A. Bashir

{pi}- and {rho}-mesons, and their diquark partners, from a contact interaction.

We present a unified Dyson-Schwinger equation treatment of static and electromagnetic properties of pseudoscalar and vector mesons, and scalar and axial-vector diquark correlations, based upon a vector-vector contact interaction. A basic motivation for this paper is the need to document a comparison between the electromagnetic form factors of mesons and those diquarks that play a material role in nucleon structure. A notable result, therefore, is the large degree of similarity between related meson and diquark form factors. The simplicity of the interaction enables computation of the form factors at arbitrarily large spacelike Q(2), which enables us to expose a zero in the rho-meson electric form factor at z(Q)(rho) approximate to root 6m(rho). Notably, r(rho)z(Q)(rho) approximate to r(D)z(Q)(D), where r(rho) and r(D) are, respectively, the electric radii of the rho-meson and deuteron.

Abelian anomaly and neutral pion production

We show that in fully self-consistent treatments of the pion, namely, its static properties and elastic and transition form factors, the asymptotic limit of the product Q{sup 2}G{sub {gamma}}{sup *}{sub {gamma}{pi}}{sup 0}(Q{sup 2}), determined a priori by the interaction employed, is not exceeded at any finite value of spacelike momentum transfer. Furthermore, in such a treatment of a vector-vector contact-interaction one obtains a {gamma}{sup *{gamma}{yields}{pi}0} transition form factor that disagrees markedly with all available data. We explain that the contact interaction produces a pion distribution amplitude that is flat and nonvanishing at the endpoints. This amplitude characterizes a pointlike pion bound state. Such a state has the hardest possible form factors (i.e., form factors that become constant at large momentum transfers and hence are in striking disagreement with completed experiments). However, interactions with QCD-like behavior produce soft pions, a valence-quark distribution amplitude that vanishes as {approx}(1-x){sup 2} for x{approx}1, and results that agree with the bulk of existing data. Our analysis supports a view that the large-Q{sup 2} data obtained by the BaBar Collaboration is not an accurate measure of the {gamma}*{gamma}{yields}{pi}{sup 0} form factor.

Delta robot: inverse, direct, and intermediate Jacobians

Abstract In the context of a parallel manipulator, inverse and direct Jacobian matrices are known to contain information which helps us identify some of the singular configurations. In this article, we employ kinematic analysis for the Delta robot to derive the velocity of the end-effector in terms of the angular joint velocities, thus yielding the Jacobian matrices. Setting their determinants to zero, several undesirable postures of the manipulator have been extracted. The analysis of the inverse Jacobian matrix reveals that singularities are encountered when the limbs belonging to the same kinematic chain lie in a plane. Two of the possible configurations which correspond to this condition are when the robot is completely extended or contracted, indicating the boundaries of the workspace. Singularities associated with the direct Jacobian matrix, which correspond to relatively more complicated configurations of the manipulator, have also been derived and commented on. Moreover, the idea of intermediate Jacobian matrices have been introduced that are simpler to evaluate but still contain the information of the singularities mentioned earlier in addition to architectural singularities not contemplated in conventional Jacobians.

Gauge-independent chiral symmetry breaking in quenched QED.

In quenched QED we construct a non-perturbative fermion-boson vertex that ensures the fermion propagator satisfies the Ward-Takahashi identity, is multiplicatively renormalizable, agrees with perturbation theory for weak couplings and has a critical coupling for dynamical mass generation that is strictly gauge independent. This is in marked contrast to the rainbow approximation in which the critical coupling changes by 50% just between the Landau and Feynman gauges. The use of such a vertex should lead to a more believable study of mass generation.

Confinement and dynamical chiral symmetry breaking in QED3.

We establish that QED3 can possess a critical number of flavors, Nfc, associated with dynamical chiral symmetry breaking if, and only if, the fermion wave function renormalization and photon vacuum polarization are homogeneous functions at infrared momenta when the fermion mass function vanishes. The Ward identity entails that the fermion-photon vertex possesses the same property and ensures a simple relationship between the homogeneity degrees of each of these functions. Simple models for the photon vacuum polarization and fermion-photon vertex are used to illustrate these observations. The existence and value of Nfc are contingent upon the precise form of the vertex but any discussion of gauge dependence is moot. We introduce an order parameter for confinement. Chiral symmetry restoration and deconfinement are coincident owing to an abrupt change in the analytic properties of the fermion propagator when a nonzero scalar self-energy becomes insupportable.

