Electromagnetic interaction vertex of $\Delta$ baryons in hard-wall AdS/QCD model

TL;DR

This paper models the electromagnetic interaction of spin-3/2 Δ baryons within the hard-wall AdS/QCD framework, deriving vertex functions and computing the charge form factor for Δ+ baryons, comparing with field theory results.

Contribution

It introduces a comprehensive bulk interaction Lagrangian for spin-3/2 fields in hard-wall AdS/QCD and derives the electromagnetic vertex coefficients for Δ baryons.

Findings

Derived vertex function coefficients for γ*ΔΔ interaction.

Calculated the charge form factor G_{E0} for Δ+ baryon.

Compared AdS/QCD results with traditional field theory calculations.

Abstract

We consider an interaction of a spin-3/2 field with the electromagnetic field in the framework of the hard-wall model of AdS/QCD. We write Lagrangian for this interaction including all kinds interaction terms in the bulk of AdS$_{5}$ space and present the scattering matrix element in integrals over the fifth coordinate. Comparing the current matrix element obtained in the boundary of this space with the one known from field theory, we find the vertex function coefficients for the $\gamma^{*}\Delta\Delta$ interaction vertex. As an example, we apply the obtained coefficients to the computation of the charge form factor $G_{E0}$ for the $\Delta^{+}$ baryon and compare the result with the one obtained in the field theory.