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May 14 – 18, 2018
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Non-perturbative study of the three-body system within the Bethe-Salpeter approach

May 17, 2018, 4:50 PM
Auditorium (Jefferson Lab - CEBAF Center)


Jefferson Lab - CEBAF Center


Dr Emanuel Ydrefors (Instituto Tecnologico de Aeronautica)


From a general point of view, understanding the interaction in terms of the fundamental degrees of freedom is very important for nuclear and particle non-perturbative physics. Since that is a very difficult problem, simple models are of great value for understanding the crucial qualitative features of the solution with more realistic kernels. Understanding the properties of relativistic three-body systems is important, in particular, for the perspective of hardron physics, e.g. for the modeling of the nucleon. Furthermore, it is well-known that in the non-relativistic approach the binding energy of this system is not bounded from below, what is known as Thomas collapse. As it was discovered in the light-front dynamics (LFD) [1,2], the relativistic repulsion prevent the Thomas collapse in the non-relativistic sense. The Bethe-Salpeter equation provides a convenient approach to perform non-perturbative studies of few-body systems in Minkowski space. Calculations of that type is important in order to access dynamical observables, such as space-like and time-like form factors. In this contribution we discuss some recent progress regarding the solution of the bound-state Bethe-Salpeter equation (BSE) for a system of three bosons interacting through a zero-range interaction. We compare the results for the binding energy and transverse amplitude computed by two different methods: 1. Solution in Minkowski space by direct integration of the BSE, by taken care of the singularities. The adopted is thus similar to the one introduced by Carbonell and Karmanov for the two-body system in Ref. [3]. 2. Solution in Euclidean space by Wick rotation of the integration contour. Our results show that, at least for moderate three-body binding energies, a fair agreement is found between the two methods, both for the binding energy and the modulus of the transverse amplitude. This is encouraging since the calculations based on direct integration of the BSE present many challenges, due to the singularities of the kernel and the Bethe-Salpeter amplitude. As our calculations in Euclidean space show [4], the contributions from higher Fock components, which are not included in the LFD treatment are very significant, both for the binding energies and the tranverse amplitudes. This can be explained in terms of an effective three-body force of relativistic origin. [1] T. Frederico, Phys. Lett. B 282 (1992) 409 [2] J. Carbonell and V. A. Karmanov, Phys. Rev. C 67 (2003) 037001 [3] J. Carbonell and V. A. Karmanov, Phys. Rev. D 90 (2014) 056002 [4] E. Ydrefors et al, Phys. Lett. B 770 (2017) 131.

Primary author

Dr Emanuel Ydrefors (Instituto Tecnologico de Aeronautica)


Mr Jorge Alvarenga Nogueira (Instituto Tecnologico de Aeronautica) Prof. Tobias Frederico (Instituto Tecnologico de Aeronautica) Prof. Vladimir Karmanov (Lebedev Physical Institute)

Presentation materials