A gauge invariant unitary theory for pion photoproduction

Abstract

The Ward-Takahashi identities are central to the gauge invariance of the photoproduction amplitude. Here we demonstrate that unitarity and in particular the inclusion of both the $\pi N$ and $\gamma \pi N$ thresholds on equal footing yields a photoproduction amplitude that satisfies both two-body unitarity and the generalized Ward-Takahashi identities. The final amplitude is a solution of a set of coupled channel integral equations for the reactions $\pi N\to \pi N$ and $\gamma N\to \pi N$. % Figures available from the authors upon request, % e-mail: [email protected] % Submitted to Physical Review C

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• Gauge-invariant approach to meson photoproduction including the final-state interaction
• Pion photoproduction in a dynamical coupled-channels model
• Pion photoproduction off the proton in a gauge-invariant chiral unitary framework
• Gauging of equations method. I. Electromagnetic currents of three distinguishable particles
• Solution of the Bethe-Salpeter equation for pion-nucleon scattering
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• Gauging the three-nucleon spectator equation
• Numerical renormalization using dimensional regularization: a simple test case in the Lippmann-Schwinger equation
• Preserving the gauge invariance of meson production currents in the presence of explicit final-state interactions
• Gauge invariance in the presence of a cutoff
• Gauge Invariant Two-Photon-Exchange Contributions in $e^{-}{\pi }^{+}\to e^{-}{\pi }^{+}$
• Electromagnetic currents of the pion-nucleon system