Abstract
A modification of the one boson exchange (OBE) kernel for the covariant spectator theory (CST) is presented and discussed. When applied to the scattering of two identical particles, the previously used kernels either introduced spurious singularities, or removed them in an ad-hoc way. The new modification not only removes these singularities, but also maintains the convergence of the two-body CST equation (sometimes called the Gross equation) when used to describe the scattering of two identical scalar particles.
Highlights
The covariant spectator theory (CST), formulated in Minkowski space, has enjoyed many successes during its long, over 50 year history
One of its shortcomings was the presence of unphysical instability singularities for total energies W ≤ 2m − μ that automatically arise when the one-boson-exchange CST equations are symmetrized for the treatment of systems of identical particles, or the treatment of qqbound states with charge conjugation symmetry
I emphasize that the principal issue with these singularities is a theoretical one: while they lead to finite results in numerical calculations they are an unpleasant sign that something is missing and leave doubts that the major physics is under control
Summary
The covariant spectator theory (CST), formulated in Minkowski space, has enjoyed many successes during its long, over 50 year history. A strong motivation for use of the CST is the cancellation theorem, which states that the higher order kernels describing the scattering of nonidentical scalar particles cancel when one of the nucleon masses approaches infinity, leaving the OBE kernel to give the exact result in that limit This theorem is violated when the diagrams are symmetrized for the description of the scattering of identical particles, and Sec. IV shows how the new method for removing singularities improves the cancellation and almost restores the cancellation theorem, justifying its introduction. Those familiar with the CST might prefer to skip parts of this introductory section, which includes subsections describing the assumptions that underly the use of the CST, a brief review of the early history of the CST, a very brief review of its major applications, and a general discussion of the different types of CST equations that describe (i) the scattering of nonidentical particles (one channel), (ii) the scattering of identical particles with exchange symmetry (two channel) and (iii) the pion as a bound state of a qqpair, that requires four channels in order to maintain both charge conjugation invariance and spontaneously broken chiral symmetry
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