Electromagnetic Effects in Meson-Nucleon Scattering

Abstract

The dominant part of pion-nucleon scattering is charge independent. In view of the apparent discrepancies in the dispersion relations for meson scattering, it is desirable to investigate the effects on meson-nucleon scattering of including the electromagnetic interaction in an otherwise charge-independent theory. The calculation, which is performed in the static-nucleon, one-meson approximation of Chew and Low, is divided into two parts. In the first part, the effects of the charged-neutral meson mass difference, which is assumed to be of electromagnetic origin, are calculated. In the second part, other electromagnetic effects involving one virtual photon are calculated in the "Coulomb approximation," in which the effects of transverse photons and of graphs in which the incoming and outgoing meson lines are crossed, are ignored. A formula is given by means of which the three meson-proton differential cross sections may be analyzed in terms of the six charge-independent $s$- and $p$-wave phase shifts which would occur in the absence of the electromagnetic interaction. Aside from simple Coulomb and kinematic effects, the most important effect in ${\pi }^{+}$-proton scattering can be expressed as an alteration of the $J=\frac{3}{2}$ phase shift for that state such as to sharpen the (3,3) resonance and move it to a higher energy. The meson mass difference effect and the Coulomb effect contribute about equally to produce a phase shift alteration of about 2° at its largest.