# Excited states of the Wick-Cutkosky model with the Nakanishi representation in the Light-Front framework

## TL;DR

This paper investigates the excited states of the Wick-Cutkosky model using the Nakanishi representation in the Light-Front framework, introducing a new integration technique and confirming eigenvalues match the Bethe-Salpeter equation.

## Contribution

A novel integration method for the Nakanishi representation in Light-Front dynamics, enabling analytical and numerical analysis of the model's excited states.

## Key findings

- Derived eigenvalue equations consistent with Cutkosky's original equations
- Developed a new technique transforming integrals into sums
- Numerical results match Bethe-Salpeter eigenvalues

## Abstract

The Wick-Cutkosky model is investigated using the framework of the Nakanishi Perturbative Integral Representation projected in the Light-Front hyperplane for an s-wave amplitude. We developed a new technique based on sucessive integration by parts of the Nakanishi Representation which enabled us to transform one of the integrations into a sum. With a set of boundary conditions it was possible to guess the format of the solution, which was in fact a distribution. The eigenequations obtained were the same as the originals of Cutkosky \cite{CutPR54}. Finally, a numerical check confirmed that the final equation reproduce the same eigenvalues as the initial Bethe-Salpeter equation.