Mass spectrum of pseudo-scalar glueballs from a Bethe-Salpeter approach with the rainbow-ladder truncation

Abstract

We suggest a framework based on the rainbow approximation to the Dyson-Schwinger and Bethe-Salpeter equations with effective parameters adjusted to lattice QCD data to calculate the masses of the ground and excited states of pseudo-scalar glueballs. The structure of the truncated Bethe-Salpeter equation with the gluon and ghost propagators as solutions of the truncated Dyson-Schwinger equations is analysed in Landau gauge. Both, the Bete-Salpeter and Dyson-Schwinger equations, are solved numerically within the same rainbow-ladder truncation with the same effective parameters which ensure consistency of the approach. We found that with a set of parameters, which provides a good description of the lattice data within the Dyson-Schwinger approach, the solutions of the Bethe Salpeter equation for the pseudo-scalar glueballs exhibit a rich mass spectrum which also includes the ground and excited states predicted by lattice calculations. The obtained mass spectrum contains also several intermediate excitations beyond the lattice approaches. The partial Bethe-Salpeter amplitudes of the pseudo-scalar glueballs are presented as well.

20 pages, 6 figures. arXiv admin note: text overlap with arXiv:1811.01479

References in corpus (15)

• Gluon and ghost propagators in the Landau gauge: Deriving lattice results from Schwinger-Dyson equations
• Infrared Properties of QCD from Dyson-Schwinger equations
• The Status of Glueballs
• Scaling behavior and positivity violation of the gluon propagator in full QCD
• Future Prospects for Hadron Physics at PANDA
• Spin Zero Glueballs in the Bethe-Salpeter Formalism
• Accounting for the analytical properties of the quark propagator from Dyson-Schwinger equation
• Two-Fermion Bound States within the Bethe-Salpeter Approach
• Exotic glueball $0^{\pm -}$ states in QCD Sum Rules
• Witten-Veneziano mechanism and pseudoscalar glueball-meson mixing in holographic QCD
• Heavy pseudoscalar mesons in a Schwinger-Dyson--Bethe-Salpeter approach
• Constituent gluon interpretation of glueballs and gluelumps
• Solving the Bethe-Salpeter Equation in Euclidean Space
• Search for the $0^{--}$ Glueball in ${\rm Y}(1S)$ and ${\rm Y}(2S)$ decays
• Bound states of relativistic nature

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