The $\sigma$-meson: four-quark vs. two-quark components and decay width in a Bethe-Salpeter approach

Abstract

We study the dynamical generation of resonances in isospin singlet channels with mixing between two- and four-quark states. To this end we generalise a Bethe-Salpeter approach to four-quark states employed previously \cite{Heupel:2012ua} to accommodate for mixing diagrams. The $q\bar{q}q\bar{q}$ and $q\bar{q}$ components of the Bethe-Salpeter wave function (with light quarks $q\in \{u,d\}$) are determined consistently in a symmetry-preserving truncation of the underlying Dyson-Schwinger equations. As a prominent example we deal with the isospin-singlet $0^{++}$ meson with light quark content. We find that the $\pi \pi$ contribution of the four-quark component is mainly responsible for the low (real part of the) mass of the resulting state. We also study the analytic structure in the complex momentum plane and find a branch cut at the two-pion threshold and a singularity in the second Riemann sheet indicating a considerable decay width. Our findings are in excellent qualitative agreement with the general picture for the $\sigma /f_0(500)$ that emerged in the past two decades from dispersive approaches \cite{Pelaez:2015qba}.

arXiv comment10 pages, 7 figures, v2: minor changes, version accepted by PRD

References in corpus (43)

• Glueballs, Hybrids, Multiquarks. Experimental facts versus QCD inspired concepts
• Dyson-Schwinger equations: a tool for hadron physics
• Mass and width of the lowest resonance in QCD
• Bethe-Salpeter Study of Vector Meson Masses and Decay Constants
• Baryons as relativistic three-quark bound states
• From controversy to precision on the sigma meson: a review on the status of the non-ordinary $f_0(500)$ resonance
• A new look at scalar mesons
• Scalar mesons above and below 1 GeV
• A Theory of Scalar Mesons
• Sketching the Bethe-Salpeter kernel
• Putative Light Scalar Nonet
• Precise determination of the f0(600) and f0(980) pole parameters from a dispersive data analysis
• Nature of the f_0(600) from its N_c dependence at two loops in unitarized Chiral Perturbation Theory
• Light mesons in QCD and unquenching effects from the 3PI effective action
• Evidence for X(3872) from DD* scattering on the lattice
• Probing the gluon self-interaction in light mesons
• Spectral functions of confined particles
• Tetraquark bound states in a Bethe-Salpeter approach
• Mixing of scalar tetraquark and quarkonia states in a chiral approach
• Scalar Mesons a0(1450) and sigma(600) from Lattice QCD
• Couplings of light I=0 scalar mesons to simple operators in the complex plane
• Lattice study of light scalar tetraquarks with I=0,2,1/2,3/2: are sigma and kappa tetraquarks?
• Experimental status of the $\pi \pi$ isoscalar S wave at low energy: $f_0(600)$ pole and scattering length
• Numerical analytic continuation of Euclidean data
• Strong and electromagnetic decays of the light scalar mesons interpreted as tetraquark states
• On light baryons and their excitations
• The light scalar mesons as tetraquarks
• Resonance poles and threshold energies for hadron physical problems by a model-independent universal algorithm
• Masses of light tetraquarks and scalar mesons in the relativistic quark model
• Bethe-Salpeter Meson Masses Beyond Ladder Approximation
• Recent developments in bound-state calculations using the Dyson-Schwinger and Bethe-Salpeter equations
• Large-Nc Properties of the rho and f0(600) Mesons from Unitary Resonance Chiral Dynamics
• Chiral Perturbation Theory, the $1/N_c$ expansion and Regge behaviour determine the structure of the lightest scalar meson
• QCD based quark description of pi-pi scattering up to the sigma and rho region
• Scattering amplitudes and contour deformations
• Identification of non-ordinary mesons from the dispersive connection between their poles and their Regge trajectories: the f0(500) resonance
• Vector mesons as dynamical resonances in the Bethe-Salpeter framework
• Hadronic decays of mesons and baryons in the Dyson-Schwinger approach
• $X(3872)$ as a four-quark state in a Dyson-Schwinger/Bethe-Salpeter approach
• On the effect of resonances in the quark-photon vertex
• Unquenching the Quark-Antiquark Green's Function
• Covariant equations for the tetraquark and more
• Scalar Mesons as qbar^2 q^2? Insight from the Lattice

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