Gauge-invariant Theory of Two-Pion Photo- and Electro-Production off the Nucleon

Haberzettl, H.; Nakayama, K.; Oh, Yongseok

doi:10.1007/s00601-012-0590-0

Cited by 3 publications

(4 citation statements)

References 5 publications

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“…One of the interesting conclusions made in [33] is that in photoproduction the background contributions to the π 0 π 0 production are as large as the resonant one. Note that the analysis of the two-pion photoproduction data is more involved due to the complications related with the gauge invariance [34]. On the other hand the non-resonant terms play only a minor role in the π − p → π 0 π 0 n scattering [33].…”

Section: Overview Of the πN → 2πn Reactionmentioning

confidence: 99%

2πproduction in the Giessen coupled-channels model

2016

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The coupled channels Lagrangian approach underlying the Giessen model (GiM) is extended to describe the πN → πN , 2πN scattering in the resonance energy region. As a feasibility study we investigate single and double pion production up to the second resonance region. The 2πN production has been significantly improved by using the isobar approximation with σN and π∆(1232) in the intermediate state. The three-body unitarity is maintained up to interference pattern between the isobar subchannels. The scattering amplitudes are obtained as a solution of the Bethe-Salpeter equation in the K matrix approximation. As a first application we perform a partial wave analysis of the πN → πN , π 0 π 0 N reactions in the Roper resonance region. We obtain R σN (1440) = 27 +4 −9 % and R π∆ (1440) = 12 +5 −3 % for the σN and π∆(1232) decay branching ratios of N * (1440) respectively. The extracted πN inelasticities and reaction amplitudes are consistent with the results from other groups.

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Section: Overview Of the πN → 2πn Reactionmentioning

confidence: 99%

2πproduction in the Giessen coupled-channels model

2016

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“…(7) amounts to the formulation of the effective charge difference across the reaction in the presence of hadronic vertices with structure. It is of paramount importance here that all three fourdivergence equations are off-shell relations, and that the off-shellness is a necessary requirement for local gauge invariance [22] since it ensures that the (off-shell) current M µ provides the correct, consistent contributions to gauge invariance even if it is embedded as an off-shell subprocess in a larger process (for example, electromagnetic production of two or more mesons [28,40]). …”

Section: A Generalized Ward-takahashi Identitiesmentioning

confidence: 99%

Preserving local gauge invariance witht-channel Regge exchange

Haberzettl

Wang

2015

Phys. Rev. C

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Considering single-meson photo-and electroproduction off a baryon, it is shown how to restore local gauge invariance that was broken by replacing standard Feynman-type meson exchange in the t-channel by exchange of a Regge trajectory. This is achieved by constructing a contact current whose four-divergence cancels the gauge-invariance-violating contributions resulting from all states above the base state on the Regge trajectory. To illustrate the procedure, modifications necessary for the process γ +p → K + +Σ * 0 are discussed in some detail. We also provide the general expression for the contact current for an arbitrary reaction.

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“…Regarding the details for the remainder current R µ , we note that the isospin structure (84) for the underlying N → KKΞ vertex has separate contributions for isospins T = 0, 1 of the KΞ subsystem in the final state. This isospin structure carries over to the contact current C µ of Eq.…”

Section: Application To γN → K K ξmentioning

confidence: 99%

“…A preliminary account of a part of the main results of the present work can be found in the conference proceedings of Ref. [84]. The present paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Theory of two-meson photo- and electroproduction off the nucleon

Haberzettl

Nakayama

2019

Phys. Rev. D

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A field-theoretical description of the electromagnetic production of two pions off the nucleon is derived and applied to photo-and electroproduction processes, assuming only one-photon exchange for the latter. The developed Lorentz-covariant theory is complete in the sense that all explicit three-body mechanisms of the interacting ππN system are considered based on three-hadron vertices. The modifications necessary for incorporating n-meson vertices for n ≥ 4 are discussed. The resulting reaction scenario subsumes and surpasses all existing approaches to the problem based on hadronic degrees of freedom. The full three-body dynamics of the interacting ππN system is accounted for by the Faddeev-type ordering structure of the Alt-Grassberger-Sandhas equations. The formulation is valid for hadronic two-point and three-point functions dressed by arbitrary internal mechanisms -even those of the self-consistent nonlinear Dyson-Schwinger type (subject to the three-body truncation) -provided all associated electromagnetic currents are constructed to satisfy their respective (generalized) Ward-Takahashi identities. It is shown that coupling the photon to the Faddeev structure of the underlying hadronic two-pion production mechanisms results in a natural expansion of the full twopion photoproduction current M µ ππ in terms of multiple dressed loops involving two-body subsystem scattering amplitudes of the ππN system that preserves gauge invariance as a matter of course order by order in the number of (dressed) loops. A closed-form expression is presented for the entire gauge-invariant current M µ ππ with complete three-body dynamics. Individually gauge-invariant truncations of the full dynamics most relevant for practical applications at the no-loop, one-loop, and two-loop levels are discussed in detail. An approximation scheme to the full two-pion amplitude for calculational purposes is also presented. It approximates, systematically, the full amplitude to any desired order of expansion in the underlying hadronic two-body amplitude. Moreover, it allows for the approximate incorporation of all neglected higher-order mechanisms in terms of a phenomenological remainder current. The effect and phenomenological usefulness of this remainder current is assessed in a tree-level calculation of the γN → KKΞ reaction.

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Gauge-invariant Theory of Two-Pion Photo- and Electro-Production off the Nucleon

Cited by 3 publications

References 5 publications

2πproduction in the Giessen coupled-channels model

2πproduction in the Giessen coupled-channels model

Preserving local gauge invariance witht-channel Regge exchange

Theory of two-meson photo- and electroproduction off the nucleon

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