107 research outputs found
Dynamical gluon mass generation and the IR sector of QCD
We review the Pinch Technique - Background Field Method (PT-BFM) framework
for formulating and solving the Schwinger-Dyson equations of Yang-Mills
theories. In particular, we show how within this framework it is possible to
write a new set of Schwinger-Dyson equations that (i) accommodate the dynamical
gluon mass generation through Schwinger's mechanism, and (ii) have much better
truncation properties than the the conventional equations. The resulting
solutions show (in the Landau gauge) an infra-red saturating gluon propagator
and ghost dressing function, in agreement with all lattice studies to date for
both SU(2) and SU(3) gauge groups as well as 3 and 4 space-time dimensions. We
also briefly discuss how a massive gluon enables self-consistently confinement
through the condensation of thick vortices, and study other infra-red
characteristic quantities such as the Kugo-Ojima function and the effective
charge.Comment: 15 pages, 8 figures; plenary talk presented at Light Cone 2010:
Relativistic Hadronic and Particle Physics, 14-18 June 2010, Valencia, Spai
The two-, three- and four-gluon sector of QCD in the Landau gauge
Due to the nonperturbative masslessness of the ghost field, ghost loops that
contribute to gluon Green's functions in the Landau gauge display infrared
divergences, akin to those one would encounter in a conventional perturbative
treatment. This is in sharp contrast with gluon loops, in which the
perturbative divergences are tamed by the dynamical generation of a gluon mass
acting as an effective infrared cutoff. In this paper, after reviewing the full
nonperturbative origin of this divergence in the two-gluon sector, we discuss
its implications for the three- and four-gluon sector, showing in particular
that some of the form factors characterizing the corresponding Green's
functions are bound to diverge in the infrared.Comment: 13 pages, 7 figures. Talk given at Discrete 2014 - Fourth Symposium
on Prospects in the Physics of Discrete Symmetries. 2-6 December, 2014 -
King's College, London, Englan
Gauge theories with non-trivial backgrounds
We review our most recent results in formulating gauge theories in the
presence of a background field on the basis of symmetry arguments only. In
particular we show how one can gain full control over the dependence on the
background field of the effective action, and how the so-called background
field method emerges naturally from the requirement of invariance under the
BRST and antiBRST symmetries.Comment: Contribution to "QCD-TNT-III: From quarks and gluons to hadronic
matter: A bridge too far?", 2-6 Sept 2013, ECT*, Trento, Italy; 7 page
The IR sector of QCD: lattice versus Schwinger-Dyson equations
Important information about the infrared dynamics of QCD is encoded in the
behavior of its (of-shell) Green's functions, most notably the gluon and the
ghost propagators. Due to recent improvements in the quality of lattice data
and the truncation schemes employed for the Schwinger-Dyson equations we have
now reached a point where the interplay between these two non-perturbative
tools can be most fruitful. In this talk several of the above points will be
reviewed, with particular emphasis on the implications for the ghost sector,
the non-perturbative effective charge of QCD, and the Kugo-Ojima function.Comment: 6 pages. Talk given at QCD@Work 2010 -International Workshop on QCD:
Theory and Experiment-, 20-23 June 2010, Martina Franca, Valle d'Itria
(Italy
IR properties of Yang-Mills theories from the Batalin-Vilkovisky formalism
The powerful quantization formalism of Batalin and Vilkovisky streamlines the
derivation of the complete set of (non-linear) identities arising from the
local BRST symmetry of Yang-Mills theories. When applied in the Background
Field Method type of gauges, it also gives rise to identities which relate
Green's functions involving background fields to Green's functions involving
quantum fields. All these identities lie at the core of the recent progress in
understanding from the continuum formulation the IR dynamics emerging from
lattice simulations. In this talk, we will first review the Batalin-Vilkovisky
formalism and then apply it to the problem of extracting the effective charge
from the available lattice data.Comment: 12 pages, 3 figures. v3: one typo in formula (2.14) corrected.
