arXiv subjects

Craig D. Roberts

Publications and source records attributed to Craig D. Roberts.

216 records · Page 12Linked to original sources

arXiv1998

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.

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arXiv1998

Infrared Behaviour of Propagators and Vertices

We elucidate constraints imposed by confinement and dynamical chiral symmetry breaking on the infrared behaviour of the dressed-quark and -gluon propagators, and dressed-quark-gluon vertex. In covariant gauges the dressing of the gluon propagator is completely specified by P(k^2):= 1/[1+Pi(k^2)], where Pi(k^2) is the vacuum polarisation. In the absence of particle-like singularities in the dressed-quark-gluon vertex, extant proposals for the dressed-gluon propagator that manifest P(k^2=0)=0 and Max[P(k^2)]~10 neither confine quarks nor break chiral symmetry dynamically. This class includes all existing estimates of P(k^2) via numerical simulations.

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arXiv1998

Nonperturbative QCD with Modern Tools

I introduce and explore a range of topics of contemporary interest in hadronic physics: from what drives the formation of a nonzero quark condensate to the effect that mechanism has on light and heavy meson form factors, and the properties of the quark-gluon plasma. The trail leads naturally through a discussion of confinement, dynamical chiral symmetry breaking and bound state structure: phenomena that require nonperturbative methods for their explanation. In all of this, the necessary momentum-dependent modification of the quark and gluon propagators plays a significant role.

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arXiv1998

Deconfinement and Hadron Properties at Extremes of Temperature and Density

After introducing essential, qualitative concepts and results, we discuss the application of Dyson-Schwinger equations to QCD at finite T and mu. We summarise the calculation of the critical exponents of two-light-flavour QCD using the chiral and thermal susceptibilities; and an algebraic model that elucidates the origin of an anticorrelation between the mu- and T-dependence of a range of meson properties. That model also provides an algebraic understanding of why the finite-T behaviour of bulk thermodynamic properties is mirrored in their mu-dependence, and why meson masses decrease with mu even though f_pi and - increase. The possibility of diquark condensation is canvassed. Its realisation is uncertain because it is contingent upon an assumption about the quark-quark scattering kernel that is demonstrably false in some applications; e.g., it predicts the existence of coloured diquarks in the strong interaction spectrum, which are not observed.

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arXiv1998

Nonperturbative effects in QCD at Finite Temperature and Density

These lecture notes illustrate the application of Dyson-Schwinger equations in QCD. The extensive body of work at zero temperature and chemical potential is represented by a selection of contemporary studies that focus on solving the Bethe-Salpeter equation, deriving an exact mass formula in QCD that describes light and heavy pseudoscalar mesons simultaneously, and the calculation of the electromagnetic pion form factor and the vector meson electroproduction cross sections. These applications emphasise the qualitative importance of the momentum-dependent dressing of elementary Schwinger functions in QCD, which provides a unifying connection between disparate phenomena. They provide a solid foundation for an extension of the approach to nonzero temperature and chemical potential. The essential, formal elements of this application are described and four contemporary studies employed to exemplify the method and its efficacy. They study the demarcation of the phase boundary for deconfinement and chiral symmetry restoration, the calculation of bulk thermodynamic properties of the quark-gluon plasma and the response of pi- and rho-meson observables to T and mu. Along the way a continuum order parameter for deconfinement is introduced, an anticorrelation between the response of masses and decay constants to T and their response to mu elucidated, and a (T,mu)-mirroring of the slow approach of bulk thermodynamic quantities to their ultrarelativistic limit highlighted. These effects too are tied to the momentum-dependent dressing of the elementary Schwinger functions.

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arXiv1998

QCD bound states and their response to extremes of temperature and density

We describe the application of Dyson-Schwinger equations to the calculation of hadron observables. The studies at zero temperature (T) and quark chemical potential (mu) provide a springboard for the extension to finite-(T,mu). Our exemplars highlight that much of hadronic physics can be understood as simply a manifestation of the nonperturbative, momentum-dependent dressing of the elementary Schwinger functions in QCD.

