An integral equation for the anomalous deuteron vertex and a comparison of two normalization conditions
"A set of coupled inhomogeneous integral equations is found for the imaginary parts of the four invariant amplitudes of the anomalous deuteron vertex. The equations are algebraically homogeneous~ however, so the possibility of an eigenvalue con= \ dition exists if unsubtracted dispersion relations are postulatedo The anomalous region is treated by means of a modification of the Nishijima continuation procedure. The equations are derived in a one pion model to illustrate the method. A partial diagrammatic analysis of the deuteron vertex is performed below the normal threshold o So = {M+~)2o In the second part a proof is given that the propagator normalization of a scalar or a vector particle is equivalent to the normalization of its electromagnetic form fqctoro The basis for the proof is the Ward identityo This permits a direct comparison of the two normalization conditions and this is done in lowest approximation for two scalar deuteron models and for the vector case as welL The normalization of the deuteron vertex is computed from the triangl,e·graph apprbximation to the deuteron ·electromagnet:i.c form factor. , I . This result is. inserted into the eXJ?ansion arising from the· dispersion relatio~ for' the inverse deuteron propagator at infinity, and an approximation to the deuteron field operator renormalization constant Z is thereby found. The result in each of the scalar models is Z = O. The vector case is more , sensitive to the form factors which enter 'in, but in a model which is in spirit comparable to the scalar examples yields Z =: o. An independent argument for Z = 0 for a vector field is advanced when no zero"":mass scalar particles are present."
coupled inhomogeneous integral equations, anomalous deutron vertex, normalization conditions, eigenvalue condition, Nishijima continuation
University of Illinois - Urbana-Champaign
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