Single pion photoproduction is studied in a single quark model in which a quark absorbs the photon and then emits the pion, propagating as a quark between the two interactions. Two different chiral bag models are used which allow for the coupling of the quarks to the pion. Surprisingly, the single quark model reproduces the results of phenomenological models and agrees with the experimental amplitudes to within 30% at threshold.

A single quark model for single pion photoproduction at threshold

We investigate the theory of finite quantum electrodynamics with, vanishing bare mass for the electron. Either the γ6 gauge symmetry is spontaneously broken with the consequent appearance of the Nambu-Goldstone boson or the axial-vector-current conservation breaks down, in which case the Goldstone theorem does not apply. We examine the Dyson-Schwinger integral equations with thefull andexact Bethe-Salpeter kernel in the case of the Goldstone mode and show that for the theory to be consistent it is necessary that the anomalous dimension x(α) of the gauge-invariant axial vector current vanishes. We present a simple argument which leads one to conclude that this condition is so stringent that the Goldstone realization of the γ5 gauge symmetry may altogether be ruled out. We offer a further argument which suggests that the condition x(α) = 0 extends to the case of the anomalous nonconservation of the axial vector current.

On the nambu-goldstone problem in quantum electrodynamics

Asymptotic behavior of the pion electromagnetic form factors in Bethe-Salpeter model

The recent attempt of Baker, Johnson and Lee at proving the existence or otherwise of zero-mass bosons in quantum electrodynamics with vanishing bare-electron mass is reexamined. It is argued that the renormalized vertex operator ${{\ensuremath{\Gamma}}_{c}}^{5}$ exists provided that the electron-pseudosclar-boson vertex renormalization constant vanishes. No conclusion about the existence or otherwise of zero-mass bosons can be reached within the framework of their high-energy approximation.

Broken Symmetry in Quantum Electrodynamics and Zero-Mass Bosons

A low-energy theorem from current-algebra techniques is employed to derive an expression for the pion photoproduction amplitude which is shown to be gauge invariant. The low-energy predictions for the differential cross sections and the multipole amplitudes are analyzed extensively and compared with the experimental data. The predictions for the production of charged pions are in as good agreement with experimental data as those of dispersion theory are. However, the current-algebra predictions for $\ensuremath{\gamma}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}p$ characteristically differ from other theoretical models, especially at threshold. Accurate low-energy experimental data for this process should therefore provide a test of the validity of the current-algebra approach.

P. Narayanaswamy

Papers

Broken Symmetry in Quantum Electrodynamics and Zero-Mass Bosons

Current Algebra and Photoproduction of Pions