Skyrmions and vector mesons.

We discuss the scattering of mesons of arbitrary spin and isospin from baryons in models in which the baryon is considered a soliton, or “skyrmion,” in an effective Lagrangian of mesons. Model-independent linear relations between partialwave amplitudes are derived for TN ---) pN and TN + wN , and, where possible, are compared with experiment. Submitted for Publication * Work supported by the Department of Energy, contract DE AC03 76SF00515. The notable success of Skyrme model calculations has lent credence to the picture of the nucleon as a soliton, or “skyrmion,” in the nonlinear sigma model of pions. lV2 Of course, if this picture is at all sensible, we ought to expect that the more realistic the theory of mesons that we start with, the more accurate our predictions of baryonic properties will be.3 In constructing a realistic theory, the most important modification to consider is the incorporation of additional low-lying mesons into the effective Lagrangian. Work along these lines is just beginning. In the “w-stabilized” Skyrme model of Adkins and Nappi, one introduces a coupling w@‘ between the w meson and the topological current of the theory. This coupling, which accounts for the decay w --) 37r, turns out to be sufficient to guarantee a stable soliton. Pleasingly, the static properties of the nucleon in this model constitute an improvement over the unadulterated Skyrme model. One can likewise construct stable solitons when the Lagrangian includes p-mesons, although the static properties of this model are as yet undetermined.5 In this paper we give a blueprint for calculating 2-body scattering amplitudes in models in which the skyrmion is coupled to an arbitrary number of different species of mesons. The processes we will focus on will be of the type where q5 and T,!J stand for generic mesons of arbitrary spin, isospin and parity, tll and B and B' denote either a nucleon or a A. The treatment will be on a general level; we will not specify a Lagrangian. Nevertheless, as we shall see, the soliton picture 11 In fact, they need not be mesons at all, but might, for instance, represent a quark interacting with a skyrmion in a ‘hybrid” model of quarks and pions.