17 research outputs found
Non-perturbative Green's functions and the QCD effective charge
Using as ingredients the non-perturbative solutions of various QCD Green's
function obtained from Schwinger-Dyson equations (SDEs), we study two versions
of the QCD effective charge. The first one obtained from the pinch technique
gluon self-energy, and the second from the ghost-gluon vertex. Despite the
distinct nature of their buildings blocks, the two effectives charges are
almost identical in the entire range of momenta, due to a fundamental identity
relating the ghost dressing function with the two form factors of Green's
function, which is of central importance in the PT-BFM formalism. In this talk,
we outline how to derive this crucial identity from the SDEs of the
aforementioned Green's functions. The renormalization procedure that preserves
the validity of this identity is discussed in detail. Most importantly, we show
that due to the infrared finiteness of the gluon propagator, the QCD charge
obtained with either definition freezes in the deep infrared, in agreement with
theoretical and phenomenological expectations.Comment: 12 pages, 8 figures. Talk presented at the International Workshop on
QCD Green's Functions, Confinement, and Phenomenology - QCD-TNT09, September
07 - 11 2009, ECT* Trento, Ital
New insights on non-perturbative Yang-Mills
In this talk we review some recent results on the infrared properties of the
gluon and ghost propagators in pure Yang-Mills theories. These results are
obtained from the corresponding Schwinger-Dyson equation formulated in a
special truncation scheme, which preserves gauge invariance. The presence of
massless poles in the three gluon vertex triggers the generation of a dynamical
gluon mass (Schwinger mechanism in d=4), which gives rise to an infrared finite
gluon propagator and ghost dressing function. As a byproduct of this analysis
we calculate the Kugo-Ojima function, required for the definition of the
non-perturbative QCD effective charge within the pinch technique framework. We
show that the numerical solutions of these non-perturbative equations are in
very good agreement with the results of SU(3) lattice simulations.Comment: Invited talk at XI Hadron Physics, Maresias, S\~ao Paulo, Brazil,
21-26 March, 201
Chiral symmetry breaking revisited: the gap equation with lattice ingredients
We study chiral symmetry breaking in QCD, using as ingredients in the quark
gap equation recent lattice results for the gluon and ghost propagators. The
Ansatz employed for the quark-gluon vertex is purely non-Abelian, introducing a
crucial dependence on the ghost dressing function and the quark-ghost
scattering amplitude. The numerical impact of these quantities is considerable:
the need to invoke confinement explicitly is avoided, and the dynamical quark
masses generated are of the order of 300 MeV. In addition, the pion decay
constant and the quark condensate are computed, and are found to be in good
agreement with phenomenology.Comment: 3 pages, 5 figures. Talk presented at the Quark Confinement and the
Hadron Spectrum - Madrid 2010, August 30th - September 3rd 2010, Madrid,
Spai
Analyzing dynamical gluon mass generation
We study the necessary conditions for obtaining infrared finite solutions
from the Schwinger-Dyson equation governing the dynamics of the gluon
propagator. The equation in question is set up in the Feynman gauge of the
background field method, thus capturing a number of desirable features. Most
notably, and in contradistinction to the standard formulation, the gluon
self-energy is transverse order-by-order in the dressed loop expansion, and
separately for gluonic and ghost contributions. Various subtle field-theoretic
issues, such as renormalization group invariance and regularization of
quadratic divergences, are briefly addressed. The infrared and ultraviolet
properties of the obtained solutions are examined in detail, and the allowed
range for the effective gluon mass is presented.Comment: 7 pages, 4 figures. Talk presented at "Infrared QCD in Rio" (IRQCD
2006), 5-9 June 2006, Rio de Janeiro, Brazi
Non-perturbative QCD effective charges
Using gluon and ghost propagators obtained from Schwinger-Dyson equations
(SDEs), we construct the non-perturbative effective charge of QCD. We employ
two different definitions, which, despite their distinct field-theoretic
origin, give rise to qualitative comparable results, by virtue of a crucial
non-perturbative identity. Most importantly, the QCD charge obtained with
