Constituent-quark model with pionic contributions: electromagnetic $N\rightarrow\Delta$ transition

TL;DR

This paper develops a relativistic constituent-quark model with pionic contributions to better understand the electromagnetic $N ightarrow riangle$ transition form factors, showing improved agreement with experimental data.

Contribution

It introduces a relativistic multichannel framework incorporating pion-cloud effects into the constituent-quark model for the $N ightarrow riangle$ transition.

Findings

Bare quark model form factors agree reasonably with data.

Including pion-cloud contributions improves data reproduction.

Relativistic treatment enhances model accuracy.

Abstract

We report on ongoing work to determine the pion-cloud contribution to the electromagnetic $N\rightarrow\Delta$ transition form factors. The starting point is an $SU(6)$ spin-flavor symmetric constituent-quark model with instantaneous confinement that is augmented by dynamical pions which couple directly to the quarks. This system is treated in a relativistically invariant way within the framework of point-form quantum mechanics using a multichannel formulation. The first step is to determine the electromagnetic form factors of the bare particles that consist only of three quarks. These form factors are basic ingredients for calculating the pion-cloud contributions. Already without the pion cloud, electromagnetic nucleon and $N\rightarrow \Delta$ transition form factors compare reasonably well with the data. By inclusion of the pion-cloud contribution coming from the $\pi$-$N$ intermediate state the reproduction of the data is further improved.