21,973 research outputs found
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
A dynamical gluon mass solution in Mandelstam's approximation
We discuss the pure gauge Schwinger-Dyson equation for the gluon propagator
in the Landau gauge within an approximation proposed by Mandelstam many years
ago. We show that a dynamical gluon mass arises as a solution. This solution is
obtained numerically in the full range of momenta that we have considered
without the introduction of any ansatz or asymptotic expression in the infrared
region. The vertex function that we use follows a prescription formulated by
Cornwall to determine the existence of a dynamical gluon mass in the light cone
gauge. The renormalization procedure differs from the one proposed by
Mandelstam and allows for the possibility of a dynamical gluon mass. Some of
the properties of this solution, such as its dependence on and
its perturbative scaling behavior are also discussed.Comment: 23 pages, 4 figures. Revised version with improved discussion on the
renormalization procedur
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
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
Phenomenological tests for the freezing of the QCD running coupling constant
We discuss phenomenological tests for the frozen infrared behavior of the
running coupling constant and gluon propagators found in some solutions of
Schwinger-Dyson equations of the gluonic sector of QCD. We verify that several
observables can be used in order to select the different expressions of alpha_s
found in the literature. We test the effect of the nonperturbative coupling in
the tau-lepton decay rate into nonstrange hadrons, in the rho vector meson
helicity density matrix that are produced in the chi_{c2} --> rho rho decay, in
the photon to pion transition form factor, and compute the cross sections for
elastic proton-proton scattering and exclusive rho production in deep inelastic
scattering. These quantities depend on the infrared behavior of the coupling
constant at different levels, we discuss the reasons for this dependence and
argue that the existent and future data can be used to test the approximations
performed to solve the Schwinger-Dyson equations and they already seems to
select one specific infrared behavior of the coupling.Comment: 15 pages, 8 figure
A brief comment on the similarities of the IR solutions for the ghost propagator DSE in Landau and Coulomb gauges
This brief note is devoted to reconcile the conclusions from a recent
analysis of the IR solutions for the ghost propagator Dyson-Schwinger equations
in Coulomb gauge with previous studies in Landau gauge.Comment: 4 pages, 1 figur
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