Gluon bound state and asymptotic freedom derived from the Bethe--Salpeter equation

Abstract

In this paper we study the two-body bound states for gluons and ghosts in a massive Yang-Mills theory which is obtained by generalizing the ordinary massless Yang-Mills theory in a manifestly Lorentz covariant gauge. First, we give a systematic derivation of the coupled Bethe-Salpeter equations for gluons and ghosts by using the Cornwall-Jackiw-Tomboulis effective action of the composite operators within the framework of the path integral quantization. Then, we obtain the numerical solutions for the Bethe-Salpeter amplitude representing the simultaneous bound states of gluons and ghosts by solving the homogeneous Bethe-Salpeter equation in the ladder approximation. We study how the inclusion of ghosts affects the two-gluon bound states in the cases of the standing and running gauge coupling constant. Moreover, we show explicitly that the approximate solutions obtained for the gluon-gluon amplitude are consistent with the ultraviolet asymptotic freedom signaled by the negative $\beta$ function.

arXiv commentIntroduction has been a bit modified and Section 7 has been completely revised. This is the version accepted for publication in PTEP

References in corpus (11)

• The Infrared Behavior of QCD Green's Functions - Confinement, Dynamical Symmetry Breaking, and Hadrons as Relativistic Bound States
• Gluon and ghost propagators in the Landau gauge: Deriving lattice results from Schwinger-Dyson equations
• Lattice gluodynamics computation of Landau-gauge Green's functions in the deep infrared
• On the infrared behavior of Landau gauge Yang-Mills theory
• The Infrared Behavior of Gluon and Ghost Propagators in Landau Gauge QCD
• A Solution to Coupled Dyson-Schwinger Equations for Gluons and Ghosts in Landau Gauge
• Running Coupling in Non-Perturbative QCD - I. Bare Vertices and y-max Approximation
• A low-energy effective Yang-Mills theory for quark and gluon confinement
• Spin Zero Glueballs in the Bethe-Salpeter Formalism
• Physical unitarity for a massive Yang-Mills theory without the Higgs field: (I) A perturbative treatment
• A nonperturbative construction of massive Yang-Mills fields without Higgs fields

Cited by in corpus (2)

• Nonperturbative Ball-Chiu construction of the three-gluon vertex
• Ghost dynamics in the soft gluon limit