# Structure of the nucleon and its first radial excitation

## TL;DR

This paper uses a Poincaré-covariant continuum approach to analyze the nucleon's ground and first excited states, revealing diquark correlations, wave function structures, and implications for electromagnetic form factors.

## Contribution

It provides a detailed quantum field theory analysis of nucleon states, highlighting diquark correlations and wave function characteristics, with observable consequences for form factors.

## Key findings

- Presence of nonpointlike diquark correlations in nucleon states
- Wave functions are largely S-wave in nature
- First excited state is a radial excitation of the ground state

## Abstract

A Poincar\'e-covariant continuum approach to the three valence-quark bound-state problem in quantum field theory is used to perform a detailed analysis of the nucleon's ground and first excited states: the so-called $N(940)\frac{1}{2}^+$ and $N(1440)\frac{1}{2}^+$. Such analysis predicts the presence of nonpointlike, fully-interacting quark-quark (diquark) correlations within them, being the isoscalar-scalar and isovector-pseudovector diquarks overwhelmingly dominant with similar relative strengths in both states. Moreover, the rest-frame wave functions of both states are largely $S$-wave in nature and the first excited state in this $1/2^+$ channel has the appearance of a radial excitation of the ground state. All these features have numerous observable consequences, we show herein those related with the nucleon's elastic, Roper's elastic and nucleon-to-Roper transition electromagnetic form factors, for both charged and neutral channels.