The Goldberger–Treiman discrepancy in SU(3)

The relativistic chiral SU (3) Lagrangian is used to describe kaon-nucleon scattering imposing constraints from the pion-nucleon sector and the axial-vector coupling constants of the baryon octet states. We solve the covariant coupled-channel BetheSalpeter equation with the interaction kernel truncated at chiral order Q 3 where we include only those terms which are leading in the large N c limit of QCD. The baryon decuplet states are an important explicit ingredient in our scheme, because together with the baryon octet states they form the large N c baryon ground states of QCD. Part of our technical developments is a minimal chiral subtraction scheme within dimensional regularization, which leads to a manifest realization of the covariant chiral counting rules. All SU(3) symmetry-breaking effects are well controlled by the combined chiral and large N c expansion, but still found to play a crucial role in understanding the empirical data. We achieve an excellent description of the data set typically up to laboratory momenta of p lab ≃ 500 MeV.

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“…(54,73)). The only non-trivial contribution arise from the on-shell reducible parts of the u-channel baryon octet terms.…”

Section: Su(3) Coupled-channel Dynamicsmentioning

confidence: 99%

“…Taking the schannel nucleon pole term as the driving term in the Bethe-Salpeter equation we derived the explicit result (54). We first discuss its implicit nucleon mass renormalization.…”

Section: Renormalization Programmentioning

confidence: 99%

Relativistic chiral SU(3) symmetry, large-Nc sum rules and meson–baryon scattering

Lutz¹,

2002

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“…Little is known about the integrand over the cut which consists of the contribution of the axial-vector (1 + ) and pseudoscalar (0 − ) intermediate states.The contribution of the low energy region(the three pion states) is suppressed by loop factors and amounts to little [8]. We expect the major part of the contribution to originate from the a1(1260) and π ′ (1300) bumps i.e from the range 1GeV 2 ≤ s ≤ 2GeV 2 .In order to eliminate this contribution,we shall consider, instead of integral (2.10), the following modified integral…”

Section: The Chiral Symmetry Breaking Correctionsmentioning

confidence: 99%

“…Currrent Algebra and PCAC (partial conservation of the axial-vector current) together with the ABJ axial-anomaly [1] expresses the two-photon decay rate of the pseudoscalar mesons (P = π 0 , η, η ′ ) in terms of the coupling constants f π 0 , f 0 and f 8 and where the axial-vector currents are given in terms of the quark fields. Unlike f π , f 0 and f 8 are not directly related to any physical process.…”

Section: Introductionmentioning

confidence: 99%

Two-photon decay of the pseudoscalars, the chiral symmetry breaking corrections

Nasrallah

2002

Phys. Rev. D

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The extrapolation of the decay amplitudes of the pseudoscalar mesons into two photons from the soft meson limit where it is obtained from the axial-anomaly to the mass shell involves the contribution of the 0 − continuum. These chiral symmetry breaking corrections turn out to be large. The effects of these corrections on the calculated π 0 decay rate, on the values of the singlet-octet mixing angle and on the ratios

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“…In accordance with Goldstone's theorem, this interaction → 0 as the pion momentum → 0. Furthermore, the coupling constant g πN can be computed from the Goldberger-Treiman relation [7] and chiral corrections [8] and is accurate to the few % level. The πN interaction is very weak in the s wave and strong in the p wave which leads to the ∆ resonance, the tensor force between nucleons, and to long range non-spherical virtual pionic contributions to hadronic structure.…”

Section: Introductionmentioning

confidence: 99%

Energy dependence of the delta resonance: Chiral dynamics in action

Bernstein¹,

Stave

2007

Few-Body Systems

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Abstract. There is an important connection between the low energy theorems of QCD and the energy dependence of the ∆ resonance in π-N scattering, as well as the closely related γ * N → N π reaction. The resonance shape is due not only to the strong π-N interaction in the p wave but the small interaction in the s wave; the latter is due to spontaneous chiral symmetry breaking in QCD (i.e. the Nambu-Goldstone nature of the pion). A brief overview of experimental tests of chiral perturbation theory and chiral based models is presented.

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The Goldberger–Treiman discrepancy in SU(3)

Abstract: The Goldberger-Treiman discrepancy in SU (3)

Cited by 28 publications

References 17 publications

Relativistic chiral SU(3) symmetry, large-Nc sum rules and meson–baryon scattering

Relativistic chiral SU(3) symmetry, large-Nc sum rules and meson–baryon scattering

Two-photon decay of the pseudoscalars, the chiral symmetry breaking corrections

Energy dependence of the delta resonance: Chiral dynamics in action

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