General Properties of Higher-Spin Fermion Interaction Currents and Their Test in πN-Scattering

Abstract

The currents of higher-spin fermion interactions with zero- and half-spin particles are derived. They can be used for the N^*(J) ↔ Nπ-transitions (N^*(J) is the
nucleon resonance with the J spin). In accordance with the theorem on currents and fields, the spin-tensors of these currents are traceless, and their products with the γ-matrices and the higher-spin fermion momentum vanish, similarly to the field spin-tensors. Such currents are derived explicitly for J=3/2
and 5/2. It is shown that, in the present approach, the scale dimension of a higher spin fermion propagator equals to –1 for any J ≥ 1/2. The calculations indicate that the off-mass-shell N^* contributions to the s-channel amplitudes correspond to J = J_πN only ( J_πN is the total angular momentum of the πN-system). As contrast, in the usually exploited approaches, such non-zero amplitudes correspond to 1/2 ≤  J_πN ≤ J. In particular, the usually exploited approaches give non-zero off-mass-shell contributions of the ∆(1232)-resonance to the amplitudes S₃₁, P₃₁( J_πN = 1/2) and P₃₃, D₃₃(J_πN = 3/2), but our approach – to P₃₃ and D₃₃ only. The comparison of these results with the data of the partial wave analysis on the S₃₁-amplitude in the ∆(1232)-region shows the better agreement for the present approach.