Current conservation and interaction currents in relativistic meson theories

Gross, Franz; Riska, D.O.

doi:10.1103/physrevc.36.1928

Cited by 230 publications

(283 citation statements)

References 20 publications

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“…This agrees with the result first derived by Gross and Riska [31]. An alternative but equivalent approach is to start with the Bethe-Salpeter equation for φ:…”

Section: B Gpds Of Two-body Bound Statessupporting

confidence: 78%

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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“…This agrees with the result first derived by Gross and Riska [31]. An alternative but equivalent approach is to start with the Bethe-Salpeter equation for φ:…”

Section: B Gpds Of Two-body Bound Statessupporting

confidence: 78%

Generalized parton distributions for dynamical equation models

Kvinikhidze

Blankleider

2007

Nuclear Physics A

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“…(24) and we are going to ensure this by choosing X µ gip accordingly after having determined [· · · ] red in (29). [We repeat here that -completely consistent with the covariant three-dimensional reduction -the off-shell T 's of (30), and of the subsequent equations in this section, are those defined by the off-shell extension (28) of (27), and not the solutions of the original Bethe-Salpeter equations (1) that appear in (24); see also the discussion surrounding Eq. (28).…”

Section: Covariant Three-dimensional Reductionmentioning

confidence: 99%

“…In the same schematic notation, the four-divergence of the interaction current V µ then is simply [23,30] …”

Section: B Gauge Invariance Of the Full Four-dimensional Amplitudementioning

confidence: 99%

“…The gauge-invariance constraints in terms of the generalized Ward-Takahashi identities, either in the form (24) for the full amplitude or as (30) for the reduced one, are just formal constraints, of course, since the only physically relevant -i.e., measurable -ramification is current conservation when all external nucleons of the bremsstrahlung process are on their respective energy shells. It is for this reason that the current-conservation constraint,…”

Section: Local Gauge Invariance: Constraining Subprocessesmentioning

confidence: 99%

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Gauge-invariant formulation ofNN→NNγ

Haberzettl

Nakayama

2012

Phys. Rev. C

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A complete, rigorous relativistic field-theory formulation of the nucleon-nucleon (N N ) bremsstrahlung reaction is presented. The resulting amplitude is unitary as a matter of course and it is gauge invariant, i.e., it satisfies a generalized Ward-Takahashi identity. The novel feature of this approach is the consistent microscopic implementation of local gauge invariance across all interaction mechanisms of the hadronic systems, thus serving as a constraint for all subprocesses. The formalism is quite readily adapted to approximations and thus can be applied even in cases where the microscopic dynamical structure of the underlying interacting hadronic systems is either not known in detail or too complex to be treated in detail. We point out how the interaction currents resulting from the photon being attached to nucleon-nucleon-meson vertices can be treated by phenomenological four-point contact currents that preserve gauge invariance. In an advance application of the present formalism [K. Nakayama and H. Haberzettl, Phys. Rev. C 80, 051001 (2009)], such interaction currents were found to contribute significantly in explaining experimental data. In addition, we provide a scheme that permits -through an introduction of phenomenological five-point contact currents -the approximate treatment of current contributions resulting from pieces of the N N interaction that cannot be incorporated exactly. In each case, the approximation procedure ensures gauge invariance of the entire bremsstrahlung amplitude. We also discuss the necessary modifications when taking into account baryonic states other than the nucleon N ; in detail, we consider the ∆(1232) resonance by incorporating the couplings of the N N to the N ∆ and ∆∆ systems, and the γN → ∆ transitions. We apply the formalism to the 280-MeV bremsstrahlung data from TRIUMF [Phys. Rev. D 41, 2689(1990] incorporating γN ∆ transition currents and find good agreement with the data.

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“…To restore current conservation, we follow the procedure of Gross and Riska [68], based on the Ward-Takahashi identity. They suggest the following replacements in the vertex functions:…”

Section: Gauge Invariancementioning

confidence: 99%