Sigma meson in pole-dominated QCD sum rules

Abstract

The properties of $\sigma$(600) meson are studied using the QCD sum rules (QSR) for the tetraquark operators. In the SU(3) chiral limit, we investigate separately SU(3) singlet and octet tetraquark states as constituents of the $\sigma$ meson, and discuss their roles for the classification of the light scalar nonets, $\sigma ,f_0,a_0$, and $\kappa$, as candidates of tetraquark states. All our analyses are performed in the the suitable Borel window which is indispensable to avoid the {\it pseudo peak} artifacts outside of the Borel window. The acceptably wide Borel window originates after preparing the favorable set up of a linear combination of operators and the inclusion of the dimension 12 terms in the OPE. Taking into account for the possible large width, we estimate masses for singlet and octet states as $700\sim 850$ MeV, $600\sim 750$ MeV, respectively, although octet states have smaller overlap with the pole than singlet state and may be strongly affected by low energy scattering states. This splitting of singlet and octet states emerges from the number of the $\bar{q}q$ annihilation diagrams, which include both color singlet annihilation processes, $qq\bar{q}\bar{q}\to (q\bar{q}{)}_1$ and color octet annihilation processes, $qq\bar{q}\bar{q}\to G(q\bar{q}{)}_8$. The mass evaluation for the $\sigma$ meson gives the value around $600\sim 800$ MeV which is much smaller than the mass obtained by 2-quark correlators, $1.0\sim 1.2$ GeV. This indicates $\sigma$ state has the large overlap with the tetraquark states.

18 pages, 15 figures

References in corpus (42)

• QCD Phenomenology based on a Chiral Effective Lagrangian
• QCD at Finite Baryon Density: Nucleon Droplets and Color Superconductivity
• Diquarks and Exotic Spectroscopy
• Chiral symmetry amplitudes in the s-wave isoscalar and isovector channels and the $\sigma ,f_0(980),a_0(980)$ scalar mesons
• Chiral Symmetry Amplitudes in the S-Wave Isoscalar and Isovector Channels and the σ, f_0(980), a_0(980) Scalar Mesons
• Glueball Spectrum and Matrix Elements on Anisotropic Lattices
• Meson-Meson interaction in a non-perturbative chiral approach
• Exotica
• N/D Description of Two Meson Amplitudes and Chiral Symmetry
• Mass and width of the lowest resonance in QCD
• A comprehensive lattice study of SU(3) glueballs
• Roy equation analysis of pi pi scattering
• Scalar mesons above and below 1 GeV
• Experimental evidence for a light and broad scalar resonance in $D^{+}\to {\pi }^{-}{\pi }^{+}{\pi }^{+}$ decay
• The inverse amplitude method in Chiral Perturbation Theory
• On the nature of light scalar mesons from their large $N_c$ behavior
• Efficient glueball simulations on anisotropic lattices
• Four Sorts of Mesons
• Putative Light Scalar Nonet
• Insight into the Scalar Mesons from a Lattice Calculation
• Scalar Quarkonium Masses and Mixing with the Lightest Scalar Glueball
• Nature of the f_0(600) from its N_c dependence at two loops in unitarized Chiral Perturbation Theory
• Quark mass dependence of the rho and sigma from dispersion relations and Chiral Perturbation Theory
• Toy model for two chiral nonets
• QCD sum rule approach for the light scalar mesons as four-quark states
• Scalar Particles in Lattice QCD
• Scalar Mesons a0(1450) and sigma(600) from Lattice QCD
• The $\sigma$ pole in $J/\psi \to \omega {\pi }^{+}{\pi }^{-}$
• QCD Tests of the Puzzling Scalar Mesons
• Light Scalar Tetraquark Mesons in the QCD Sum Rule
• A lattice study of the masses of singlet 0++ mesons
• Another look at $\pi \pi$ scattering in the scalar channel
• QCD Sum Rule Study of the Masses of Light Tetraquark Scalar Mesons
• Mixings of 4-quark components in light non-singlet scalar mesons in QCD sum rules
• Analysis the $0^{++}$ nonet mesons as four-quark states with the QCD sum rules
• An estimate of the chiral condensate from unquenched lattice QCD
• Instanton interpolating current for $\sigma$--tetraquark
• A QCD sum rule study of the light scalar mesons
• Diquark Bose-Einstein condensation
• Are the pentaquark sum rules reliable?
• Pentaquark state in pole-dominated QCD sum rules
• Exotic Hadron in Pole-dominated QCD Sum Rules

Cited by in corpus (24)

• From controversy to precision on the sigma meson: a review on the status of the non-ordinary $f_0(500)$ resonance
• Vacuum Properties of Mesons in a Linear Sigma Model with Vector Mesons and Global Chiral Invariance
• Existence of the critical endpoint in the vector meson extended linear sigma model
• Heavy quarkonium correlators at finite temperature: QCD sum rule approach
• A QCD sum rule study for a charged bottom-strange scalar meson
• Mass spectra for $qc\bar{q}\bar{c}$, $sc\bar{s}\bar{c}$, $qb\bar{q}\bar{b}$, $sb\bar{s}\bar{b}$ tetraquark states with $J^{PC}=0^{++}$ and $2^{++}$
• Theoretical support for the $\pi (1300)$ and the recently claimed $f_0(1790)$ as molecular resonances
• The B_{s0} meson and the B_{s0}B K coupling from QCD sum rules
• Nature of the sigma meson as revealed by its softening process
• Diquarks: a QCD sum rule perspective
• The structure, mixing angle, mass and couplings of the light scalar $f_0(500)$ and $f_0(980)$ mesons
• Testing the tetraquark mixing framework from QCD sum rules for $a_0(980)$
• Determination of $f_0-a_0^0$ mixing angle from QCD sum rules
• The strong decays of the light scalar mesons $f_0(500)$ and $f_0(980)$
• The new $a_1(1420)$ state: structure, mass and width
• Spin-3/2 Pentaquark in QCD Sum Rules
• Possible quantum numbers of the pentaquark Θ^+(1540) in QCD sum rules
• Can the nucleon axial charge be O(Nc^0)?
• Sigma meson in QCD sum rules using a two quark current with derivatives
• Understanding light scalar meson by color-magnetic wavefunction in QCD sum rule
• QCD Sum Rules and 1/$N_c$ expansion: On the low energy dominance and separation of scattering backgrounds
• QCD Sum Rules and 1/$N_c$ expansion
• Scalar Nonets in Pole-Dominated QCD Sum Rules
• Transition form factors for $D/B$ to $a_0(980)$ from light-cone QCD sum rules