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

Abstract

In this paper, we implement the use of a πN1(1232) vertex interaction containing both first- and second-order derivative 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 results indicate that the usual π derivative plus the spin-3/2 gauge invariant (derivative also in the 1 field) should be included in amplitude calculations, as also all higher derivative interactions respecting chiral invariance. We show that both interactions make essentially the same resonant contribution to the elastic π+ p cross section, so changing 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, which has poor fit within both interactions separately, can be much improved in the same energy range by tuning the ratio between both coupling constants.