }_{bJ}$ ($J$ = 0, 1, 2) near $\sqrt{s}=10.746$ GeV at Belle II
• Improved measurement of Born cross sections for ${\chi }_{bJ}\omega$ and ${\chi }_{bJ}({\pi }^{+}{\pi }^{-}{\pi }^0{)}_{\mathrm{non}-\omega }$ ($J$ = 0, 1, 2) at Belle and Belle II
• Precision dispersive approaches versus unitarized Chiral Perturbation Theory for the lightest scalar resonances $\sigma /f_0(500)$ and $\kappa /K_0^{\ast }(700)$
• Coupled-channel meson-meson scattering in the diabatic framework