A Simple Model for Two-Channel Reaction in Field Theory and Its Application to theY*Problem

Abstract

A simple two-cannel model in field theory is presented in order to known characteristic features of the problems concerning Y^* recently observed. Four particles, K_-, N, π and Λ, all assumed to be spinless, are considered, and the S-state amplitudes are calculated in the chain approximation. The calculated amplitudes satisfy the unitarity condition and reproduce bound states, resonances, and other features of the reactions. From the examples treated it is concluded that a strong attractive force between K_- and N such that there is a bound state and a weak coupling between K_-N and πΛ channels are essential for the appearance of a sharp peak both in the K_-N total cross section and the K_-+N→π+Λ cross section in the unphysical region. The relation between height and width is such that the peak tends to a δ-function if the width tends to an infinitesimal. This conclusion remains unchanged even if a force between π and Λ is varied over a wide range. According to the variety of a πΛ force, the πΛ cross section exhibits either a peak or a dip near the energy at which the K_-N total cross section exhibits a peak. Furthermore an attractive or a repulsive πΛ force contributes to make a peak broader or narrower, respectively.