Rho-meson, Bethe-Salpeter equation, and the far infrared

Abstract

The Bethe-Salpeter equation in QCD connects the gauge-dependent gluon and quark degrees of freedom with the gauge-invariant properties of mesons. We study the rho meson mass and decay constant for various versions of the gauge-dependent input functions discussed in the literature, which start to differ generically below the hadronic scale, and show qualitative different infrared behavior. We find that, once the gauge-dependent quark-gluon vertex is permitted to vary as well, the rho mass and decay constant is reproduced equally well for all forms investigated. A possible conclusion from this is that these $\rho$-meson properties are only sensitive to changes in the input at scales above a few hundred MeV.

5 pages, 3 figures, 2 tables; introduction and conclusion modified, some details and one figure panel added, some further minor modifications and added references, version to appear in PRD

References in corpus (18)

• Infrared Properties of QCD from Dyson-Schwinger equations
• Lattice gluodynamics computation of Landau-gauge Green's functions in the deep infrared
• Pinch Technique: Theory and Applications
• Constraints on the IR behavior of the ghost propagator in Yang-Mills theories
• The quark-gluon vertex in Landau gauge QCD: Its role in dynamical chiral symmetry breaking and quark confinement
• Scaling behavior and positivity violation of the gluon propagator in full QCD
• Three-point vertices in Landau-gauge Yang-Mills theory
• Vector meson form factors and their quark-mass dependence
• Uniqueness of infrared asymptotics in Landau gauge Yang-Mills theory II
• Chiral and deconfinement transition from Dyson-Schwinger equations
• Gribov no-pole condition, Zwanziger horizon function, Kugo-Ojima confinement criterion, boundary conditions, BRST breaking and all that
• More on Gribov copies and propagators in Landau-gauge Yang-Mills theory
• Building the Full Fermion-Photon Vertex of QED by Imposing Multiplicative Renormalizability of the Schwinger-Dyson Equations for the Fermion and Photon Propagators
• Quark-gluon vertex in general kinematics
• Large volume behaviour of Yang-Mills propagators
• Delta-baryon mass in a covariant Faddeev approach
• Consequences Of Fully Dressing Quark-Gluon Vertex Function With Two-Point Gluon Lines
• Effective chiral restoration in the rho'-meson in lattice QCD

Cited by in corpus (4)

• Nucleon electromagnetic form factors from the covariant Faddeev equation
• A covariant study of tensor mesons
• Matrix algorithms for solving (in)homogeneous bound state equations
• Infrared scaling solutions beyond the Landau gauge: The maximally Abelian gauge and Abelian infrared dominance