MesonMeson Scattering Term in PseudoscalarPseudoscalar Meson Theory
Abstract
The mesonmeson scattering term has been investigated within the static approximation for a nucleon. First a static Hamiltonian is constructed from the renormalizable covariant meson theory in a manner similar to that proposed by one of the present authors. Improvements are that the mesonmeson scattering term is included besides the pseudoscalarpseudoscalar coupling term and that an argument is presented to show that the Foldy transformation is the unique one generating a valid static Hamiltonian, though it was left undetermined before. The resulting static Hamiltonian is then analyzed, for the cases of lowenergy S and Pwave pionnucleon scattering and threshold photomeson production, in terms of the onemeson approximation of the ChewLowWick formalism, without recourse to perturbation expansion. It is shown in particular that the mesonmeson scattering term modifies the ChewLow effective range plot of the δ_{33}phase shift, making the renormalized Pwave coupling constant smaller than the conventional plot gives, for a positive coefficient of the mesonmeson scattering term in the Hamiltonian. Empirical values of the coupling constant determined through the conventional ChewLow plot and threshold photomeson extrapolation are shown to be interpretable in terms of the renormalized Pwave coupling constant of 0.08 and the mesonmeson scattering term with a coefficient of ~+4 (ℏ=c=1). The present treatment of threshold photoproduction of mesons, however, does not agree with the relativistic dispersion relation. General features of the static model resulting from the psps meson theory are summarized in the final section, together with the conclusions obtained. The effects of strange particles and of renormalization have been neglected.
 Publication:

Physical Review
 Pub Date:
 September 1959
 DOI:
 10.1103/PhysRev.115.1310
 Bibcode:
 1959PhRv..115.1310S