Power-law running of the effective gluon mass

Abstract

The dynamically generated effective gluon mass is known to depend non-trivially on the momentum, decreasing sufficiently fast in the deep ultraviolet, in order for the renormalizability of QCD to be preserved. General arguments based on the analogy with the constituent quark masses, as well as explicit calculations using the operator-product expansion, suggest that the gluon mass falls off as the inverse square of the momentum, relating it to the gauge-invariant gluon condensate of dimension four. In this article we demonstrate that the power-law running of the effective gluon mass is indeed dynamically realized at the level of the non-perturbative Schwinger-Dyson equation. We study a gauge-invariant non-linear integral equation involving the gluon self-energy, and establish the conditions necessary for the existence of infrared finite solutions, described in terms of a momentum-dependent gluon mass. Assuming a simplified form for the gluon propagator, we derive a secondary integral equation that controls the running of the mass in the deep ultraviolet. Depending on the values chosen for certain parameters entering into the Ansatz for the fully-dressed three-gluon vertex, this latter equation yields either logarithmic solutions, familiar from previous linear studies, or a new type of solutions, displaying power-law running. In addition, it furnishes a non-trivial integral constraint, which restricts significantly (but does not determine fully) the running of the mass in the intermediate and infrared regimes. The numerical analysis presented is in complete agreement with the analytic results obtained, showing clearly the appearance of the two types of momentum-dependence, well-separated in the relevant space of parameters. Open issues and future directions are briefly discussed.

37 pages, 5 figures

References in corpus (2)

• Gluon mass generation in the PT-BFM scheme
• The Form Factors of the Gauge-Invariant Three-Gluon Vertex

Cited by in corpus (21)

• Pinch Technique: Theory and Applications
• Non-perturbative comparison of QCD effective charges
• Chiral symmetry breaking with lattice propagators
• On the massive gluon propagator, the PT-BFM scheme and the low-momentum behaviour of decoupling and scaling DSE solutions
• On the analytic structure of scalar glueball operators at Born level
• The gluon and ghost propagators in Euclidean Yang-Mills theory in the maximal Abelian gauge: taking into account the effects of the Gribov copies and of the dimension two condensates
• anQCD: a Mathematica package for calculations in general analytic QCD models
• QCD effective charge and the structure function $F_2$ at small-$x$
• Infrared finite ghost propagator in the Feynman gauge
• Renormalon-motivated evaluation of QCD observables
• Two-loop three-gluon vertex from the Curci-Ferrari model and its leading infrared behavior to all loop orders
• Non-perturbative momentum dependence of the coupling constant and hadronic models
• Gluon mass scale through the Schwinger mechanism
• Perturbative QCD in acceptable schemes with holomorphic coupling
• Polyakov loop, gluon mass, gluon condensate and its asymmetry near deconfinement
• Nonperturbative gluon exchange in $pp$ elastic scattering at TeV energies
• Vacuum energy as a c-function for theories with dynamically generated masses
• A window on infrared QCD with small expansion parameters
• The gap equations of background field invariant Refined Gribov-Zwanziger action proposals and the deconfinement transition
• Charmless $B_c\to VV$ decays in the QCD factorization approach
• One-loop analytic structure of the deep-infrared Landau-gauge gluon propagator at finite temperature