73 research outputs found
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
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
Nonperturbative aspects of the quark-photon vertex
The electromagnetic interaction with quarks is investigated through a
relativistic, electromagnetic gauge-invariant treatment. Gluon dressing of the
quark-photon vertex and the quark self-energy functions is described by the
inhomogeneous Bethe-Salpeter equation in the ladder approximation and the
Schwinger-Dyson equation in the rainbow approximation respectively. Results for
the calculation of the quark-photon vertex are presented in both the time-like
and space-like regions of photon momentum squared, however emphasis is placed
on the space-like region relevant to electron scattering. The treatment
presented here simultaneously addresses the role of dynamically generated
vector bound states and the approach to asymptotic behavior. The
resulting description is therefore applicable over the entire range of momentum
transfers available in electron scattering experiments. Input parameters are
limited to the model gluon two-point function, which is chosen to reflect
confinement and asymptotic freedom, and are largely constrained by the obtained
bound-state spectrum.Comment: 8 figures available on request by email, 25 pages, Revtex,
DOE/ER/40561-131-INT94-00-5
Goldstone Theorem and Diquark Confinement Beyond Rainbow-Ladder Approximation
The quark Dyson-Schwinger equation and meson Bethe-Salpeter equation are
studied in a truncation scheme that extends the rainbow-ladder approximation
such that, in the chiral limit, the isovector, pseudoscalar meson remains
massless. Quark-quark (diquark) correlations, which are bound in rainbow-ladder
approximation, are destabilised by repulsive contributions that only appear at
higher order in the Bethe-Salpeter kernel. The net effect of higher order terms
on the meson bound-state masses is small.Comment: 11 pages, LaTeX, elsart.sty, 3 EPS figure
Mesons as qbar-q Bound States from Euclidean 2-Point Correlators in the Bethe-Salpeter Approach
We investigate the 2-point correlation function for the vector current. The
gluons provide dressings for both the quark self energy as well as the vector
vertex function, which are described consistently by the rainbow
Dyson-Schwinger equation and the inhomogeneous ladder Bethe-Salpeter equation.
The form of the gluon propagator at low momenta is modeled by a 2-parameter
ansatz fitting the weak pion decay constant. The quarks are confined in the
sense that the quark propagator does not have a pole at timelike momenta. We
determine the ground state mass in the vector channel from the Euclidean time
Fourier transform of the correlator, which has an exponential falloff at large
times. The ground state mass lies around 590 MeV and is almost independent of
the model form for the gluon propagator. This method allows us to stay in
Euclidean space and to avoid analytic continuation of the quark or gluon
propagators into the timelike region.Comment: 21 pages (REVTEX), 8 Postscript figure
Low-energy QCD: Chiral coefficients and the quark-quark interaction
A detailed investigation of the low-energy chiral expansion is presented
within a model truncation of QCD. The truncation allows for a phenomenological
description of the quark-quark interaction in a framework which maintains the
global symmetries of QCD and permits a expansion. The model dependence
of the chiral coefficients is tested for several forms of the quark-quark
interaction by varying the form of the running coupling, , in the
infrared region. The pattern in the coefficients that arises at tree level is
consistent with large QCD, and is related to the model truncation.Comment: 28 pages, Latex, 6 postscript figures available on request to
[email protected]
A dynamical, confining model and hot quark stars
We explore the consequences of an equation of state (EOS) obtained in a
confining Dyson-Schwinger equation model of QCD for the structure and stability
of nonstrange quark stars at finite-T, and compare the results with those
obtained using a bag-model EOS. Both models support a temperature profile that
varies over the star's volume and the consequences of this are model
independent. However, in our model the analogue of the bag pressure is
(T,mu)-dependent, which is not the case in the bag model. This is a significant
qualitative difference and comparing the results effects a primary goal of
elucidating the sensitivity of quark star properties to the form of the EOS.Comment: 13 pages, 5 figures, epsfig.sty, elsart.sty. Shortened version to
appear in Phys. Lett. B, qualitatively unmodifie
Deconfinement at finite chemical potential
In a confining, renormalisable, Dyson-Schwinger equation model of two-flavour
QCD we explore the chemical-potential dependence of the dressed-quark
propagator, which provides a means of determining the behaviour of the chiral
and deconfinement order parameters, and low-energy pion observables. We find
coincident, first order deconfinement and chiral symmetry restoration
transitions at \mu_c = 375 MeV. f_\pi is insensitive to \mu until \mu \approx
\mu_0 = 0.7 mu_c when it begins to increase rapidly. m_\pi is weakly dependent
on \mu, decreasing slowly with \mu and reaching a minimum 6% less than its
\mu=0 value at \mu=\mu_0. In a two-flavour free-quark gas at \mu=\mu_c the
baryon number density would be approximately 3 \rho_0, where \rho_0=0.16
fm^{-3}; while in such a gas at \mu_0 the density is \rho_0.Comment: 11 pages, 3 figures, epsfig.sty, elsart.st
Nonperturbative Aspect of Axial Vector Vertex in the Global Color Symmetry Model
It is shown how the axial vector current of current quarks is related to that
of constituent quarks within the framework of the global color symmetry model.
Gluon dressing of the axial vector vertex and the quark self-energy functions
is described by the inhomogeneous Bethe-Salpeter equation in the ladder
approximation and the Schwinger-Dyson equation in the rainbow approximation,
respectively.Comment: 10 page
Nucleon form factors and a nonpointlike diquark
Nucleon form factors are calculated on q^2 in [0,3] GeV^2 using an Ansatz for
the nucleon's Fadde'ev amplitude motivated by quark-diquark solutions of the
relativistic Fadde'ev equation. Only the scalar diquark is retained, and it and
the quark are confined. A good description of the data requires a nonpointlike
diquark correlation with an electromagnetic radius of 0.8 r_pi. The composite,
nonpointlike nature of the diquark is crucial. It provides for diquark-breakup
terms that are of greater importance than the diquark photon absorption
contribution.Comment: 5 pages, REVTEX, epsfig, 3 figure
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