The nature of $\sigma$, $\kappa$, $a_0(980)$ and $f_0(980)$

Abstract

Masses and widths of the four light scalar mesons $\sigma$, $\kappa$, $a_0$(980) and $f_0$(980) may be reproduced in a model where mesons scatter via a $q\bar{q}$ loop. A transition potential is used to couple mesons to $q\bar{q}$ at a radius of $\sim 0.57$ fm. Inside this radius, there is an infinite bare spectrum of confined $q\bar{q}$ states, for which a harmonic oscillator is chosen here. The coupled-channel system approximately reproduces the features of both light and heavy meson spectroscopy. The generation of $\sigma$, $\kappa$, $a_0(980)$ and $f_0(980)$ is a balance between attraction due to the $q\bar{q}$ loop and suppression of the amplitudes at the Adler zeros. Phase shifts increase more rapidly as the coupling constant to the mesons increases. This leads to resonant widths which decrease with increasing coupling constant - a characteristically non-perturbative effect.

Plain LaTeX, 10 pages, 3 EPS figures; v2: 11 pages, better-quality figures, extra references, version accepted for publication in Phys. Lett. B

References in corpus (3)

• A low-lying scalar meson nonet in a unitarized meson model
• The K^*_0(800) scalar resonance from Roy-Steiner representations of pi K scattering
• Reconclining phi radiative decays with other data for a0(980), fo(980), pi-pi -> KK and pi-pi -> eta-eta

Cited by in corpus (42)

• Glueballs, Hybrids, Multiquarks. Experimental facts versus QCD inspired concepts
• Dynamically Generated Open and Hidden Charm Meson Systems
• Is f0(1710) a glueball?
• How Resonances can synchronise with Thresholds
• Effects of S-wave thresholds
• D_{sJ}(2860) as the first radial excitation of the D_{s0}^*(2317)
• Chromomagnetism, flavour symmetry breaking and S-wave tetraquarks
• The mass of the sigma pole
• Study of $K_0^{\ast }(1430)$ and $a_0(980)$ from $B\to K_0^{\ast }(1430)\pi$ and $B\to a_0(980)K$ Decays
• Hadron Spectroscopy: Theory and Experiment
• Dispersive $\pi K\to \pi K$ and $\pi \pi \to K\bar{K}$ amplitudes from scattering data, threshold parameters and the lightest strange resonance $\kappa$ or $K_0^{\ast }(700)$
• $I=1/2$ $S$-wave and $P$-wave $K\pi$ scattering and the $\kappa$ and $K^{\ast }$ resonances from lattice QCD
• Modern meson spectroscopy: the fundamental role of unitarity
• Towards an understanding of the light scalar mesons
• Propagator poles and an emergent stable state below threshold: general discussion and the E(38) state
• The role of the next-to-leading order triangle-shaped diagram in two-body hadronic decays
• Scalar resonances in the $D^{+}\to K^{-}{K}^{+}{K}^{+}$ decay
• Two-pole structures in a relativistic Friedrichs-Lee-QPC scheme
• The $D_s^{+}\to a_0(980)e^{+}{\nu }_e$ reaction and the $a_0(980)-f_0(980)$ mixing
• Remarks on meson loop effects on quark models
• $a_0(980)-f_0(980)$ mixing in ${\chi }_{c1}\to {\pi }^0{f}_0(980)\to {\pi }^0{\pi }^{+}{\pi }^{-}$ and ${\chi }_{c1}\to {\pi }^0{a}_0(980)\to {\pi }^0{\pi }^0\eta$
• Multichannel calculation of the very narrow $D_{s0}^{\ast }(2317)$ and the very broad $D_0^{\ast }(2300-2400)$
• Do near-threshold molecular states mix with neighbouring $\bar{Q}Q$ states?
• Synchonisation of Resonances with Thresholds
• Constituent and current quark masses at low chiral energies
• Hadron Spectroscopy in 2006
• The scalar-isovector sector in the extended Linear Sigma Model
• Low-mass enhancement of kaon pairs in $B^{+}\to {\bar{D}}^{(\ast )0}{K}^{+}{\bar{K}}^0$ and $B^0\to D^{(\ast )-}{K}^{+}{\bar{K}}^0$ decays
• S-wave and P-wave pion-pion and kaon-pion contributions to three-body decay processes in the Resonance-Spectrum Expansion
• Observation of $D^{+}\to f_0(500){\mu }^{+}{\nu }_{\mu }$ and study of $D^{+}\to {\pi }^{+}{\pi }^{-}{\ell }^{+}{\nu }_{\ell }$ decay dynamics
• Experimental disagreements with Extended Unitarity
• A helpful analogy between the covalent bond and Particle Spectroscopy
• Comment on "Scrutinizing pion-pion scattering in light of recent lattice phase shifts"
• Role of the $\sigma$-resonance in determining the convergence of chiral perturbation theory
• How we discovered the nonet of light scalar mesons
• $N_C$ evolution of the light meson resonances
• Unitary model analysis of $f_0(500)$ pole positions by continuously varying $m_{\pi }$: comparison with discrete lattice predictions
• Understanding the $f_0(980)$ and $a_0(980)$ masses as well as their widths
• Study of conventional and non-conventional scalar and vector mesons
• Dynamical generation of hadronic resonances in effective models with derivative interactions
• New c-cbar structure around 3764 MeV at BES and predictions from unquenching the confinement spectrum
• Precision dispersive approaches versus unitarized Chiral Perturbation Theory for the lightest scalar resonances $\sigma /f_0(500)$ and $\kappa /K_0^{\ast }(700)$