Study of relativistic bound states for scalar theories in the Bethe-Salpeter and Dyson-Schwinger formalism

Sauli, Vladimir; Adam, J.

doi:10.1103/physrevd.67.085007

Cited by 40 publications

(81 citation statements)

References 27 publications

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“…In nuclear and hadronic physics, the Nakanishi PTIR has been applied to a wide range of physical problems, but so far restricted to the boundstate case, as shown, e.g., in Refs. [9,[11][12][13][15][16][17][18][19][20]. The relativistic scattering states play a relevant role in many hadronic processes, like in the light-meson decays of heavy hadron resonances (see, e.g., for a recent study [21]), or even in more exotic cases (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Two-body scattering states in Minkowski space and the Nakanishi integral representation onto the null plane

2012

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The Nakanishi perturbative integral representation of the four-dimensional T-matrix is investigated in order to get a workable treatment for scattering states, solutions of the inhomogeneous Bethe-Salpeter Equation, in Minkowski space. The projection onto the null-plane of the fourdimensional inhomogeneous Bethe-Salpeter Equation plays a key role for devising an equation for the Nakanishi weight function (a real function), as in the homogeneous case that corresponds to bound states and it has been already studied within different frameworks. In this paper, the whole formal development is illustrated in detail and applied to a system, composed by two massive scalars interacting through the exchange of a massive scalar. The explicit expression of the scattering integral equations are also obtained in ladder approximation, and, as simple applications of our formalism, some limiting cases, like the zero-energy limit and the Wick-Cutkosky model in the continuum, are presented.

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Section: Introductionmentioning

confidence: 99%

Two-body scattering states in Minkowski space and the Nakanishi integral representation onto the null plane

2012

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“…The exploration of the method to include kernels beyond the ladder has successfully been performed in [8,9]. Moreover, in [10], within the NIR the effect of the self-energy contribution to the binding energy of the ground state has been explored in the scalar theory. It is important to point out that the very relevant problem of two-fermion bound state has been investigated within the NIR framework in [11,12], for the case J π = 0 + , where J is the total spin and π the parity of the bound state.…”

Section: Introductionmentioning

confidence: 99%

Minkowski space approach for the Bethe-Salpeter equation

2017

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Abstract. The bound-state energy spectrum for two-boson system with a fixed exchanged massive boson is investigated by considering the scalar Bethe-Salpeter (BS) equation in Minkowski space within the ladder-approximation framework. The approach is extending to excited states a previous study performed for the ground state. The number of states in the spectrum is restricted by the coupling strength of the two-body interaction, as well as the mass of the exchanged boson. In the present approach, we use the Nakanishi Integral Representation and the formally exact null-plane projection. As usual a comparison between eigenvalues obtained in the Minkowski and Euclidean space is presented. Within such scheme, the light-front momentum-space valence wave functions are obtained for the ground and excited states, together with the corresponding quantities in the impactparameter space. Among relevant features emerging from this study, we can point out the node structure of light-front wave function and the leading exponential fall-off of the valence wave function in the impact-parameter space.

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“…The scalar polarization correlator Π is then equal to the sum of expressions (28), (29) and (30). Further analytical integration is possible as well, for instance the integration over the variable x 2 gives for (29)…”

Section: Shifting the Branch Pointmentioning

confidence: 99%

“…depending on what we mean by the vertex Γ and the propagator(s) G. While the results do not support too much the old conjecture of quark-hadron duality, the integral representation derived thorough this paper can actually be used in practice for bound states and form factor calculations. Remembering here its weak coupling prerequisite: the Perturbation Theory Integral Representation [29], which has found its own application in bound state calculations [30,31] in non-confining theory.…”

Section: Introductionmentioning

confidence: 99%

Analytical solution for the correlator with Gribov propagators

Sauli

2016

Open Physics

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Abstract:Propagators approximated by meromorphic functions with complex conjugated poles are widely used to model the infrared behavior of QCD Green's functions. In this paper, analytical solutions for two point correlators made out of functions with complex conjugated poles or branch points have been obtained in the Minkowski space for the first time. As a special case the Gribov propagator has been considered as well. The result is different from the naive analytical continuation of the correlator primarily defined in the Euclidean space. It is free of ultraviolet divergences and instead of Lehmann it rather satisfies Gribov integral representation.

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Study of relativistic bound states for scalar theories in the Bethe-Salpeter and Dyson-Schwinger formalism

Cited by 40 publications

References 27 publications

Two-body scattering states in Minkowski space and the Nakanishi integral representation onto the null plane

Two-body scattering states in Minkowski space and the Nakanishi integral representation onto the null plane

Minkowski space approach for the Bethe-Salpeter equation

Analytical solution for the correlator with Gribov propagators

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