U_A(1) anomaly and eta' mass from an infrared singular quark-gluon vertex

Abstract

The $U_A(1)$ problem of QCD is inevitably tied to the infrared behaviour of quarks and gluons with its most visible effect being the ${\eta }^{\prime }$ mass. A dimensional argument of Kogut and Susskind showed that the mixing of the pseudoscalar flavour-singlet mesons with gluons can provide a screening of the Goldstone pole in this channel if the full quark-quark interaction is strongly infrared singular as $\sim 1/k^4$. We investigate this idea using previously obtained results for the Landau gauge ghost and gluon propagator, together with recent determinations for the singular behaviour of the quark-gluon vertex. We find that, even with an infrared vanishing gluon propagator, the singular structure of the quark-gluon vertex for certain kinematics is apposite for yielding a non-zero screening mass.

arXiv comment8 pages, 4 figures. Version to appear in EPJA

References in corpus (38)

• Big-Bang nucleosynthesis (Particle Data Group mini-review)
• The Cosmological Parameters 2006
• Dyson-Schwinger Equations and the Application to Hadronic Physics
• The Infrared Behavior of QCD Green's Functions - Confinement, Dynamical Symmetry Breaking, and Hadrons as Relativistic Bound States
• Mixing and Decay Constants of Pseudoscalar Mesons
• Dyson-Schwinger equations: a tool for hadron physics
• Infrared Properties of QCD from Dyson-Schwinger equations
• The Infrared Behavior of Gluon and Ghost Propagators in Landau Gauge QCD
• Periodic Instantons with non-trivial Holonomy
• SU(2) Calorons and Magnetic Monopoles
• On the Infrared Exponent for Gluon and Ghost Propagation in Landau Gauge QCD
• Non-perturbative Propagators, Running Coupling and Dynamical Quark Mass of Landau gauge QCD
• Non-perturbative Landau gauge and infrared critical exponents in QCD
• Analytic properties of the Landau gauge gluon and quark propagators
• Infrared behaviour and fixed points in Landau gauge QCD
• Masses, decays and mixings of gluonia in QCD
• Vertex functions and infrared fixed point in Landau gauge SU(N) Yang-Mills theory
• The quark-gluon vertex in Landau gauge QCD: Its role in dynamical chiral symmetry breaking and quark confinement
• Topological susceptibility in the SU(3) gauge theory
• Uniqueness of infrared asymptotics in Landau gauge Yang-Mills theory II
• Uniqueness of infrared asymptotics in Landau gauge Yang-Mills theory
• Topological effects in QCD and the problem of short-distance singularities
• Infrared singularities in Landau gauge Yang-Mills theory
• Center vortex model for the infrared sector of Yang-Mills theory - Topological Susceptibility
• The U_A(1) Problem on the Lattice with Ginsparg-Wilson Fermions
• Quark Confinement: The Hard Problem of Hadron Physics
• Flavour symmetry breaking and meson masses
• Topological susceptibility in full QCD with Ginsparg-Wilson fermions
• Some more remarks on the Witten-Veneziano formula for the ${\eta }^{\prime }$ mass
• Signals of confinement in Green functions of SU(2) Yang-Mills theory
• Topological Susceptibility of Yang-Mills Center Projection Vortices
• Calorons, instantons and constituent monopoles in SU(3) lattice gauge theory
• Calculation of the anomalous $\gamma {\pi }^{\ast }\to \pi \pi$ form factor
• Off-Shell Axial Anomaly via the γ^* π^0 -> γTransition
• Analytic structure of the gluon and quark propagators in Landau gauge QCD
• Dynamically induced scalar quark confinement
• Calorons in SU(3) lattice gauge theory
• Microscopic quark study of the eta and eta' masses

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