An effective field theory of the Delta-resonance

TL;DR

This paper develops a consistent effective field theory for the Delta-resonance, accurately modeling its interactions with nucleons, pions, and photons without unphysical degrees of freedom, and computes relevant scattering cross-sections.

Contribution

It introduces a novel, intrinsically consistent field theory for the Delta-resonance using Weinberg's formalism, avoiding ad hoc manipulations required in previous models.

Findings

Derived interactions with nucleons, pions, and photons.

Computed cross-sections for pion-nucleon scattering.

Established a unique operator structure for couplings.

Abstract

We present an effective field theory of the $\Delta$-resonance as an interacting Weinberg's $(3/2,0)\oplus (0,3/2)$ field in the multi-spinor formalism. We derive its interactions with nucleons $N$, pions $\pi$ and photons $\gamma$, and compute the $\Delta$-resonance cross-sections in pion-nucleon scattering and pion photo-production. The theory contains only the physical spin-3/2 degrees of freedom. Thus, it is intrinsically consistent at the Hamiltonian level and, unlike the commonly used Rarita-Schwinger framework, does not require any additional ad hoc manipulation of couplings or propagators. The symmetries of hadronic physics select a unique operator for each coupling $N\pi\Delta$ and $\gamma\pi\Delta$. The proposed framework can be extended to also describe other higher-spin hadronic resonances.