either definition freezes in the deep infrared, in agreement with theoretical
and phenomenological expectations. The various theoretical ingredients
necessary for this construction are reviewed in detail, and some conceptual
subtleties are briefly discussed.Comment: Invited talk at Light Cone 2009: Relativistic Nuclear and Particle
Physics (LC2009), Sao Jose dos Campos, Brazil, 8-13 July, 200
Gluon mass generation without seagull divergences
Dynamical gluon mass generation has been traditionally plagued with seagull
divergences, and all regularization procedures proposed over the years yield
finite but scheme-dependent gluon masses. In this work we show how such
divergences can be eliminated completely by virtue of a characteristic
identity, valid in dimensional regularization. The ability to trigger the
aforementioned identity hinges crucially on the particular Ansatz employed for
the three-gluon vertex entering into the Schwinger-Dyson equation governing the
gluon propagator. The use of the appropriate three-gluon vertex brings about an
additional advantage: one obtains two separate (but coupled) integral
equations, one for the effective charge and one for the gluon mass. This system
of integral equations has a unique solution, which unambiguously determines
these two quantities. Most notably, the effective charge freezes in the
infrared, and the gluon mass displays power-law running in the ultraviolet, in
agreement with earlier considerations.Comment: 37 pages, 9 figures; minor typos corrected and a few brief
explanatory remarks adde
Effective gluon mass and infrared fixed point in QCD
We report on a special type of solutions for the gluon propagator of pure
QCD, obtained from the corresponding non-linear Schwinger-Dyson equation
formulated in the Feynman gauge of the background field method. These solutions
reach a finite value in the deep infrared and may be fitted using a massive
propagator, with the crucial characteristic that the effective ``mass''
employed depends on the momentum transfer. Specifically, the gluon mass falls
off as the inverse square of the momentum, as expected from the
operator-product expansion. In addition, one may define a dimensionless
quantity, which constitutes the generalization in a non-Abelian context of the
universal QED effective charge. This strong effective charge displays
asymptotic freedom in the ultraviolet whereas in the low-energy regime it
freezes at a finite value, giving rise to an infrared fixed point for QCD.Comment: 6 pages, 2 figures, Talk given at QCD@work 2007, Martina Franca,
Italy, 16-20 June 200
Gluon mass generation in the PT-BFM scheme
In this article we study the general structure and special properties of the
Schwinger-Dyson equation for the gluon propagator constructed with the pinch
technique, together with the question of how to obtain infrared finite
solutions, associated with the generation of an effective gluon mass.
Exploiting the known all-order correspondence between the pinch technique and
the background field method, we demonstrate that, contrary to the standard
formulation, the non-perturbative gluon self-energy is transverse
order-by-order in the dressed loop expansion, and separately for gluonic and
ghost contributions. We next present a comprehensive review of several subtle
issues relevant to the search of infrared finite solutions, paying particular
attention to the role of the seagull graph in enforcing transversality, the
necessity of introducing massless poles in the three-gluon vertex, and the
incorporation of the correct renormalization group properties. In addition, we
present a method for regulating the seagull-type contributions based on
dimensional regularization; its applicability depends crucially on the
asymptotic behavior of the solutions in the deep ultraviolet, and in particular
on the anomalous dimension of the dynamically generated gluon mass. A
linearized version of the truncated Schwinger-Dyson equation is derived, using
a vertex that satisfies the required Ward identity and contains massless poles
belonging to different Lorentz structures. The resulting integral equation is
then solved numerically, the infrared and ultraviolet properties of the
obtained solutions are examined in detail, and the allowed range for the
effective gluon mass is determined. Various open questions and possible
connections with different approaches in the literature are discussed.Comment: 54 pages, 24 figure