206 research outputs found
Schwinger functions and light-quark bound states
We examine the applicability and viability of methods to obtain knowledge
about bound-states from information provided solely in Euclidean space.
Rudimentary methods can be adequate if one only requires information about the
ground and first excited state and assumptions made about analytic properties
are valid. However, to obtain information from Schwinger functions about higher
mass states, something more sophisticated is necessary. A method based on the
correlator matrix can be dependable when operators are carefully tuned and
errors are small. This method is nevertheless not competitive when an
unambiguous analytic continuation of even a single Schwinger function to
complex momenta is available.Comment: 27 pages, 14 figure
Aspects and consequences of a dressed-quark-gluon vertex
Features of the dressed-quark-gluon vertex and their role in the gap and
Bethe-Salpeter equations are explored. It is argued that quenched lattice data
indicate the existence of net attraction in the colour-octet projection of the
quark-antiquark scattering kernel. This attraction affects the uniformity with
which solutions of truncated equations converge pointwise to solutions of the
complete gap and vertex equations. For current-quark masses less than the scale
set by dynamical chiral symmetry breaking, the dependence of the
dressed-quark-gluon vertex on the current-quark mass is weak. The study employs
a vertex model whose diagrammatic content is explicitly enumerable. That
enables the systematic construction of a vertex-consistent Bethe-Salpeter
kernel and thereby an exploration of the consequences for the strong
interaction spectrum of attraction in the colour-octet channel. With rising
current-quark mass the rainbow-ladder truncation is shown to provide an
increasingly accurate estimate of a bound state's mass. Moreover, the
calculated splitting between vector and pseudoscalar meson masses vanishes as
the current-quark mass increases, which argues for the mass of the pseudoscalar
partner of the \Upsilon(1S) to be above 9.4 GeV. The absence of
colour-antitriplet diquarks from the strong interaction spectrum is contingent
upon the net amount of attraction in the octet projected quark-antiquark
scattering kernel. There is a window within which diquarks appear. The amount
of attraction suggested by lattice results is outside this domain.Comment: 22 pages, 12 figure
Single-particle spectral function for the classical one-component plasma
The spectral function for an electron one-component plasma is calculated
self-consistently using the GW0 approximation for the single-particle
self-energy. In this way, correlation effects which go beyond the mean-field
description of the plasma are contained, i.e. the collisional damping of
single-particle states, the dynamical screening of the interaction and the
appearance of collective plasma modes. Secondly, a novel non-perturbative
analytic solution for the on-shell GW0 self-energy as a function of momentum is
presented. It reproduces the numerical data for the spectral function with a
relative error of less than 10% in the regime where the Debye screening
parameter is smaller than the inverse Bohr radius, kappa<1/a_B. In the limit of
low density, the non-perturbative self-energy behaves as n^(1/4), whereas a
perturbation expansion leads to the unphysical result of a density independent
self-energy [W. Fennel and H. P. Wilfer, Ann. Phys. Lpz._32_, 265 (1974)]. The
derived expression will greatly facilitate the calculation of observables in
correlated plasmas (transport properties, equation of state) that need the
spectral function as an input quantity. This is demonstrated for the shift of
the chemical potential, which is computed from the analytical formulae and
compared to the GW0-result. At a plasma temperature of 100 eV and densities
below 10^21 cm^-3, both approaches deviate less than 10% from each other.Comment: 14 pages, 9 figures accepted for publication in Phys. Rev. E v2:
added section V (application of presented formalism to chemical potential of
the OCP
On Nucleon Electromagnetic Form Factors: A Pre'cis
Electron scattering at large Q^2 probes a nucleon's quark core. This core's
contribution to electromagnetic form factors may be calculated using Poincare'
covariant Faddeev amplitudes combined with a nucleon-photon vertex that
automatically fulfills a Ward-Takahashi identity for on-shell nucleons. The
calculated behaviour of G_E^p(Q^2)/G_M^p(Q^2) on 2<Q^2(GeV^2)<6 agrees with
that inferred from polarisation transfer data, and exhibits a zero at
Q^2\approx 6.5 GeV^2. There is some evidence that F_2(Q^2)/F_1(Q^2) \propto
[\ln(Q^2/\Lambda^2)]^2/Q^2 for Q^2>6 GeV^2.Comment: Contribution to the proceedings of "Baryons 04," the 10th
International Conference on the Structure of Baryons, 25-29/Oct./04, Ecole
Polytechnique, Palaiseau; 5 pages, 3 figure
Mean field exponents and small quark masses
We demonstrate that the restoration of chiral symmetry at finite-T in a class
of confining Dyson-Schwinger equation (DSE) models of QCD is a mean field
transition, and that an accurate determination of the critical exponents using
the chiral and thermal susceptibilities requires very small values of the
current-quark mass: log_{10}(m/m_u) < -5. Other classes of DSE models
characterised by qualitatively different interactions also exhibit a mean field
