Gauge invariance in two-particle scattering

Borasoy, B.; Bruns, Peter C.; Meißner, Ulf‐G.; Nißler, Robert

doi:10.1103/physrevc.72.065201

Cited by 69 publications

(109 citation statements)

References 28 publications

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“…The coupling of the γ to the baryon in the first loop vanishes in the heavy baryon limit and is very small otherwise. A general discussion of issues of gauge invariance, chiral invariance, etc., within the context of unitarized chiral theories can be found in [32,33]. In Ref.…”

Section: Radiative Decaymentioning

confidence: 99%

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Radiative decay of theΛ*(1520)

2006

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A recently developed non-perturbative chiral approach to dynamically generate the 3/2 − baryon resonances has been extended to investigate the radiative decays Λ * (1520) → γΛ(1116) and Λ * (1520) → γΣ 0 (1193). We show that the Λ * (1520) decay into γΛ is an ideal test for the need of extra components of the resonance beyond those provided by the chiral approach since the largest meson-baryon components give no contribution to this decay. The case is different for γΣ decay where the theory agrees with experiment, though the large uncertainties of these data call for more precise measurements.

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Section: Radiative Decaymentioning

confidence: 99%

“…In Ref. [32] one proved that gauge invariance is preserved when the photon is coupled to internal as well as external lines and vertices. An extra discussion on this issue is given in [33].…”

Section: Radiative Decaymentioning

confidence: 99%

Radiative decay of theΛ*(1520)

2006

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“…For scattering amplitudes similar formalisms were discussed in Refs. [16,17,18]. The relevant equations in the two limiting cases A and B introduced above will appear as special cases of these general equations.…”

Section: Bethe-salpeter Approachmentioning

confidence: 99%

Two-photon decays of hadronic molecules

Hanhart

Kalashnikova²,

Kudryavtsev³

et al. 2007

Phys. Rev. D

119

139

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In many calculations of the two-photon decay of hadronic molecules, the decay matrix element is estimated using the wave function at the origin prescription, in analogy to the two-photon decay of parapositronium. We question the applicability of this procedure to the two-photon decay of hadronic molecules for it introduces an uncontrolled model dependence into the calculation. As an alternative approach, we propose an explicit evaluation of the hadron loop. For shallow bound states, this can be done as an expansion in powers of the range of the molecule binding force 1/β. In the leading order one gets the well-known pointlike limit answer. We estimate, in a self-consistent and gauge invariant way, the leading range corrections for the two-photon decay width of weakly bound hadronic molecules emerging from kaon loops. We find them to be small, of order O(mε/β 2 ), where m and ε denote the mass of the constituents and the binding energy, respectively. The role of possible shortranged operators and of the width of the scalars remains to be investigated.

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“…[10]. Due to the mixing of nucleon and Roper, two new diagrams can contribute to the Roper self-energy, and the non-diagonal terms should be included in the baryon mass matrix M B ,…”

Section: Theoretical Frameworkmentioning

confidence: 99%

“…As a first step, we reconsider the Roper self-energy [10,11] to next-to-next-to-leading order (NNLO) including explicitly the pion-mass dependence of the mixing between nucleon and Roper. We also calculate the virtual Roper effects on the nucleon and Delta self-energies to the same order.…”

Section: Introductionmentioning

confidence: 99%

Roper mass in chiral perturbation theory

Ren¹

2016

Proceedings of the 8th International Workshop on Chiral Dynamics — PoS(CD15)

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Understanding the nature of the Roper resonance is of particular interest. Its mass, for example, shows a very unusual pattern: it is lower than the negative parity state N(1535). Also, the Roper is expected to play a role in low energy observables due to its closeness to the nucleon and Delta. We report on a systematic study of the nucleon, Delta, and Roper masses in chiral perturbation theory up to next-to-next-to-leading order. For the first time, the contributions due to the mixing between the nucleon and the Roper allowed by chiral symmetry are taken into account. Recently, several lattice QCD collaborations have reported some results on the Roper mass, assuming this particle is always stable. A chiral extrapolation of these data is also presented as an application of our results.

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Gauge invariance in two-particle scattering

Abstract: It is shown how gauge invariance is obtained for the coupling of a photon to a two-body state described by the solution of the Bethe-Salpeter equation. This is illustrated both for a complex scalar field theory and for interaction kernels derived from chiral effective Lagrangians.

Cited by 69 publications

References 28 publications

Radiative decay of theΛ*(1520)

Radiative decay of theΛ*(1520)

Two-photon decays of hadronic molecules

Roper mass in chiral perturbation theory

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