21,936 research outputs found
On dynamical gluon mass generation
The effective gluon propagator constructed with the pinch technique is
governed by a Schwinger-Dyson equation with special structure and gauge
properties, that can be deduced from the correspondence with the background
field method. Most importantly the non-perturbative gluon self-energy is
transverse order-by-order in the dressed loop expansion, and separately for
gluonic and ghost contributions, a property which allows for a meanigfull
truncation. A linearized version of the truncated Schwinger-Dyson equation is
derived, using a vertex that satisfies the required Ward identity and contains
massless poles. The resulting integral equation, subject to a properly
regularized constraint, is solved numerically, and the main features of the
solutions are briefly discussed.Comment: Special Article - QNP2006: 4th International Conference on Quarks and
Nuclear Physics, Madrid, Spain, 5-10 June 200
Gluon mass and freezing of the QCD coupling
Infrared finite solutions for the gluon propagator of pure QCD are obtained
from the gauge-invariant non-linear Schwinger-Dyson equation formulated in the
Feynman gauge of the background field method. These solutions may be fitted
using a massive propagator, with the special characteristic that the effective
mass employed drops asymptotically as the inverse square of the momentum
transfer, in agreement with general operator-product expansion arguments. Due
to the presence of the dynamical gluon mass the strong effective charge
extracted from these solutions freezes at a finite value, giving rise to an
infrared fixed point for QCD.Comment: 3 pages, 2 figures, based on talk given at the 2007 Europhysics
Conference on High Energy Physics, Manchester, 19-25 Jul
Chiral symmetry breaking with lattice propagators
We study chiral symmetry breaking using the standard gap equation,
supplemented with the infrared-finite gluon propagator and ghost dressing
function obtained from large-volume lattice simulations. One of the most
important ingredients of this analysis is the non-abelian quark-gluon vertex,
which controls the way the ghost sector enters into the gap equation.
Specifically, this vertex introduces a numerically crucial dependence on the
ghost dressing function and the quark-ghost scattering amplitude. This latter
quantity satisfies its own, previously unexplored, dynamical equation, which
may be decomposed into individual integral equations for its various form
factors. In particular, the scalar form factor is obtained from an approximate
version of the "one-loop dressed" integral equation, and its numerical impact
turns out to be rather considerable. The detailed numerical analysis of the
resulting gap equation reveals that the constituent quark mass obtained is
about 300 MeV, while fermions in the adjoint representation acquire a mass in
the range of (750-962) MeV.Comment: 32 pages, 13 figure
Nonperturbative results on the quark-gluon vertex
We present analytical and numerical results for the Dirac form factor of the
quark-gluon vertex in the quark symmetric limit, where the incoming and
outgoing quark momenta have the same magnitude but opposite sign. To accomplish
this, we compute the relevant components of the quark-ghost scattering kernel
at the one-loop dressed approximation, using as basic ingredients the full
quark propagator, obtained as a solution of the quark gap equation, and the
gluon propagator and ghost dressing function, obtained from large-volume
lattice simulations.Comment: 8 pages, 6 figures. Talk presented by A.C.A at Xth Quark Confinement
and the Hadron Spectrum, 8-12 October 2012, TUM Campus Garching, Munich,
German
QCD effective charges from lattice data
We use recent lattice data on the gluon and ghost propagators, as well as the
Kugo-Ojima function, in order to extract the non-perturbative behavior of two
particular definitions of the QCD effective charge, one based on the pinch
technique construction, and one obtained from the standard ghost-gluon vertex.
The construction relies crucially on the definition of two dimensionful
quantities, which are invariant under the renormalization group, and are built
out of very particular combinations of the aforementioned Green's functions.
The main non-perturbative feature of both effective charges, encoded in the
infrared finiteness of the gluon propagator and ghost dressing function used in
their definition, is the freezing at a common finite (non-vanishing) value, in
agreement with a plethora of theoretical and phenomenological expectations. We
discuss the sizable discrepancy between the freezing values obtained from the
present lattice analysis and the corresponding estimates derived from several
phenomenological studies, and attribute its origin to the difference in the
gauges employed. A particular toy calculation suggests that the modifications
induced to the non-perturbative gluon propagator by the gauge choice may indeed
account for the observed deviation of the freezing values.Comment: 23 pages, 7 figure
Infrared finite effective charge of QCD
We show that the gauge invariant treatment of the Schwinger-Dyson equations
of QCD leads to an infrared finite gluon propagator, signaling the dynamical
generation of an effective gluon mass, and a non-enhanced ghost propagator, in
qualitative agreement with recent lattice data. The truncation scheme employed
is based on the synergy between the pinch technique and the background field
method. One of its most powerful features is that the transversality of the
gluon self-energy is manifestly preserved, exactly as dictated by the BRST
symmetry of the theory. We then explain, for the first time in the literature,
how to construct non-perturbatively a renormalization group invariant quantity
out of the conventional gluon propagator. This newly constructed quantity
serves as the natural starting point for defining a non-perturbative effective
charge for QCD, which constitutes, in all respects, the generalization in a
non-Abelian context of the universal QED effective charge. This strong
effective charge displays asymptotic freedom in the ultraviolet, while in the
low-energy regime it freezes at a finite value, giving rise to an infrared
fixed point for QCD. Some possible pitfalls related to the extraction of such
an effective charge from infrared finite gluon propagators, such as those found
on the lattice, are briefly discussed.Comment: Invited talk given at LIGHT CONE 2008 Relativistic Nuclear and
Particle Physics, July 7-11 2008 Mulhouse, Franc
Nonperturbative gluon and ghost propagators for d=3 Yang-Mills
We study a manifestly gauge invariant set of Schwinger-Dyson equations to
determine the nonperturbative dynamics of the gluon and ghost propagators in
Yang-Mills. The use of the well-known Schwinger mechanism, in the Landau
gauge, leads to the dynamical generation of a mass for the gauge boson (gluon
in ), which, in turn, gives rise to an infrared finite gluon propagator
and ghost dressing function. The propagators obtained from the numerical
solution of these nonperturbative equations are in very good agreement with the
results of lattice simulations.Comment: 25 pages, 8 figure
The gluon mass generation mechanism: a concise primer
We present a pedagogical overview of the nonperturbative mechanism that
endows gluons with a dynamical mass. This analysis is performed based on pure
Yang-Mills theories in the Landau gauge, within the theoretical framework that
emerges from the combination of the pinch technique with the background field
method. In particular, we concentrate on the Schwinger-Dyson equation satisfied
by the gluon propagator and examine the necessary conditions for obtaining
finite solutions within the infrared region. The role of seagull diagrams
receives particular attention, as do the identities that enforce the
cancellation of all potential quadratic divergences. We stress the necessity of
introducing nonperturbative massless poles in the fully dressed vertices of the
theory in order to trigger the Schwinger mechanism, and explain in detail the
instrumental role of these poles in maintaining the Becchi-Rouet-Stora-Tyutin
symmetry at every step of the mass-generating procedure. The dynamical equation
governing the evolution of the gluon mass is derived, and its solutions are
determined numerically following implementation of a set of simplifying
assumptions. The obtained mass function is positive definite, and exhibits a
power law running that is consistent with general arguments based on the
operator product expansion in the ultraviolet region. A possible connection
between confinement and the presence of an inflection point in the gluon
propagator is briefly discussed.Comment: 37 pages, 11 figures. Based on the talk given at the Workshop
Dyson-Schwinger equations in modern mathematics and physics, ECT* (Trento)
22-26 September 2014. Review article contribution to the special issue of
Frontiers of Physics (Eds. M. Pitschmann and C. D. Roberts
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