# Pion-cloud contribution to the $N\rightarrow \Delta$ transition form factors

## TL;DR

This paper investigates how the pion cloud influences the electromagnetic transition form factors between the nucleon and Delta resonance using a relativistic hybrid constituent-quark model that includes non-valence components.

## Contribution

It introduces a relativistic model incorporating pion cloud effects in the $N
ightarrow riangle$ transition form factors, providing predictions for sensitive ratios.

## Key findings

- Predictions for $R_{EM}$ and $R_{SM}$ ratios.
- Pion cloud significantly affects transition form factors.
- Relativistic invariance achieved via point-form quantum mechanics.

## Abstract

We examine the contribution of the pion cloud to the electromagnetic $N \rightarrow \Delta$ transition form factors within a relativistic hybrid constituent-quark model. In this model baryons consist not only of the $3q$ valence component, but contain, in addition, a $3 q \pi$ non-valence component. We start with constituent quarks which are subject to a scalar, isoscalar confining force. This leads to an $SU(6)$ spin-flavor symmetric spectrum with degenerate nucleon and Delta masses. Mass splitting is caused by pions which are assumed to couple directly to the quarks. The point-form of relativistic quantum mechanics is employed to achieve a relativistically invariant description of this system. The $N \rightarrow \Delta$ transition current is then determined from the one-photon exchange contribution to the $\Delta$ electroproduction amplitude. We will give predictions for the ratios $R_{EM}$ and $R_{SM}$ of electric to magnetic and Coulomb to magnetic form factors, which are supposed to be most sensitive to pion-cloud effects.