Effects of divergent ghost loops on the Green's functions of QCD

Author(s)

Aguilar, A. C. ^[1] ; Binosi, D. ^{[2, 3]} ; Ibanez, D. ^{[2, 3]} ; Papavassiliou, J. ^{[4, 5, 6]}

Affiliation

^[1] Univ Estadual Campinas, UNICAMP, Inst Phys Gleb Wataghin, BR-13083859 Sao Paulo - Brazil

^[2] European Ctr Theoret Studies Nucl Phys & Related, I-38123 Villazzano, Trento - Italy

^[3] Fdn Bruno Kessler, I-38123 Villazzano, Trento - Italy

^[4] Univ Valencia, Dept Theoret Phys, E-46100 Valencia - Spain

^[5] Univ Valencia, IFIC, E-46100 Valencia - Spain

^[6] CSIC, E-46100 Valencia - Spain

• Document type: Journal article
• Source: Physical Review D; v. 89, n. 8 APR 3 2014.
• Web of Science Citations: 45

Abstract

In the present work, we discuss certain characteristic features encoded in some of the fundamental QCD Green's functions, for which the origin can be traced back to the nonperturbative masslessness of the ghost field, in the Landau gauge. Specifically, the ghost loops that contribute to these Green's functions display infrared divergences, akin to those encountered in the perturbative treatment, in contradistinction to the gluonic loops, for which perturbative divergences are tamed by the dynamical generation of an effective gluon mass. In d = 4, the aforementioned divergences are logarithmic, thus causing a relatively mild impact, whereas in d = 3 they are linear, giving rise to enhanced effects. In the case of the gluon propagator, these effects do not interfere with its finiteness, but make its first derivative diverge at the origin, and introduce a maximum in the region of infrared momenta. The three-gluon vertex is also affected, and the induced divergent behavior is clearly exposed in certain special kinematic configurations, usually considered in lattice simulations; the sign of the corresponding divergence is unambiguously determined. The main underlying concepts are developed in the context of a simple toy model, which demonstrates clearly the interconnected nature of the various effects. The picture that emerges is subsequently corroborated by a detailed nonperturbative analysis, combining lattice results with the dynamical integral equations governing the relevant ingredients, such as the nonperturbative ghost loop and the momentumdependent gluon mass. (AU)

• FAPESP's process: 12/15643-1 - Schwinger-Dyson equations: a tool for non-perturbative QCD
• Grantee: Arlene Cristina Aguilar
• Support Opportunities: Regular Research Grants