The Rarita--Schwinger field: renormalization and phenomenology

Abstract

We discuss renormalization of propagator of interacting Rarita--Schwinger field. Spin-3/2 contribution after renormalization takes usual resonance form. For non-leading spin-1/2 terms we found procedure, which guarantees absence of poles in energy plane. The obtained renormalized propagator has one free parameter and is a straight generalization of the famous free propagator of Moldauer and Case. Application of this propagator for production of ${\Delta }^{++}(1232)$ in ${\pi }^{+}\text{particle}p\to {\pi }^{+}\text{particle}p$ leads to good description of total cross-section and to reasonable agreement with results of partial wave analysis.

Comments: 19 pages, 3 figures, revtex4; misprints, min editorial changes