Semirelativistic approximation to the $\gamma^\ast N \to N(1520)$ and $\gamma^\ast N \to N(1535)$ transition form factors

TL;DR

This paper introduces a semirelativistic approach to model the transition form factors of nucleon resonances N(1520) and N(1535), successfully predicting data at high momentum transfer by focusing on valence quark contributions.

Contribution

It proposes a novel semirelativistic approximation that simplifies the orthogonality condition between states with different masses, enabling parameter-free predictions of transition form factors.

Findings

Predictions align well with experimental data at high momentum transfer.

The approach effectively isolates valence quark contributions.

The method simplifies the relativistic treatment of nucleon resonances.

Abstract

The representation of the wave functions of the nucleon resonances within a relativistic framework is a complex task. In a nonrelativistic framework the orthogonality between states can be imposed naturally. In a relativistic generalization, however, the derivation of the orthogonality condition between states can be problematic, particularly when the states have different masses. In this work we study the $N(1520)$ and $N(1535)$ states using a relativistic framework. We considered wave functions derived in previous works, but impose the orthogonality between the nucleon and resonance states using the properties of the nucleon, ignoring the difference of masses between the states (semirelativistic approximation). The $N(1520)$ and $N(1535)$ wave functions are then defined without any adjustable parameters and are used to make predictions for the valence quark contributions to the transition form factors. The predictions compare well with the data particularly for high momentum transfer, where the dominance of the quark degrees of freedom is expected.