336 research outputs found
Quark number susceptibilities of hot QCD up to g^6ln(g)
The pressure of hot QCD has recently been determined to the last
perturbatively computable order g^6 ln(g) by Kajantie et al. using
three-dimensional effective theories. A similar method is applied here to the
pressure in the presence of small but non-vanishing quark chemical potentials,
and the result is used to derive the quark number susceptibilities in the limit
mu = 0. The diagonal quark number susceptibility of QCD with n_f flavours of
massless quarks is evaluated to order g^6ln(g) and compared with recent lattice
simulations. It is observed that the results qualitatively resemble the lattice
ones, and that when combined with the fully perturbative but yet undetermined
g^6 term they may well explain the behaviour of the lattice data for a wide
range of temperatures.Comment: 11 pages, 3 figures Typos corrected, references added, figures
modifie
On the screening of static electromagnetic fields in hot QED plasmas
We study the screening of static magnetic and electric fields in massless
quantum electrodynamics (QED) and massless scalar electrodynamics (SQED) at
temperature . Various exact relations for the static polarisation tensor are
first reviewed and then verified perturbatively to fifth order (in the
coupling) in QED and fourth order in SQED, using different resummation
techniques. The magnetic and electric screening masses squared, as defined
through the pole of the static propagators, are also calculated to fifth order
in QED and fourth order in SQED, and their gauge-independence and
renormalisation-group invariance is checked. Finally, we provide arguments for
the vanishing of the magnetic mass to all orders in perturbation theory.Comment: 37 pages, 8 figure
The Non-Trapping Degree of Scattering
We consider classical potential scattering. If no orbit is trapped at energy
E, the Hamiltonian dynamics defines an integer-valued topological degree. This
can be calculated explicitly and be used for symbolic dynamics of
multi-obstacle scattering.
If the potential is bounded, then in the non-trapping case the boundary of
Hill's Region is empty or homeomorphic to a sphere.
We consider classical potential scattering. If at energy E no orbit is
trapped, the Hamiltonian dynamics defines an integer-valued topological degree
deg(E) < 2. This is calculated explicitly for all potentials, and exactly the
integers < 2 are shown to occur for suitable potentials.
The non-trapping condition is restrictive in the sense that for a bounded
potential it is shown to imply that the boundary of Hill's Region in
configuration space is either empty or homeomorphic to a sphere.
However, in many situations one can decompose a potential into a sum of
non-trapping potentials with non-trivial degree and embed symbolic dynamics of
multi-obstacle scattering. This comprises a large number of earlier results,
obtained by different authors on multi-obstacle scattering.Comment: 25 pages, 1 figure Revised and enlarged version, containing more
detailed proofs and remark
Jet quenching in hot strongly coupled gauge theories simplified
Theoretical studies of jet stopping in strongly-coupled QCD-like plasmas have
used gauge-gravity duality to find that the maximum stopping distance scales
like E^{1/3} for large jet energies E. In recent work studying jets that are
created by finite-size sources in the gauge theory, we found an additional
scale: the typical (as opposed to maximum) jet stopping distance scales like
(EL)^{1/4}, where L is the size of the space-time region where the jet is
created. In this paper, we show that the results of our previous, somewhat
involved computation in the gravity dual, and the (EL)^{1/4} scale in
particular, can be very easily reproduced and understood in terms of the
distance that high-energy particles travel in AdS_5-Schwarzschild space before
falling into the black brane. We also investigate how stopping distances depend
on the conformal dimension of the source operator used to create the jet.Comment: 30 pages, 10 figure
Solution to the Perturbative Infrared Catastrophe of Hot Gauge Theories
The free energy of a nonabelian gauge theory at high temperature can be
calculated to order using resummed perturbation theory, but the method
breaks down at order . A new method is developed for calculating the free
energy to arbitrarily high accuracy in the high temperature limit. It involves
the construction of a sequence of two effective field theories by first
integrating out the momentum scale and then integrating out the momentum
scale . The free energy decomposes into the sum of three terms,
corresponding to the momentum scales , , and . The first term can
be calculated as a perturbation series in , where is the running
coupling constant. The second term in the free energy can be calculated as a
perturbation series in , beginning at order . The third term can
also be expressed as a series in beginning at order , with
coefficients that can be calculated using lattice simulations of 3-dimensional
QCD. Leading logarithms of and of can be summed up using
renormalization group equations.Comment: 11 pages LaTeX, NUHEP-TH-94-2
Linking and causality in globally hyperbolic spacetimes
The linking number is defined if link components are zero homologous.