Pion form factor from a contact interaction

The pion has a unique place in the Standard Model. It is a bound-state of a dressed-quark and -antiquark, and also that almost-massless collective excitation which is the Goldstone mode arising from the dynamical breaking of chiral symmetry. This dichotomy can only be understood by merging the study of many-body aspects of the QCD vacuum with the symmetry-preserving analysis of two-body bound-states. Furthermore, the possibility that this dichotomous nature could have wide-ranging effects on pion properties has made the empirical investigation of these properties highly desirable, despite the difficulty in preparing a system that can act as a pion target and the concomitant complexities in the interpretation of the experiments; e.g., [1–4]. A true understanding of the pion is achievable via QCD’s Dyson-Schwinger equations (DSEs) [5]. Key to this is the existence of a nonperturbative symmetrypreserving truncation scheme [6–8], which enables: the connection to be made between dynamical chiral symmetry breaking (DCSB) and the bound-state pion [9]; and the use of experiment to chart QCD’s �-function. The �function’s perturbative evolution is well-known but this new feedback between experiment and nonperturbative theory may provide access to its long-range behaviour. Studying the electromagnetic pion form factor, F em

Pion and kaon valence-quark parton distribution functions.

A rainbow-ladder truncation of QCDs Dyson-Schwinger equations, constrained by existing applications to hadron physics, is employed to compute the valence-quark parton distribution functions of the pion and kaon. Comparison is made to pi-N Drell-Yan data for the pions u-quark distribution and to Drell-Yan data for the ratio u(K)(x)/u(pi)(x): the environmental influence of this quantity is a parameter-free prediction, which agrees well with existing data. Our analysis unifies the computation of distribution functions with that of numerous other properties of pseudoscalar mesons.

Dynamical chiral symmetry breaking and the fermion-gauge-boson vertex

We present a workable model for the fermion-photon vertex, which is expressed solely in terms of functions that appear in the fermion propagator and independent of the angle between the relative momenta, and does not explicitly depend on the covariant-gauge parameter. It nevertheless produces a critical coupling for dynamical chiral symmetry breaking that is practically independent of the covariant-gauge parameter and an anomalous magnetic moment distribution for the dressed fermion that agrees in important respects with realistic numerical solutions of the inhomogeneous vector Bethe-Salpeter equation. The last decade has seen a crystallisation of ideas regarding the nature of the dressed-gluon and -quark propagators in QCD. In Landau gauge the dressed gluon two-point function is widely held to be described by a momentum-dependent mass function, m 2(k 2 ). Its magnitude is large at infrared momenta: m 2(k 2 ∼ 0) ≃ (2 − 4�QCD) 2 . However, it vanishes with increasing spacelike momenta: m 2 (k 2 ≫ � 2 ) ∼ 1/k 2 , thereby maintaining full accord with perturbative QCD. Background and context for these observations may be found, e.g., in Refs.[1–5], and citations therein and thereto.

Structure of the neutral pion and its electromagnetic transition form factor

The γ*γ→π0 transition form factor, G(Q2), is computed on the entire domain of spacelike momenta using a continuum approach to the two valence body bound-state problem in relativistic quantum field theory: the result agrees with data obtained by the CELLO, CLEO, and Belle Collaborations. The analysis unifies this prediction with that of the pion’s valence-quark parton distribution amplitude (PDA) and elastic electromagnetic form factor and demonstrates, too, that a fully self-consistent treatment can readily connect a pion PDA that is a broad, concave function at the hadronic scale with the perturbative QCD prediction for the transition form factor in the hard photon limit. The normalization of that limit is set by the scale of dynamical chiral symmetry breaking, which is a crucial feature of the Standard Model. Understanding of the latter will thus remain incomplete until definitive transition form factor data are available on Q2>10  GeV2.

Gauge invariance of a critical number of flavours in QED3

The fermion propagator in an arbitrary covariant gauge can be obtained from the Landau gauge result via a Landau–Khalatnikov–Fradkin transformation. This transformation can be written in a practically useful form in both configuration and momentum space. It is therefore possible to anticipate effects of a gauge transformation on the propagator’s analytic properties. These facts enable one to establish that if a critical number of flavours for chiral symmetry restoration and deconfinement exists in noncompact QED3, then its value is independent of the gauge parameter. This is explicated using simple forms for the fermion–photon vertex and the photon vacuum polarisation. The illustration highlights pitfalls that must be avoided in order to arrive at valid conclusions. Landau gauge is seen to be the covariant gauge in which the propagator avoids modification by a non-dynamical gauge-dependent exponential factor, whose presence can obscure truly observable features of the theory.