Contribution for the workshop "The many faces of QCD", 1-5 Nov 2010, Ghent,
Belgiu
A dynamical study of the Kugo-Ojima function
As has been recently realized, a certain two-point function -- and
its associated form factors G and L -- play a prominent role in the PT-BFM
formulation of the Schwinger-Dyson equations used to study gauge-invariantly
the gluon and ghost propagators. After showing that in the (background) Landau
gauge fully constrains the QCD ghost sector, we show that G coincides
with the Kugo-Ojima function u, whose infrared behavior has traditionally
served as the standard criterion for the realization of the Kugo-Ojima
confinement mechanism. The determination of the behavior of G for all momenta
through a combination of the available lattice data on the gluon and ghost
propagators, as well as the dynamical equation G satisfies, will be then
discussed. In particular we will show that in the deep infrared the function
deviates considerably from the value associated with the realization of the
Kugo-Ojima confinement scenario; the dependence on the renormalization point of
u, and especially of its value at q=0, will be also briefly discussed.Comment: 3 pages, 3 figures. Talk presented at the Quark Confinement and the
Hadron Spectrum - Madrid 2010, August 30th - September 3rd 2010, Madrid,
Spai
Off-shell renormalization in Higgs effective field theories
The off-shell one-loop renormalization of a Higgs effective field theory
possessing a scalar potential
with arbitrary is presented. This is achieved by renormalizing the theory
once reformulated in terms of two auxiliary fields , which, due to the
invariance under an extended Becchi-Rouet-Stora-Tyutin symmetry, are tightly
constrained by functional identities. The latter allow in turn the explicit
derivation of the mapping onto the original theory, through which the
(divergent) multi-Higgs amplitude are generated in a purely algebraic fashion.
We show that, contrary to naive expectations based on the loss of power
counting renormalizability, the Higgs field undergoes a linear Standard Model
like redefinition, and evaluate the renormalization of the complete set of
Higgs self-coupling in the case.Comment: 33 pages, no figures. v3: complete one-loop off-shell renormalization
for a BSM potential involving arbitrary powers of
presented; Higgs wavefunction
renormalization shown to be SM like; renormalization of the complete set of
Higgs self-coupling in the case discussed. v3 matches the
published on
Off-shell renormalization in the presence of dimension 6 derivative operators. I. General theory
The consistent recursive subtraction of UV divergences order by order in the
loop expansion for spontaneously broken effective field theories with
dimension-6 derivative operators is presented for an Abelian gauge group. We
solve the Slavnov-Taylor identity to all orders in the loop expansion by
homotopy techniques and a suitable choice of invariant field coordinates (named
bleached variables) for the linearly realized gauge group. This allows one to
disentangle the gauge-invariant contributions to off-shell 1-PI amplitudes from
those associated with the gauge-fixing and (generalized) non-polynomial field
redefinitions (that do appear already at one loop). The tools presented can be
easily generalized to the non-Abelian case.Comment: 37 pages, 3 figures; updated version to match the published on
Gauge invariant Ansatz for a special three-gluon vertex
We construct a general Ansatz for the three-particle vertex describing the
interaction of one background and two quantum gluons, by simultaneously solving
the Ward and Slavnov-Taylor identities it satisfies. This vertex is known to be
essential for the gauge-invariant truncation of the Schwinger-Dyson equations
of QCD, based on the pinch technique and the background field method. A key
step in this construction is the formal derivation of a set of crucial
constraints (shown to be valid to all orders), relating the various form
factors of the ghost Green's functions appearing in the aforementioned
Slavnov-Taylor identity. When inserted into the Schwinger-Dyson equation for
the gluon propagator, this vertex gives rise to a number of highly non-trivial
cancellations, which are absolutely indispensable for the self-consistency of
the entire approach.Comment: 26 pages, 4 figures; v3: more typos correcte
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