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arXiv1998

Pseudovector components of the pion, pi^0 -> gamma gamma, and F_pi(q^2)

As a consequence of dynamical chiral symmetry breaking the pion Bethe-Salpeter amplitude necessarily contains terms proportional to gamma_5 gamma.P and gamma_5 gamma.k, where k is the relative and P the total momentum of the constituents. These terms are essential for the preservation of low energy theorems, such as the Gell-Mann--Oakes-Renner relation and those describing anomalous decays of the pion, and to obtaining an electromagnetic pion form factor that falls as 1/q^2 for large q^2, up to calculable ln(q^2)-corrections. In a simple model, which correlates low- and high-energy pion observables, we find q^2 F_pi(q^2) ~ 0.12 - 0.19 GeV^2 for q^2 >~10 GeV^2.

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arXiv1996

Confinement, Diquarks and Goldstone's theorem

Determinations of the gluon propagator in the continuum and in lattice simulations are compared. A systematic truncation procedure for the quark Dyson-Schwinger and bound state Bethe-Salpeter equations is described. The procedure ensures the flavour-octet axial-vector Ward identity is satisfied order-by-order, thereby guaranteeing the preservation of Goldstone's theorem; and identifies a mechanism that simultaneously ensures the absence of diquarks in QCD and their presence in QCD$^{N_c=2}$, where the colour singlet diquark is the ``baryon'' of the theory.

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arXiv1996

Renormalization and Chiral Symmetry Breaking in Quenched QED in Arbitrary Covariant Gauge

We extend a previous Landau-gauge study of subtractive renormalization of the fermion propagator Dyson-Schwinger equation (DSE) in strong-coupling, quenched QED_4 to arbitrary covariant gauges. We use the fermion-photon proper vertex proposed by Curtis and Pennington with an additional correction term included to compensate for the small gauge-dependence induced by the ultraviolet regulator. We discuss the chiral limit and the onset of dynamical chiral symmetry breaking in the presence of nonperturbative renormalization. We extract the critical coupling in several different gauges and find evidence of a small residual gauge-dependence in this quantity.

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arXiv1996

Continuum study of deconfinement at finite temperature

Deconfinement and chiral symmetry restoration are explored in a confining, renormalisable, Dyson-Schwinger equation model of two-flavour QCD. An order parameter for deconfinement is introduced and used to establish that, in the chiral limit, deconfinement and chiral symmetry restoration are coincident at $T_c\approx 150\,$MeV. The transitions are second order and each has the same critical exponent: $β\approx 0.3$. The deconfinement transition is found to exhibit sensitivity to the current-quark mass. $f_π$ and $m_π$ change by no more than 10\% for $T<0.7\,T_c$, however, as $T\to T_c$, thermal fluctuations cause the pion bound state contribution to the four-point quark-antiquark correlation function to disappear.

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arXiv1996

Electromagnetic Pion Form Factor and Neutral Pion Decay Width

The electromagnetic pion form factor, $F_π(q^2)$, is calculated for spacelike-$q^2$ in impulse approximation using a confining quark propagator, $S$, and a dressed quark-photon vertex, $Γ_μ$, obtained from realistic, nonperturbative Dyson-Schwinger equation studies. Good agreement with the available data is obtained for $F_π(q^2)$ and other pion observables, including the decay $π^0 \rightarrow γ\,γ$. This calculation suggests that soft, nonperturbative contributions dominate $F_π(q^2)$ at presently accessible~$q^2$.

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arXiv1994

Pion Observables and QCD

The nonperturbative, Dyson-Schwinger equation approach to solving QCD provides a straightforward, microscopic description of dynamical chiral symmetry breaking and confinement. It is an ideal tool for the study of pion observables. This is illustrated via its application to the calculation of: the $π$-$π$ scattering lengths $a_0^0$, $a_0^2$, $a_1^1$, $a_2^0$, $a_2^2$ and associated partial wave amplitudes; the $π^0\rightarrow γγ$ decay width; and the charged pion form factor, $F_π(q^2)$.

