Electromagnetic currents of the pion-nucleon system

Pion photoproduction amplitudes are calculated from a set of equations that have been derived by coupling an external photon to all places in a dressed pion-nucleon vertex. The calculation is consistent with gauge invariance, charge conservation, unitarity, and covariance. To provide input to the photoproduction amplitude, a photon-nucleon vertex is calculated from a set of equations derived by complete attachment of photons to a dressed nucleon propagator. We check the accuracy of this vertex by extracting its nucleon electromagnetic form factors.

Figure 1

The photon-nucleon vertex of Eq. (18). The dashed, solid, and wiggly lines denote pions, nucleons, and photons, respectively.

Figure 2

The singly gauged amplitude of Eq. (29a).

Figure 3

Diagram needed to describe certain $\gamma N\to \pi N$ data that cannot be obtained by gauging.

Figure 4

Phase shifts for $j=1/2$. Fit A results (dotted lines) are almost indistinguishable from those for Fit B (solid lines). The data are taken from [28].

Figure 5

Nucleon electromagnetic form factors. The meaning of the different line types is explained in the text.

Figure 6

Terms that contribute to $\gamma N\to \pi N$ but which are not included in our model.

Figure 7

Proton multipole amplitudes for $j=1/2, t=1/2$. The various line styles denote the same cases as in Fig. 5, while the data are taken from [28].

Figure 8

Neutron multipole amplitudes for $j=1/2, t=1/2$. The various line styles denote the same cases as in Fig. 5.