341 research outputs found
Phase transition and critical behaviour of the d=3 Gross-Neveu model
A second order phase transition for the three dimensional Gross-Neveu model
is established for one fermion species N=1. This transition breaks a paritylike
discrete symmetry. It constitutes its peculiar universality class with critical
exponent \nu = 0.63 and scalar and fermionic anomalous dimension \eta_\sigma =
0.31 and \eta_\psi = 0.11, respectively. We also compute critical exponents for
other N. Our results are based on exact renormalization group equations.Comment: 4 pages, 1 figure; v4 corresponds to the published articl
O(1/N_f) Corrections to the Thirring Model in 2<d<4
The Thirring model, that is, a relativistic field theory of fermions with a
contact interaction between vector currents, is studied for dimensionalities
2<d<4 using the 1/N_f expansion, where N_f is the number of fermion species.
The model is found to have no ultraviolet divergences at leading order provided
a regularization respecting current conservation is used. Explicit O(1/N_f)
corrections are computed, and the model shown to be renormalizable at this
order in the massless limit; renormalizability appears to hold to all orders
due to a special case of Weinberg's theorem. This implies there is a universal
amplitude for four particle scattering in the asymptotic regime. Comparisons
are made with both the Gross-Neveu model and QED.Comment: 22 pages in plain TeX, with 7 figs included using psfig.tex (Minor
conceptual changes - algebra unaffected
A study of the gauge invariant, nonlocal mass operator in Yang-Mills theories
The nonlocal mass operator is
considered in Yang-Mills theories in Euclidean space-time. It is shown that the
operator can be cast in local
form through the introduction of a set of additional fields. A local and
polynomial action is thus identified. Its multiplicative renormalizability is
proven by means of the algebraic renormalization in the class of linear
covariant gauges. The anomalous dimensions of the fields and of the mass
operator are computed at one loop order. A few remarks on the possible role of
this operator for the issue of the gauge invariance of the dimension two
condensates are outlined.Comment: 34 page
The infrared behavior of the gluon and ghost propagators in SU(2) Yang-Mills theory in the maximal Abelian gauge
We report on some recent analytical results on the behaviour of the gluon and
ghost propagators in Euclidean SU(2) Yang-Mills theory quantized in the maximal
Abelian gauge (MAG). This gauge is of particular interest for the dual
superconductivity picture to explain color confinement. Two kinds of effects
are taken into account: those arising from a treatment of Gribov copies in the
MAG and those arising from a dynamical mass originating in a dimension two
gluon condensate. The diagonal component of the gluon propagator displays the
typical Gribov-type behaviour, while the off-diagonal component is of the
Yukawa type due to the dynamical mass. These results are in qualitative
agreement with available lattice data on the gluon propagators. The
off-diagonal ghost propagator exhibits an infrared enhancement due to the
Gribov restriction, while the diagonal one remains unaffected.Comment: 6 pages. Talk given by S.P. Sorella at the "I Latin American Workshop
on High Energy Phenomenology (I LAWHEP)", December 1-3 2005, Instituto de
Fisica, UFRGS, Porto Alegre, Rio Grande Do Sul, Brasi
The Landau gauge gluon and ghost propagator in the refined Gribov-Zwanziger framework in 3 dimensions
In previous works, we have constructed a refined version of the
Gribov-Zwanziger action in 4 dimensions, by taking into account a novel
dynamical effect. In this paper, we explore the 3-dimensional case. Analogously
as in 4 dimensions, we obtain a ghost propagator behaving like in the
infrared, while the gluon propagator reaches a finite nonvanishing value at
zero momentum. Simultaneously, a clear violation of positivity by the gluon
propagator is also found. This behaviour of the propagators turns out be in
agreement with the recent numerical simulations.Comment: 26 pages, 16 .eps figures. v3: version accepted for publication in
Phys Rev
A multiloop improvement of non-singlet QCD evolution equations
An approach is elaborated for calculation of "all loop" contributions to the
non-singlet evolution kernels from the diagrams with renormalon chain
insertions. Closed expressions are obtained for sums of contributions to
kernels for the DGLAP equation and for the "nonforward" ER-BL
equation from these diagrams that dominate for a large value of , the
first -function coefficient. Calculations are performed in the covariant
-gauge in a MS-like scheme. It is established that a special choice of the
gauge parameter generalizes the standard "naive nonabelianization"
approximation. The solutions are obtained to the ER-BL evolution equation
(taken at the "all loop" improved kernel), which are in form similar to
one-loop solutions. A consequence for QCD descriptions of hard processes and
the benefits and incompleteness of the approach are briefly discussed.Comment: 13 pages, revtex, 2 figures are enclosed as eps-file, the text style
and figures are corrected following version, accepted for publication to
Phys. Rev.
A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results
Recent lattice data have reported an infrared suppressed, positivity
violating gluon propagator which is nonvanishing at zero momentum and a ghost
propagator which is no longer enhanced. This paper discusses how to obtain
analytical results which are in qualitative agreement with these lattice data
within the Gribov-Zwanziger framework. This framework allows one to take into
account effects related to the existence of gauge copies, by restricting the
domain of integration in the path integral to the Gribov region. We elaborate
to great extent on a previous short paper by presenting additional results,
also confirmed by the numerical simulations. A detailed discussion on the soft
breaking of the BRST symmetry arising in the Gribov-Zwanziger approach is
provided.Comment: 38 pages, 9 figures, the content of section V has been extended and
adapte
(Borel) convergence of the variationally improved mass expansion and the O(N) Gross-Neveu model mass gap
We reconsider in some detail a construction allowing (Borel) convergence of
an alternative perturbative expansion, for specific physical quantities of
asymptotically free models. The usual perturbative expansions (with an explicit
mass dependence) are transmuted into expansions in 1/F, where
for while for m \lsim \Lambda,
being the basic scale and given by renormalization group
coefficients. (Borel) convergence holds in a range of which corresponds to
reach unambiguously the strong coupling infrared regime near , which
can define certain "non-perturbative" quantities, such as the mass gap, from a
resummation of this alternative expansion. Convergence properties can be
further improved, when combined with expansion (variationally improved
perturbation) methods. We illustrate these results by re-evaluating, from
purely perturbative informations, the O(N) Gross-Neveu model mass gap, known
for arbitrary from exact S matrix results. Comparing different levels of
approximations that can be defined within our framework, we find reasonable
agreement with the exact result.Comment: 33 pp., RevTeX4, 6 eps figures. Minor typos, notation and wording
corrections, 2 references added. To appear in Phys. Rev.
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