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 $q\bar{q}$ 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 $1/N_c$ 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, $\alpha (q^2)$, in the infrared region. The pattern in the coefficients that arises at tree level is consistent with large $N_c$ 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