Three-body bound states with zero-range interaction in the Bethe–Salpeter approach

Ydrefors, E.; Nogueira, J. H. Alvarenga; Gigante, V.; Frederico, T.; Karmanov, V. A.

doi:10.1016/j.physletb.2017.04.035

Cited by 16 publications

(48 citation statements)

References 13 publications

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“…In our method, we reproduced the binding energies found in Ref. [8,9,10] and also the transverse amplitude found via Euclidean space calculation [10]. This confirms the validity of our approach and correctness of our results.…”

Section: Discussionsupporting

confidence: 85%

“…It is important to mention that in the Euclidean calculations of Ref. [10] the full infinite domains of the variables q v and q 4 (and also k v and k 4 ) were considered by using a mapping procedure. However, due to the many singularities, this is difficult to do in the Minkowski space calculations keeping the same numerical precision, as sizable numbers of basis functions and gauss points are already needed for achieving the aforementioned results.…”

Section: Resultsmentioning

confidence: 99%

“…The transverse amplitudes -double integrals of the Minkowski BS amplitude over k + and k − , and of the corresponding Euclidean amplitude over k 0 , k z , -are then the same (up to a Jacobian). Below we will calculate the transverse amplitudes using the Minkowski BS amplitude, so we can compare the solution of this paper with the one found previously through the BS equation solved in Euclidean space [10]. In this section we will perform the integrations over k + and k − .…”

Section: Transverse Amplitudesmentioning

confidence: 97%

“…Although the LF equation is fully defined in Minkowski space, it gives access only to the valence component, which is far from enough for relativistic calculations. According to [10], the contributions from higher-Fock components are remarkable and cannot be neglected, as already anticipated in [11]. This is an important motivation for going beyond the approaches based on the valence component of the LF wave function introduced in [8].…”

Section: Introductionmentioning

confidence: 95%

“…[9]. The three-body BS equation [8] was also recently solved, for the first time, in Euclidean space [10]. Although the LF equation is fully defined in Minkowski space, it gives access only to the valence component, which is far from enough for relativistic calculations.…”

Section: Introductionmentioning

confidence: 99%

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Solving the three-body bound-state Bethe-Salpeter equation in Minkowski space

et al. 2019

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The scalar three-body Bethe-Salpeter equation, with zero-range interaction, is solved in Minkowski space by direct integration of the four-dimensional integral equation. The singularities appearing in the propagators are treated properly by standard analytical and numerical methods, without relying on any ansatz or assumption. The results for the binding energies and transverse amplitudes are compared with the results computed in Euclidean space. A fair agreement between the calculations is found.

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Section: Discussionsupporting

confidence: 85%

Section: Resultsmentioning

confidence: 99%

Section: Transverse Amplitudesmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

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Solving the three-body bound-state Bethe-Salpeter equation in Minkowski space

et al. 2019

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Bethe-Salpeter Approach to Three-Body Bound States with Zero-Range Interaction

Ydrefors

Nogueira

Karmanov

et al. 2020

Recent Progress in Few-Body Physics

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The Bethe-Salpeter equation for three scalar bosons, with zero-range interaction, is solved in Minkowski space by direct integration of the four-dimensional integral equation. The singularities occuring in the propagators are treated properly by standard analytical and numerical methods, without relying on any ansatz for the Bethe-Salpeter amplitude. The results for the binding energies and transverse amplitudes are compared with the results computed in Euclidean space. A fair agreement between the calculations is obtained.

show abstract