Higher derivative terms in the {\pi}{\Delta}N interaction: some phenomenological consequences

TL;DR

This paper introduces a combined first and second order derivative {}N{}(1232) vertex interaction for the {}N{} system, improving scattering descriptions at tree level by addressing formal issues and including gauge invariance.

Contribution

It is the first implementation of a {}N{} vertex with both derivative orders, resolving formal problems and enhancing scattering amplitude calculations.

Findings

Improved total {}N{} scattering description at tree level.

Both derivative interactions should be included for accurate amplitudes.

Formal problems with derivative interactions can be addressed perturbatively.

Abstract

In this paper we implement for the first time the use of a {\pi}N{\Delta}(1232) vertex interaction containing both first and second order derivative terms, as required by renormalization considerations. As as was previously shown both interactions present formal problems, but can be implemented pertubatively. We put an end point to the discussion of which type of interaction is the apropriate one: both the usual pi-derivative and the "spin 3/2" gauge invariant that include also a derivative in the {\Delta} field should be included in amplitude calculations. We show that when working within a tree level approach the description of total {\pi}N{\Delta} scattering in the different channels is improved.