Projecting the Bethe–Salpeter Equation onto the Light-Front and Back: A Short Review

Frederico, T.; Salmè, G.

doi:10.1007/s00601-010-0163-z

Cited by 29 publications

(15 citation statements)

References 47 publications

(125 reference statements)

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“…[9]. The essential point about the method is to recognise that the effective dynamics of the LF valence wave function is able to describe the complexity of the BSE projected onto the light-front [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Bound States in Minkowski Space in 2 + 1 Dimensions

et al. 2015

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The Nakanishi perturbative integral representation of the Bethe-Salpeter amplitude in threedimensions (2 + 1) is used to solve the corresponding homogeneous Bethe-Salpeter equation in Minkowski space. The projection of this equation onto the null-plane, as reported here, leads to a bound-state equation for the Nakanishi weight function. The explicit forms of the integral equation for the Nakanishi weight function are shown in the ladder approximation. In addition, the valence light-front wave function is presented. The formal steps of the formalism are illustrated to some extend, with the resulting equation being applied to a bound state system composed by two identical scalar particles of mass m, interacting through the exchange of another massive scalar particle of mass μ. The results reported in this contribution show quite good agreement between our calculations obtained from the Bethe-Salpeter amplitude with the Nakanishi weight function with direct solutions obtained in the Euclidean space.

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Section: Introductionmentioning

confidence: 99%

Bound States in Minkowski Space in 2 + 1 Dimensions

et al. 2015

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“…We use a parametrization of the Kπ scattering amplitude in I = 1/2 and 3/2, which is input to the bachelor integral equations, and constitutes one source of the energy dependence seen in the D + → K − π + π + S-wave phase shift, besides the phase of the Kπ amplitude. Technically, we perform the light-front projection of the equations [31][32][33][34][35][36][37], to simplify the numerical computation of the observables by three-dimensional integrations. These techniques are well exemplified in the reviews of applications of light-front field theory to nuclear and hadron physics [38,39].…”

Section: Jhep08(2014)135mentioning

confidence: 99%

“…[31] based on the quasi-potential approach (QPA). The reduced amplitudes derived using the tools developed in a series of works [31][32][33][34][35] and reviewed in [36], depends only three-dimensional variables, namely, the kinematical LF momentum k ≡ (k + , k ⊥ ), defined by k + = k 0 + k 3 and k ⊥ = {k x , k y }. The phase-space integration is normalized according to dk…”

Section: Fsi Light-front Dynamics In Heavy Meson Decaymentioning

confidence: 99%

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Final state interaction in D + → K − π + π + with Kπ I = 1/2 and 3/2 channels

Guimaraes

Lourenço

Paula

et al. 2014

J. High Energ. Phys.

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The final state interaction contribution to D + decays is computed for the K − π + π + channel within a light-front relativistic three-body model for the final state interaction. The rescattering process between the kaon and two pions in the decay channel is considered. The off-shell decay amplitude is a solution of a four-dimensional Bethe-Salpeter equation, which is decomposed in a Faddeev form. The projection onto the light-front of the coupled set of integral equations is performed via a quasi-potential approach. The S-wave Kπ interaction is introduced in the resonant isospin 1/2 and the non-resonant isospin 3/2 channels. The numerical solution of the light-front tridimensional inhomogeneous integral equations for the Faddeev components of the decay amplitude is performed perturbatively. The loop-expansion converges fast, and the three-loop contribution can be neglected in respect to the two-loop results for the practical application. The dependence on the model parameters in respect to the input amplitude at the partonic level is exploited and the phase found in the experimental analysis, is fitted with an appropriate choice of the real weights of the isospin components of the partonic amplitude. The data suggests a small mixture of total isospin 5/2 to the dominant 3/2 one. The modulus of the unsymmetrized decay amplitude, which presents a deep valley and a following increase for Kπ masses above 1.5 GeV, is fairly reproduced. This suggests the assignment of the quantum numbers 0 + to the isospin 1/2 K * (1630) resonance.

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“…Thus, in 2006 Karmanov and Carbonell proposed a new technique based on the application of the Nakanishi representation to the BS equation and then projecting it in the Light-Front hyperplane [9,10,11,12], and this resulted in an generalized integral equation with smooth kernels. Then Frederico, Salme and Viviani extended the Light Front projected BS equation for scattering states and also developed a new method based on the uniqueness of the Nakanishi representation [13,14,15].…”

Section: Introductionmentioning

confidence: 99%

Excited States of the Wick–Cutkosky Model with the Nakanishi Representation in the Light-Front Framework

Pimentel¹,

Paula²

2016

Few-Body Syst

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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 [1]. Finally, a numerical check confirmed that the final equation reproduce the same eigenvalues as the initial Bethe-Salpeter equation.

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Projecting the Bethe–Salpeter Equation onto the Light-Front and Back: A Short Review

Cited by 29 publications

References 47 publications

Bound States in Minkowski Space in 2 + 1 Dimensions

Bound States in Minkowski Space in 2 + 1 Dimensions

Final state interaction in D + → K − π + π + with Kπ I = 1/2 and 3/2 channels

Excited States of the Wick–Cutkosky Model with the Nakanishi Representation in the Light-Front Framework

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