296 research outputs found
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
Three loop MSbar renormalization of QED in the 't~Hooft-Veltman gauge
Quantum electrodynamics (QED) fixed in the 't~Hooft-Veltman gauge is
renormalized to three loops in the MSbar scheme. The beta-functions and
anomalous dimensions are computed as functions of the usual QED coupling and
the additional coupling, xi, which is introduced as part of the nonlinear gauge
fixing condition. Similar to the maximal abelian gauge of quantum
chromodynamics, the renormalization of the gauge parameter is singular.Comment: 8 latex page
Critical behaviour and scaling functions of the three-dimensional O(6) model
We numerically investigate the three-dimensional O(6) model on 12^3 to 120^3
lattices within the critical region at zero magnetic field, as well as at
finite magnetic field on the critical isotherm and for several fixed couplings
in the broken and the symmetric phase. We obtain from the Binder cumulant at
vanishing magnetic field the critical coupling J_c=1.42865(3). The universal
value of the Binder cumulant at this point is g_r(J_c)=-1.94456(10). At the
critical coupling, the critical exponents \gamma=1.604(6), \beta=0.425(2) and
\nu=0.818(5) are determined from a finite-size-scaling analysis. Furthermore,
we verify predicted effects induced by massless Goldstone modes in the broken
phase. The results are well described by the perturbative form of the model's
equation of state. Our O(6)-result is compared to the corresponding Ising, O(2)
and O(4) scaling functions. Finally, we study the finite-size-scaling behaviour
of the magnetisation on the pseudocritical line.Comment: 13 pages, 20 figures, REVTEX, fixed an error in the determination of
R_\chi and changed the corresponding line in figure 13
Quantum properties of a non-Abelian gauge invariant action with a mass parameter
We continue the study of a local, gauge invariant Yang-Mills action
containing a mass parameter, which we constructed in a previous paper starting
from the nonlocal gauge invariant mass dimension two operator F_{\mu\nu}
(D^2)^{-1} F_{\mu\nu}. We return briefly to the renormalizability of the model,
which can be proven to all orders of perturbation theory by embedding it in a
more general model with a larger symmetry content. We point out the existence
of a nilpotent BRST symmetry. Although our action contains extra
(anti)commuting tensor fields and coupling constants, we prove that our model
in the limit of vanishing mass is equivalent with ordinary massless Yang-Mills
theories. The full theory is renormalized explicitly at two loops in the MSbar
scheme and all the renormalization group functions are presented. We end with
some comments on the potential relevance of this gauge model for the issue of a
dynamical gluon mass generation.Comment: 17 pages. v2: version accepted for publication in Phys.Rev.
(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.
Two-Loop Neutrino Masses and the Solar Neutrino Problem
The addition of singlet right-handed neutrinos to the Standard Model
leads to radiatively generated mass corrections for the doublet
neutrinos. For those neutrinos which are massless at the tree level after this
addition, this implies a small mass generated at the two-loop level via
exchange. We calculate these mass corrections exactly by obtaining an
analytic form for the general case of doublets and singlets. As a
phenomenological application, we consider the case and examine the masses
and mixings of the doublet neutrinos which arise as a result of the two-loop
correction in the light of experimental data from two sources which may shed
light on the question of neutrino masses. These are(a) the neutrino detectors
reporting a solar neutrino deficit (and its resolution via
Mikheyev-Smirnov-Wolfenstein matter oscillations), and
(b) the COBE satellite data on the non-zero angular variations of the cosmic
microwave background temperature (and its possible implications for hot dark
matter). Within the framework of the extension considered here, which leaves
the gauge group structure of the Standard Model intact, we show that it is
possible for neutrinos to acquire small masses naturally, with values which are
compatible with current theoretical bias and experimental data.Comment: 24 pages, Two figures, attached as postscript files at the end,
Latex, CTP-TAMU-76/93, MRI-PHY-12/93, LTH-32
Non-Equilibrium Quantum Fields in the Large N Expansion
An effective action technique for the time evolution of a closed system
consisting of one or more mean fields interacting with their quantum
fluctuations is presented. By marrying large expansion methods to the
Schwinger-Keldysh closed time path (CTP) formulation of the quantum effective
action, causality of the resulting equations of motion is ensured and a
systematic, energy conserving and gauge invariant expansion about the
quasi-classical mean field(s) in powers of developed. The general method
is exposed in two specific examples, symmetric scalar \l\F^4 theory
and Quantum Electrodynamics (QED) with fermion fields. The \l\F^4 case is
well suited to the numerical study of the real time dynamics of phase
transitions characterized by a scalar order parameter. In QED the technique may
be used to study the quantum non-equilibrium effects of pair creation in strong
electric fields and the scattering and transport processes in a relativistic
plasma. A simple renormalization scheme that makes practical the
numerical solution of the equations of motion of these and other field theories
is described.Comment: 43 pages, LA-UR-94-783 (PRD, in press), uuencoded PostScrip
On the infrared behaviour of Gluons and Ghosts in Ghost-Antighost symmetric gauges
To investigate the possibility of a ghost-antighost condensate the coupled
Dyson--Schwinger equations for the gluon and ghost propagators in Yang--Mills
theories are derived in general covariant gauges, including ghost-antighost
symmetric gauges. The infrared behaviour of these two-point functions is
studied in a bare-vertex truncation scheme which has proven to be successful in
Landau gauge. In all linear covariant gauges the same infrared behaviour as in
Landau gauge is found: The gluon propagator is infrared suppressed whereas the
ghost propagator is infrared enhanced. This infrared singular behaviour
provides indication against a ghost-antighost condensate. In the
ghost-antighost symmetric gauges we find that the infrared behaviour of the
gluon and ghost propagators cannot be determined when replacing all dressed
vertices by bare ones. The question of a BRST invariant dimension two
condensate remains to be further studied.Comment: 34 pages, 6 figures, Version to be published in Phys. Rev.
Critical exponents of the Gross-Neveu model from the effective average action
The phase transition of the Gross-Neveu model with N fermions is investigated
by means of a non-perturbative evolution equation for the scale dependence of
the effective average action. The critical exponents and scaling amplitudes are
calculated for various values of N in d=3. It is also explicitely verified that
the Neveu-Yukawa model belongs to the same universality class as the
Gross-Neveu model.Comment: RevTeX, 4 pages, 2 figures, 1 table. Typos corrected in equation
Polarized Parton Distribution Functions in the Nucleon
Polarized parton distribution functions are determined by using world data
from the longitudinally polarized deep inelastic scattering experiments. A new
parametrization of the parton distribution functions is adopted by taking into
account the positivity and the counting rule. From the fit to the asymmetry
data A_1, the polarized distribution functions of u and d valence quarks, sea
quarks, and gluon are obtained. The results indicate that the quark spin
content is \Delta\Sigma=0.20 and 0.05 in the leading order (LO) and the
next-to-leading-order (NLO) MS-bar scheme, respectively. However, if x
dependence of the sea-quark distribution is fixed at small x by "perturbative
QCD" and Regge theory, it becomes \Delta \Sigma=0.24 ~ 0.28 in the NLO. The
small-x behavior cannot be uniquely determined by the existing data, which
indicates the importance of future experiments. From our analysis, we propose
one set of LO distributions and two sets of NLO ones as the
longitudinally-polarized parton distribution functions.Comment: 51 pages, REVTeX, aps.sty, aps12.sty, epsfig.sty, prabib.sty,
revtex.sty, revtex.cls, 17 eps figures. Submitted for publication. Email:
[email protected]
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