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arXiv1994

Gauge covariant fermion propagator in quenched, chirally-symmetric quantum electrodynamics

We discuss the chirally symmetric solution of the massless, quenched, Dyson-Schwinger equation for the fermion propagator in three and four dimensions. The solutions are manifestly gauge covariant. We consider a gauge covariance constraint on the fermion--gauge-boson vertex, which motivates a vertex Ansatz that both satisfies the Ward identity when the fermion self-mass is zero and ensures gauge covariance of the fermion propagator.

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arXiv1994

Dynamical chiral symmetry breaking and confinement with an infrared-vanishing gluon propagator?

We study a model Dyson-Schwinger equation for the quark propagator closed using an {\it Ansatz} for the gluon propagator of the form \mbox{$D(q) \sim q^2/[(q^2)^2 + b^4]$} and two {\it Ansätze} for the quark-gluon vertex: the minimal Ball-Chiu and the modified form suggested by Curtis and Pennington. Using the quark condensate as an order parameter, we find that there is a critical value of $b=b_c$ such that the model does not support dynamical chiral symmetry breaking for $b>b_c$. We discuss and apply a confinement test which suggests that, for all values of $b$, the quark propagator in the model {\bf is not} confining. Together these results suggest that this Ansatz for the gluon propagator is inadequate as a model since it does not yield the expected behaviour of QCD.

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arXiv1993

Pion Loop Contribution to the Electromagnetic Pion Charge Radius

A phenomenological Dyson-Schwinger equation approach to QCD, formalised in terms of a QCD based model field theory, is used to calculate the electromagnetic charge radius of the pion. The contributions from the quark core and pion loop, as defined in this approach, are identified and compared. It is shown explicitly that the divergence of the charge radius in the chiral limit is due to the pion loop and that, at the physical value of the pion mass, this loop contributes less than 15\% to $\langle r^2_π\rangle$; i.e. the quark core is the dominant determining characteristic for the pion. This suggests that quark based models which fail to reproduce the $\ln\,m_π$ divergence of $\langle r^2_π\rangle$ may nevertheless incorporate the dominant characteristic of the pion: its quark core.

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arXiv1993

pi-pi scattering in a QCD based model field theory

A model field theory, in which the interaction between quarks is mediated by dressed vector boson exchange, is used to analyse the pionic sector of QCD. It is shown that this model, which incorporates dynamical chiral symmetry breaking, asymptotic freedom and quark confinement, allows one to calculate $f_π$, $m_π$, $r_π$ and the partial wave amplitudes in $π$-$π$ scattering and obtain good agreement with the experimental data, with the latter being well described up to energies \mbox{$E\simeq 700$ MeV}.

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arXiv1993

Schwinger-Dyson equations: Dynamical Chiral Symmetry Breaking and Confinement

A representative but not exhaustive review of the Schwinger-Dyson equation (SDE) approach to the nonperturbative study of QCD is presented. The main focus is the SDE for the quark self energy but studies of the gluon propagator and quark-gluon vertex are also discussed insofar as they are important to the quark SDE. The scope of this article is the application of these equations to the study of dynamical chiral symmetry breaking, quark confinement and the phenomenology of the spectrum and dynamics of QCD.

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arXiv1993

Gauge covariance and the fermion-photon vertex in three- and four- dimensional, massless quantum electrodynamics

In the quenched approximation, the gauge covariance properties of three vertex Ansätze in the Schwinger-Dyson equation for the fermion self energy are analysed in three- and four- dimensional quantum electrodynamics. Based on the Cornwall-Jackiw-Tomboulis effective action, it is inferred that the spectral representation used for the vertex in the gauge technique cannot support dynamical chiral symmetry breaking. A criterion for establishing whether a given Ansatz can confer gauge covariance upon the Schwinger-Dyson equation is presented and the Curtis and Pennington Ansatz is shown to satisfy this constraint. We obtain an analytic solution of the Schwinger-Dyson equation for quenched, massless three-dimensional quantum electrodynamics for arbitrary values of the gauge parameter in the absence of dynamical chiral symmetry breaking.

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