Covariant three-body equations in φ3 field theory

We derive covariant equations for a system of two quarks and two antiquarks where the effect of quark-antiquark annihilation is taken into account. In our approach, only pair-wise interactions are retained, while all possibilities of overcounting are excluded by (i) keeping terms in the kernel that are consistent with a meson-meson and diquark-antidiquark substructure, and (ii) introducing 4-body equations with a novel structure that specifically avoids the generation of overcounted terms. The resulting tetraquark bound state equations are given for the case of general two-body interactions, and for the specific case of separable interactions that lead to a description of the tetraquark in terms of meson-meson and diquark-antidiquark degrees of freedom where the effects of quark-antiquark annihilation is included. The inclusion of 2q2q-and qq-channel coupling in our approach enables a wide variety of applications of our equations to other processes within the 2q2q system, and to other 2-particle plus 2-antiparticle systems.

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“…where G (2) is the full two-body qq Green function, and G (4) ir is the qq irreducible part of the full 2q2q Green function G (4) ; further, G…”

Section: Double Counting Problemmentioning

confidence: 99%

“…Such overcounting problems have been solved in the last two decades for a number of cases [3][4][5][6][7][8]. One of these is the case of four-quark equations where even the seemingly natural task of summing pair interaction kernels leads to overcounting [1,3].…”

Section: Introductionmentioning

confidence: 99%

Covariant equations for the tetraquark and more

Kvinikhidze

Blankleider

2014

Phys. Rev. D

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“…However, when overcounting occurs within the scattering integral equations themselves, the way to solve the overcounting problem becomes highly non-trivial. Indeed, only recently has such an overcounting problem been solved in the context of four-dimensional integral equations for the NN − πNN system [5,6].…”

Section: Introductionmentioning

confidence: 99%

Gauging of equations method. I. Electromagnetic currents of three distinguishable particles

Kvinikhidze

Blankleider²

1999

Phys. Rev. C

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103

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We present a general method for incorporating an external electromagnetic field into descriptions of few-body systems whose strong interactions are described by integral equations. In particular, we address the case where the integral equations are those of quantum field theory and effectively sum up an infinite number of Feynman diagrams. The method involves the idea of gauging the integral equations themselves, and results in electromagnetic amplitudes where an external photon is effectively coupled to every part of every strong interaction diagram in the model. Current conservation is therefore implemented in the way prescribed by quantum field theory. We apply our gauging procedure to the four-dimensional integral equations describing a system of three distinguishable relativistic particles. In this way we obtain the expressions needed to calculate all possible electromagnetic processes of the three-body system. An interesting aspect of our results is the natural appearance of a subtraction term needed to avoid the overcounting of diagrams.

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“…In this regard we should mention that applying techniques of the present paper to the πNN equations derived in Ref. [19,33], and their electromagnetic currents [20], would lead to a comprehensive description of the GPDs for the transitions NN → πNN,d → πd, etc.…”

Section: Final Commentsmentioning

confidence: 94%

“…This method not only solves the problem of extracting charge and current conserving electromagnetic currents, but it does so in accordance with strict adherence to theory: the external electromagnetic field is attached to all possible places in the nonperturbative strong interaction processes defined by the dynamic equation model. A further feature of the method is that it automatically takes care of all the overcounting problems that plague 4D approaches [15,19,20]. Indeed, the gauging of equations method has since been instrumental in the construction of current conserving electromagnetic interactions [21,22,23,24], and in enabling careful analyses of the overcounting problem [24,25,26].…”

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confidence: 99%

Generalized parton distributions for dynamical equation models

Kvinikhidze

Blankleider

2007

Nuclear Physics A

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We show how generalized parton distributions (GPDs) can be determined in the case where hadrons are described in terms of their partonic degrees of freedom through solutions of dynamical equations. We demonstrate our approach on the example of two-quark bound states described by the Bethe-Salpeter equation, and three-quark bound states described by three-and four-dimensional Faddeev-like equations. Within the model of strong interactions defined by the dynamical equations, all possible mechanisms contributing to the GPDs are taken into account, and all GPD sum rules are satisfied automatically. The formulation is general and can be applied to determine generalized quark distributions, generalized gluon distributions, transition GPDs, nucleon distributions in nuclei, etc. Our approach is based on the gauging of equations method.

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Covariant three-body equations in φ3 field theory

Cited by 27 publications

References 5 publications

Covariant equations for the tetraquark and more

Covariant equations for the tetraquark and more

Gauging of equations method. I. Electromagnetic currents of three distinguishable particles

Generalized parton distributions for dynamical equation models

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