Higher derivative terms in the π Δ N interaction: Some phenomenological consequences

Abstract

In this paper, we implement the use of a πN(1232) vertex interaction containing both first- and second-orderderivative terms, as required by renormalization and power-counting considerations. As was previously shown,both interactions present quantization shortcomings but can be used in a pertubative calculation. Our resultsindicate that the usual π derivative plus the spin-3/2 gauge invariant (derivative also in the field) should beincluded in amplitude calculations, as also all higher derivative interactions respecting chiral invariance. Weshow that both interactions make essentially the same resonant contribution to the elastic π+p cross section, sochanging the ratio between both coupling constants amounts to a correction of the background. The elastic π+p cross section up to 300 MeV changes only mildly when that ratio is changed, but the total π−p scattering, whichhas poor fit within both interactions separately, can be much improved in the same energy range by tuning theratio between both coupling constants.