Nonperturbative comparison of QCD effective charges

Journal Article · Thu Oct 15 04:00:00 EDT 2009 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.80.085018· OSTI ID:21325408

Aguilar, A C ^[1]; Binosi, D ^[2]; Papavassiliou, J ^[3]; Rodriguez-Quintero, J ^[4]

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1. Federal University of ABC, CCNH, Rua Santa Adelia 166, CEP 09210-170, Santo Andre (Brazil)
2. European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT), Villa Tambosi, Strada delle Tabarelle 286, I-38050 Villazzano (Italy)
3. Department of Theoretical Physics and IFIC, University of Valencia-CSIC, E-46100, Valencia (Spain)
4. Department of Applied Physics, University of Huelva, E-21071 Huelva (Spain)

We study the nonperturbative behavior of two versions of the QCD effective charge, one obtained from the pinch technique gluon self-energy, and one from the ghost-gluon vertex. Despite their distinct theoretical origin, due to a fundamental identity relating various ingredients appearing in their respective definitions, the two effective charges are almost identical in the entire range of physical momenta, and coincide exactly in the deep infrared, where they freeze at a common finite value. Specifically, the dressing function of the ghost propagator is related to the two form factors in the Lorentz decomposition of a certain Green's function, appearing in a variety of field-theoretic contexts. The central identity, which is valid only in the Landau gauge, is derived from the Schwinger-Dyson equations governing the dynamics of the aforementioned quantities. The renormalization procedure that preserves the validity of the identity is carried out, and various relevant kinematic limits and physically motivated approximations are studied in detail. A crucial ingredient in this analysis is the infrared finiteness of the gluon propagator, which is inextricably connected with the aforementioned freezing of the effective charges. Some important issues related to the consistent definition of the effective charge in the presence of such a gluon propagator are resolved. We finally present a detailed numerical study of a special set of Schwinger-Dyson equations, whose solutions determine the nonperturbative dynamics of the quantities composing the two effective charges.

• OSTI ID: 21325408
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 8 Vol. 80; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
APPROXIMATIONS
COMPARATIVE EVALUATIONS
DECOMPOSITION
EFFECTIVE CHARGE
EQUATIONS
FORM FACTORS
GLUONS
GREEN FUNCTION
LORENTZ INVARIANCE
MATHEMATICAL SOLUTIONS
NUMERICAL ANALYSIS
PROPAGATOR
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
RENORMALIZATION
SELF-ENERGY