Ward identities and sum rules for composite systems described in the dispersion relation technique: The deuteron as a composite two-nucleon system

Abstract

Here we develop an approach to the description of composite systems, using dispersion integrals over the composite-particle mass. A corresponding diagram technique, based on the dispersion relation N/ D method, is constructed. Lorentz covariant amplitudes for a two-particle composite system interacting with external fields are built up in the framework of this technique. Ambiguities connected with the subtraction terms in double dispersion relations are removed due to the requirements of gauge invariance and analyticity. Sum rules for energy-momentum and discrete quantum numbers are shown to be valid for the elastic form factors and deep inelastic structure functions of the composite system. We carry out realistic description of the structure of the deuteron within the framework of the developed technique. We take into account relativistic effects, using nucleon degrees of freedom only. The pn phase-shift data (δ S, δ D and ε) for J P = 1 + at kinetic energies up to 0.6 GeV were used for a determination of the deuteron vertices (which are the relativistic analogues of the deuteron wave function). We obtained a good description of the following deuteron properties: (i) the form factor combinations A( Q 2) and B( Q 2) up to Q ⩽ 1 GeV/ c; (ii) the deuteron binding energy, magnetic and quadrupole moments. The performed investigation can be considered as a reference frame for extracting non-nucleonic degrees of freedom in the deuteron.