Remarks on the origin of Castillejo-Dalitz-Dyson poles

TL;DR

This paper explores a new type of Castillejo-Dalitz-Dyson (CDD) pole linked to primitives, extending Low's scattering equation and illustrating the connection with nucleon-nucleon phase shifts.

Contribution

It introduces a novel CDD pole associated with primitives and generalizes Low's scattering equation for amplitudes involving these primitives.

Findings

Identifies a new CDD pole type connected to zeros of the D function on the unitary cut.

Generalizes Low's scattering equation to include primitives.

Demonstrates the relationship through nucleon-nucleon phase shift analysis.

Abstract

Castillejo-Dalitz-Dyson (CDD) poles are known to be connected with bound states and resonances. We discuss a new type of CDD pole associated with primitives i.e., poles of the P matrix that correspond to zeros of the D function on the unitary cut. Low's scattering equation is generalized for amplitudes with primitives. The relationship between the CDD poles and the primitives is illustrated by a description of the S-wave nucleon-nucleon phase shifts.