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

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.

References in corpus (3)

• Quantitative studies of the homogeneous Bethe-Salpeter Equation in Minkowski space
• Solving Bethe-Salpeter equation for two fermions in Minkowski space
• Projecting the Bethe-Salpeter Equation onto the Light-Front and back: A Short Review

Cited by in corpus (5)

• Fermionic bound states in Minkowski-space: Light-cone singularities and structure
• Thermodynamical phases in a PNJL model at zero temperature
• Bound states of relativistic nature
• Pion inspired by QCD: Nakanishi and Light-Front Integral Representations
• The Bethe-Salpeter approach to bound states: from Euclidean to Minkowski space