3,314 research outputs found
Perturbative renormalization of the electric field correlator
The momentum diffusion coefficient of a heavy quark in a hot QCD plasma can
be extracted as a transport coefficient related to the correlator of two
colour-electric fields dressing a Polyakov loop. We determine the perturbative
renormalization factor for a particular lattice discretization of this
correlator within Wilson's SU(3) gauge theory, finding a ~12% NLO correction
for values of the bare coupling used in the current generation of simulations.
The impact of this result on existing lattice determinations is commented upon,
and a possibility for non-perturbative renormalization through the gradient
flow is pointed out.Comment: 15 pages. v2: published versio
A remark on higher dimension induced domain wall defects in our world
There has been recent interest in new types of topological defects arising in
models with compact extra dimensions. We discuss in this context the old
statement that if only SU(N) gauge fields and adjoint matter live in the bulk,
and the coupling is weak, then the theory possesses a spontaneously broken
global Z(N) symmetry, with associated domain wall defects in four dimensions.
We discuss the behaviour of this symmetry at high temperatures. We argue that
the symmetry gets restored, so that cosmological domain wall production could
be used to constrain such models.Comment: 12 pages. Presentation clarified, references added; to appear in
Phys.Lett.
Four-loop lattice-regularized vacuum energy density of the three-dimensional SU(3) + adjoint Higgs theory
The pressure of QCD admits at high temperatures a factorization into purely
perturbative contributions from "hard" thermal momenta, and slowly convergent
as well as non-perturbative contributions from "soft" thermal momenta. The
latter can be related to various effective gluon condensates in a dimensionally
reduced effective field theory, and measured there through lattice simulations.
Practical measurements of one of the relevant condensates have suffered,
however, from difficulties in extrapolating convincingly to the continuum
limit. In order to gain insight on this problem, we employ Numerical Stochastic
Perturbation Theory to estimate the problematic condensate up to 4-loop order
in lattice perturbation theory. Our results seem to confirm the presence of
"large" discretization effects, going like , where is the
lattice spacing. For definite conclusions, however, it would be helpful to
repeat the corresponding part of our study with standard lattice perturbation
theory techniques.Comment: 35 pages. v2: minor corrections, published versio
Thermodynamics of the QCD plasma and the large-N limit
The equilibrium thermodynamic properties of the SU(N) plasma at finite
temperature are studied non-perturbatively in the large-N limit, via lattice
simulations. We present high-precision numerical results for the pressure,
trace of the energy-momentum tensor, energy density and entropy density of
SU(N) Yang-Mills theories with N=3, 4, 5, 6 and 8 colors, in a temperature
range from 0.8T_c to 3.4T_c (where T_c denotes the critical deconfinement
temperature). The results, normalized according to the number of gluons, show a
very mild dependence on N, supporting the idea that the dynamics of the
strongly-interacting QCD plasma could admit a description based on large-N
models. We compare our numerical data with general expectations about the
thermal behavior of the deconfined gluon plasma and with various theoretical
descriptions, including, in particular, the improved holographic QCD model
recently proposed by Kiritsis and collaborators. We also comment on the
relevance of an AdS/CFT description for the QCD plasma in a phenomenologically
interesting temperature range where the system, while still strongly-coupled,
approaches a `quasi-conformal' regime characterized by approximate scale
invariance. Finally, we perform an extrapolation of our results to the N to
limit.Comment: 1+38 pages, 13 eps figures; v2: added reference
Four-loop pressure of massless O(N) scalar field theory
Inspired by the corresponding problem in QCD, we determine the pressure of
massless O(N) scalar field theory up to order g^6 in the weak-coupling
expansion, where g^2 denotes the quartic coupling constant. This necessitates
the computation of all 4-loop vacuum graphs at a finite temperature: by making
use of methods developed by Arnold and Zhai at 3-loop level, we demonstrate
that this task is manageable at least if one restricts to computing the