transition. Incipient in this observation is the suggestion that mean field
exponents are a result of the gap equation's fermion substructure and not of
the interaction.Comment: 13 pages, 3 figures, REVTEX, epsfi
Survey of nucleon electromagnetic form factors
A dressed-quark core contribution to nucleon electromagnetic form factors is
calculated. It is defined by the solution of a Poincare' covariant Faddeev
equation in which dressed-quarks provide the elementary degree of freedom and
correlations between them are expressed via diquarks. The nucleon-photon vertex
involves a single parameter; i.e., a diquark charge radius. It is argued to be
commensurate with the pion's charge radius. A comprehensive analysis and
explanation of the form factors is built upon this foundation. A particular
feature of the study is a separation of form factor contributions into those
from different diagram types and correlation sectors, and subsequently a
flavour separation for each of these. Amongst the extensive body of results
that one could highlight are: r_1^{n,u}>r_1^{n,d}, owing to the presence of
axial-vector quark-quark correlations; and for both the neutron and proton the
ratio of Sachs electric and magnetic form factors possesses a zero.Comment: 43 pages, 17 figures, 12 tables, 5 appendice
Current quark mass dependence of nucleon magnetic moments and radii
A calculation of the current-quark-mass-dependence of nucleon static
electromagnetic properties is necessary in order to use observational data as a
means to place constraints on the variation of Nature's fundamental parameters.
A Poincare' covariant Faddeev equation, which describes baryons as composites
of confined-quarks and -nonpointlike-diquarks, is used to calculate this
dependence The results indicate that, like observables dependent on the
nucleons' magnetic moments, quantities sensitive to their magnetic and charge
radii, such as the energy levels and transition frequencies in Hydrogen and
Deuterium, might also provide a tool with which to place limits on the allowed
variation in Nature's constants.Comment: 23 pages, 2 figures, 4 tables, 4 appendice
Diquarks: condensation without bound states
We employ a bispinor gap equation to study superfluidity at nonzero chemical
potential: mu .neq. 0, in two- and three-colour QCD. The two-colour theory,
QC2D, is an excellent exemplar: the order of truncation of the quark-quark
scattering kernel: K, has no qualitative impact, which allows a straightforward
elucidation of the effects of mu when the coupling is strong. In rainbow-ladder
truncation, diquark bound states appear in the spectrum of the three-colour
theory, a defect that is eliminated by an improvement of K. The corrected gap
equation describes a superfluid phase that is semi-quantitatively similar to
that obtained using the rainbow truncation. A model study suggests that the
width of the superfluid gap and the transition point in QC2D provide reliable
quantitative estimates of those quantities in QCD.Comment: 7 pages, 3 figures, REVTEX, epsfi
Sigma Terms of Light-Quark Hadrons
A calculation of the current-quark mass dependence of hadron masses can help
in using observational data to place constraints on the variation of nature's
fundamental parameters. A hadron's sigma-term is a measure of this dependence.
The connection between a hadron's sigma-term and the Feynman-Hellmann theorem
is illustrated with an explicit calculation for the pion using a rainbow-ladder
truncation of the Dyson-Schwinger equations: in the vicinity of the chiral
limit sigma_pi = m_pi/2. This truncation also provides a decent estimate of
sigma_rho because the two dominant self-energy corrections to the rho-meson's
mass largely cancel in their contribution to sigma_rho. The truncation is less
accurate for the omega, however, because there is little to compete with an
omega->rho+pi self-energy contribution that magnifies the value of sigma_omega
by ~25%. A Poincare' covariant Faddeev equation, which describes baryons as
composites of confined-quarks and -nonpointlike-diquarks, is solved to obtain
the current-quark mass dependence of the masses of the nucleon and Delta, and
thereby sigma_N and sigma_Delta. This "quark-core" piece is augmented by the
"pion cloud" contribution, which is positive. The analysis yields sigma_N~60MeV
and sigma_Delta~50MeV.Comment: 22 pages, reference list expande
Nucleon electromagnetic form factors
Elastic electromagnetic nucleon form factors have long provided vital
information about the structure and composition of these most basic elements of
nuclear physics. The form factors are a measurable and physical manifestation
of the nature of the nucleons' constituents and the dynamics that binds them
together. Accurate form factor data obtained in recent years using modern
experimental facilities has spurred a significant reevaluation of the nucleon
and pictures of its structure; e.g., the role of quark orbital angular
momentum, the scale at which perturbative QCD effects should become evident,
the strangeness content, and meson-cloud effects. We provide a succinct survey
of the experimental studies and theoretical interpretation of nucleon
electromagnetic form factors.Comment: Topical review invited by Journal of Physics G: Nuclear and Particle
Physics; 34 pages (contents listed on page 34), 11 figure
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