Nonperturbative comparison of QCD effective charges

By A. C. Aguilar, Daniele Binosi, J. Papavassiliou, J. Rodríguez-Quintero. 2009

142 citations recorded by the source corpus.

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.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/0fbe24f9ac3839838182e1dc928627bd62d42af9

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Citations in the corpus

The Gribov problem and QCD dynamics (2012, methodology): “t was shown that one can parameterize the ghost propagator, deﬁned as follows D ca( p)cb(p) E =dabG(p2); (3.119) in terms of8 G(p2) = 1 p2(1+u(p2)+w(p2)) : (3.120) This relation was also discussed in [22, 20, 23, 24, 25]. It is usually assumed that9 w(p2)=0, so that u = 1 implies an enhanced ghost p”
STUDIES OF NUCLEON RESONANCE STRUCTURE IN EXCLUSIVE MESON ELECTROPRODUCTION (2012, background): “7GeV is typical [93, 94]; and the infrared value of the coupling, αRL(M 2 g )/π = 2.”
The QCD running coupling (2016, background): “It has been shown to be closely related to α s in the Landau gauge [235].”
The Infrared Behaviour of the Pure Yang–Mills Green Functions (2005, methodology): “[188] through a so-called background quantum identity [178] and can be, in virtue of the ghost propagator DSE, connected to the ghost propagator [29,187].”