Our affine linking invariant generalizes to the case of linked
submanifolds with arbitrary homology classes. We apply to the study of
causality in Lorentz manifolds. Let be a spacelike Cauchy surface in a
globally hyperbolic spacetime . The spherical cotangent bundle
is identified with the space of all null geodesics in
Hence the set of null geodesics passing through a point gives an
embedded -sphere in called the sky of Low observed
that if the link is nontrivial, then are causally
related. This motivated the problem (communicated by Penrose) on the Arnold's
1998 problem list to apply link theory to the study of causality. The spheres
are isotopic to fibers of They are nonzero
homologous and is undefined when is closed, while is well defined. Moreover, if is not an
odd-dimensional rational homology sphere. We give a formula for the increment
of \alk under passages through Arnold dangerous tangencies. If is
such that takes values in and is conformal to having all
the timelike sectional curvatures nonnegative, then are causally
related if and only if . We show that in
nonrefocussing are causally unrelated iff can be deformed
to a pair of -fibers of by an isotopy through skies. Low
showed that if (\ss, g) is refocussing, then is compact. We show that the
universal cover of is also compact.Comment: We added: Theorem 11.5 saying that a Cauchy surface in a refocussing
space time has finite pi_1; changed Theorem 7.5 to be in terms of conformal
classes of Lorentz metrics and did a few more changes. 45 pages, 3 figures. A
part of the paper (several results of sections 4,5,6,9,10) is an extension
and development of our work math.GT/0207219 in the context of Lorentzian
geometry. The results of sections 7,8,11,12 and Appendix B are ne
Small, Dense Quark Stars from Perturbative QCD
As a model for nonideal behavior in the equation of state of QCD at high
density, we consider cold quark matter in perturbation theory. To second order
in the strong coupling constant, , the results depend sensitively on
the choice of the renormalization mass scale. Certain choices of this scale
correspond to a strongly first order chiral transition, and generate quark
stars with maximum masses and radii approximately half that of ordinary neutron
stars. At the center of these stars, quarks are essentially massless.Comment: ReVTeX, 5 pages, 3 figure
Indication of asymptotic scaling in the reactions H, He and
It is shown that the differential cross sections of the reactions and measured at c.m.s.scattering angle
in the interval of the deuteron beam energy 0.5 - 1.2 GeV demonstrate the
scaling behaviour,, which follows from constituent
quark counting rules. It is found also that the differential cross section of
the elastic scattering at follows
the scaling regime at beam energies 0.5 - 5 GeV. These data are
parameterized here using the Reggeon exchange.Comment: 6 pages, Latex, 2 eps figures; final version accepted by Pis'ma v
ZHETF, corrected and completed reference
Approximately self-consistent resummations for the thermodynamics of the quark-gluon plasma. I. Entropy and density
We propose a gauge-invariant and manifestly UV finite resummation of the
physics of hard thermal/dense loops (HTL/HDL) in the thermodynamics of the
quark-gluon plasma. The starting point is a simple, effectively one-loop
expression for the entropy or the quark density which is derived from the fully
self-consistent two-loop skeleton approximation to the free energy, but subject
to further approximations, whose quality is tested in a scalar toy model. In
contrast to the direct HTL/HDL-resummation of the one-loop free energy, in our
approach both the leading-order (LO) and the next-to-leading order (NLO)
effects of interactions are correctly reproduced and arise from kinematical
regimes where the HTL/HDL are justifiable approximations. The LO effects are
entirely due to the (asymptotic) thermal masses of the hard particles. The NLO
ones receive contributions both from soft excitations, as described by the
HTL/HDL propagators, and from corrections to the dispersion relation of the
hard excitations, as given by HTL/HDL perturbation theory. The numerical
evaluations of our final expressions show very good agreement with lattice data
for zero-density QCD, for temperatures above twice the transition temperature.Comment: 62 pages REVTEX, 14 figures; v2: numerous clarifications, sect. 2C
shortened, new material in sect. 3C; v3: more clarifications, one appendix
removed, alternative implementation of the NLO effects, corrected eq. (5.16
Thermodynamics of Large-N_f QCD at Finite Chemical Potential
We extend the previously obtained results for the thermodynamic potential of
hot QCD in the limit of large number of fermions to non-vanishing chemical
potential. We give exact results for the thermal pressure in the entire range
of temperature and chemical potential for which the presence of a Landau pole
is negligible numerically. In addition we compute linear and non-linear quark
susceptibilities at zero chemical potential, and the entropy at small
temperatures. We compare with the available perturbative results and determine
their range of applicability. Our numerical accuracy is sufficiently high to
check and verify existing results, including the recent perturbative results by
Vuorinen on quark number susceptibilities and the older results by Freedman and
McLerran on the pressure at zero temperature and high chemical potential. We
also obtain a number of perturbative coefficients at sixth order in the
coupling that have not yet been calculated analytically. In the case of both
non-zero temperature and non-zero chemical potential, we investigate the range
of validity of a scaling behaviour noticed recently in lattice calculations by
Fodor, Katz, and Szabo at moderately large chemical potential and find that it
breaks down rather abruptly at , which points to a
presumably generic obstruction for extrapolating data from small to large
chemical potential. At sufficiently small temperatures , we find
dominating non-Fermi-liquid contributions to the interaction part of the
entropy, which exhibits strong nonlinearity in the temperature and an excess
over the free-theory value.Comment: 18 pages, 7 figures, JHEP style; v2: several updates, rewritten and
extended sect. 3.4 covering now "Entropy at small temperatures and
non-Fermi-liquid behaviour"; v3: additional remarks at the end of sect. 3.4;
v4: minor corrections and additions (version to appear in JHEP
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