537 research outputs found
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
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
Heavy quark medium polarization at next-to-leading order
We compute the imaginary part of the heavy quark contribution to the photon
polarization tensor, i.e. the quarkonium spectral function in the vector
channel, at next-to-leading order in thermal QCD. Matching our result, which is
valid sufficiently far away from the two-quark threshold, with a previously
determined resummed expression, which is valid close to the threshold, we
obtain a phenomenological estimate for the spectral function valid for all
non-zero energies. In particular, the new expression allows to fix the overall
normalization of the previous resummed one. Our result may be helpful for
lattice reconstructions of the spectral function (near the continuum limit),
which necessitate its high energy behaviour as input, and can in principle also
be compared with the dilepton production rate measured in heavy ion collision
experiments. In an appendix analogous results are given for the scalar channel.Comment: 43 pages. v2: a figure and other clarifications added, published
versio
On bulk viscosity and moduli decay
This pedagogically intended lecture, one of four under the header "Basics of
thermal QCD", reviews an interesting relationship, originally pointed out by
Bodeker, that exists between the bulk viscosity of Yang-Mills theory (of
possible relevance to the hydrodynamics of heavy ion collision experiments) and
the decay rate of scalar fields coupled very weakly to a heat bath (appearing
in some particle physics inspired cosmological scenarios). This topic serves,
furthermore, as a platform on which a number of generic thermal field theory
concepts are illustrated. The other three lectures (on the QCD equation of
state and the rates of elastic as well as inelastic processes experienced by
heavy quarks) are recapitulated in brief encyclopedic form.Comment: 12 pages. To appear in the proceedings of New Frontiers in QCD,
Kyoto, Japan, January 18 - March 19, 2010. v2: reference added, final versio
Heavy Quark Thermalization in Classical Lattice Gauge Theory: Lessons for Strongly-Coupled QCD
Thermalization of a heavy quark near rest is controlled by the correlator of
two electric fields along a temporal Wilson line. We address this correlator
within real-time, classical lattice Yang-Mills theory, and elaborate on the
analogies that exist with the dynamics of hot QCD. In the weak-coupling limit,
it can be shown analytically that the dynamics on the two sides are closely
related to each other. For intermediate couplings, we carry out
non-perturbative simulations within the classical theory, showing that the
leading term in the weak-coupling expansion significantly underestimates the
heavy quark thermalization rate. Our analytic and numerical results also yield
a general understanding concerning the overall shape of the spectral function
corresponding to the electric field correlator, which may be helpful in
subsequent efforts to reconstruct it from Euclidean lattice Monte Carlo
simulations.Comment: 22 pages. v2: a reference and clarifications added; published versio
Thermal gluo-magnetic vacuum of SU(N) gauge theory
The magnetic sector of SU(N) Yang-Mills theory at finite temperature is
studied. At low temperatures, T<2T_c, the analytic expressions for the
temperature dependence of the magnetic correlator, of the magnetic gluon
condensate and of the spatial string tension are obtained. Fair agreement with
lattice calculations for spatial string tension is obtained for SU(2) and SU(3)
gauge theories. The relative contribution given by non-zero Matsubara modes to
the spatial string tension is calculated. At T=2T_c this contribution is of the
order of 5%. The behavior of magnetic correlator at high temperatures is
investigated and it is shown that gluo-magnetic condensate increases with
temperature as (T)= const g^8(T) T^4.Comment: 12 pages, 3 figures; minor corrections, to appear in Phys.Lett.
Towards 4-loop NSPT result for a 3-dimensional condensate-contribution to hot QCD pressure
Thanks to dimensional reduction, the contributions to the hot QCD pressure
coming from so-called soft modes can be studied via an effective
three-dimensional theory named Electrostatic QCD (spatial Yang-Mills fields
plus an adjoint Higgs scalar). The poor convergence of the perturbative series
within EQCD suggests to perform lattice measurements of some of the associated
gluon condensates. These turn out, however, to be plagued by large
discretization artifacts. We discuss how Numerical Stochastic Perturbation
Theory can be exploited to determine the full lattice spacing dependence of one
of these condensates up to 4-loop order, and sharpen our tools on a concrete
2-loop example.Comment: Presented at 25th International Symposium on Lattice Field Theory,
Regensburg, Germany, 30 Jul - 4 Aug 2007, 7 page
A non-perturbative contribution to jet quenching
It has been argued by Caron-Huot that infrared contributions to the jet
quenching parameter in hot QCD, denoted by qhat, can be extracted from an
analysis of a certain static-potential related observable within the
dimensionally reduced effective field theory. Following this philosophy, the
order of magnitude of a non-perturbative contribution to qhat from the
colour-magnetic scale, g^2T/pi, is estimated. The result is small; it is
probably below the parametrically perturbative but in practice slowly
convergent contributions from the colour-electric scale, whose all-orders
resummation therefore remains an important challenge.Comment: 4 pages. v2: clarifications, published versio
Plaquette expectation value and gluon condensate in three dimensions
In three dimensions, the gluon condensate of pure SU(3) gauge theory has
ultraviolet divergences up to 4-loop level only. By subtracting the
corresponding terms from lattice measurements of the plaquette expectation
value and extrapolating to the continuum limit, we extract the finite part of
the gluon condensate in lattice regularization. Through a change of
regularization scheme to MSbar and (inverse) dimensional reduction, this result
would determine the first non-perturbative coefficient in the weak-coupling
expansion of hot QCD pressure.Comment: 11 page
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