logarithmic terms analytically, while handling the ``constant'' 4-loop
contributions numerically. We also inspect the numerical convergence of the
weak-coupling expansion after the inclusion of the new terms. Finally, we point
out that while the present computation introduces strategies that should be
helpful for the full 4-loop computation on the QCD-side, it also highlights the
need to develop novel computational techniques, in order to be able to complete
this formidable task in a systematic fashion.Comment: 34 page
The leading non-perturbative coefficient in the weak-coupling expansion of hot QCD pressure
Using Numerical Stochastic Perturbation Theory within three-dimensional pure
SU(3) gauge theory, we estimate the last unknown renormalization constant that
is needed for converting the vacuum energy density of this model from lattice
regularization to the MSbar scheme. Making use of a previous non-perturbative
lattice measurement of the plaquette expectation value in three dimensions,
this allows us to approximate the first non-perturbative coefficient that
appears in the weak-coupling expansion of hot QCD pressure.Comment: 16 pages. v2: published versio
Renormalization of infrared contributions to the QCD pressure
Thanks to dimensional reduction, the infrared contributions to the QCD
pressure can be obtained from two different three-dimensional effective field
theories, called the Electrostatic QCD (Yang-Mills plus adjoint Higgs) and the
Magnetostatic QCD (pure Yang-Mills theory). Lattice measurements have been
carried out within these theories, but a proper interpretation of the results
requires renormalization, and in some cases also improvement, i.e. the removal
of terms of O(a) or O(a^2). We discuss how these computations can be
implemented and carried out up to 4-loop level with the help of Numerical
Stochastic Perturbation Theory.Comment: 7 pages, 4 figures, talk presented at Lattice 2006 (High temperature
and density
Finite temperature Z(N) phase transition with Kaluza-Klein gauge fields
If SU(N) gauge fields live in a world with a circular extra dimension,
coupling there only to adjointly charged matter, the system possesses a global
Z(N) symmetry. If the radius is small enough such that dimensional reduction
takes place, this symmetry is spontaneously broken. It turns out that its fate
at high temperatures is not easily decided with straightforward perturbation
theory. Utilising non-perturbative lattice simulations, we demonstrate here
that the symmetry does get restored at a certain temperature T_c, both for a
3+1 and a 4+1 dimensional world (the latter with a finite cutoff). To avoid a
cosmological domain wall problem, such models would thus be allowed only if the
reheating temperature after inflation is below T_c. We also comment on the
robustness of this phenomenon with respect to small modifications of the model.Comment: 18 pages. Revised version, to appear in Nucl.Phys.
Determination of the weak Hamiltonian in the SU(4) chiral limit through topological zero-mode wave functions
A new method to determine the low-energy couplings of the weak
Hamiltonian is presented. It relies on a matching of the topological poles in
of three-point correlators of two pseudoscalar densities and a
four-fermion operator, measured in lattice QCD, to the same observables
computed in the -regime of chiral perturbation theory. We test this
method in a theory with a light charm quark, i.e. with an SU(4) flavour
symmetry. Quenched numerical measurements are performed in a 2 fm box, and
chiral perturbation theory predictions are worked out up to next-to-leading
order. The matching of the two sides allows to determine the weak low-energy
couplings in the SU(4) limit. We compare the results with a previous
determination, based on three-point correlators containing two left-handed
currents, and discuss the merits and drawbacks of the two procedures.Comment: 38 pages, 9 figure
Weak low-energy couplings from topological zero-mode wavefunctions
We discuss a new method to determine the low-energy couplings of the weak Hamiltonian in the -regime. It relies on a matching of the
topological poles in of three-point functions of two pseudoscalar
densities and a four-fermion operator computed in lattice QCD, to the same
observables in the Chiral Effective Theory. We present the results of a NLO
computation in chiral perturbation theory of these correlation functions
together with some preliminary numerical results.Comment: 7 pages. Contribution to Lattice 200
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