Axial current matrix elements and pentaquark decay widths in chiral soliton models

Weigel, H.

doi:10.1103/physrevd.75.114018

Cited by 11 publications

(9 citation statements)

References 29 publications

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“…In the flavor symmetric case it contains only a single collective coordinate operator and is thus very different from estimates that extract an effective Yukawa coupling from the axial current matrix element. 3) Since our approach matches the exact large N C result, we must conclude that those axial current scenarios are erroneous 14) and that the cancellation among contributions to this matrix element is an invalid argument for a small pentaquark width.…”

Section: Resultsmentioning

confidence: 57%

On the Width of Collective Excitations in Chiral Soliton Models

Weigel

2007

Prog. Theor. Phys. Suppl.

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In chiral soliton models for baryons the computation of hadronic decay widths of baryon resonances is a long standing problem. For the three flavor Skyrme model I present a solution to this problem that satisfies large-N C consistency conditions. As an application I focus on the hadronic decay of the Θ and Θ * pentaquarks. §1. Statement of the problem Hadronic decays of baryon resonances are commonly described by a Yukawa interaction of the generic structurewhere B is the resonance that decays into baryon B and meson φ and g is a coupling constant. It is crucial that this interaction Lagrangian is linear in the meson field. If φ is a pseudoscalar meson this interaction yields the decay width Γ (B → Bφ) ∝ g 2 | p φ | 3 , with p φ being the momentum of the outgoing meson. The situation is significantly different in soliton models that are based on action functionals of only meson degrees of freedom, Γ = Γ [Φ]. These action functionals contain classical (static) soliton solutions, Φ sol , that are identified as baryons. The interaction of these baryons with mesons is described by the (small) meson fluctuations about the soliton: Φ = Φ sol + φ. By pure definition we haveThus there is no term linear in φ to be associated with the Yukawa interaction, Eq. (1 . 1). This puzzle has become famous as the Yukawa problem in soliton models. However, this does not mean that soliton models cannot describe resonance widths. On the contrary, these widths can be extracted from meson baryon scattering amplitudes, just as in experiment. In soliton models two-meson processes acquire contributions from the second order termThis expansion simultaneously represents an expansion in N C , the number of color degrees of freedom: Γ = O(N C ) and Γ (2) = O(N 0 C ). Terms O(φ 3 ) vanish in the limit N C → ∞. This implies that Γ (2) contains all large-N C information about hadronic decays of resonances. We may reverse this statement to argue about any computation of hadronic decay widths in soliton models: For N C → ∞ it must identically match * )On the Width of Collective Excitations 79 the result obtained from Γ (2) . Unfortunately, the most prominent baryon resonance, the ∆ isobar, becomes degenerate with the nucleon as N C → ∞. It is stable in that limit and its decay is not subject to the above described litmus-test. The situation is more interesting in soliton models for flavor SU (3). In the so-called rigid rotator approach (RRA), that generates baryon states as (flavor) rotational excitations of the soliton, exotic resonances emerge that dwell in the anti-decuplet representation of flavor SU (3). 1) The most discussed (and disputed) such state is the Θ + pentaquark with zero isospin and strangeness S = +1. In the limit N C → ∞ the (would-be) anti-decuplet states maintain a non-zero mass difference with respect to the nucleon. Therefore the properties of Θ + predicted from any model treatment must also be seen in the S-matrix for koan-nucleon scattering as computed from Γ (2) . This (seemingly alternative) quantization of strangeness deg...

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Section: Resultsmentioning

confidence: 57%

On the Width of Collective Excitations in Chiral Soliton Models

Weigel

2007

Prog. Theor. Phys. Suppl.

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“…To conclude, if Θ + happens to be a narrow resonance, one can find its width from the ΘKN transition axial coupling or, thanks to the Goldberger-Treiman relation, from the transition pseudoscalar coupling (it is contrary to the recent claim of Ref. 29,43 ). This is how the narrow Θ + has been first predicted 5 and how a more stringent estimate of the width Γ Θ ∼ 1 MeV has been recently performed.…”

Section: 71)mentioning

confidence: 75%

Exotic Baryon Resonances in the Skyrme Model

Diakonov¹,

Петров²

2010

The Multifaceted Skyrmion

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We outline how one can understand the Skyrme model from the modern perspective. We review the quantization of the SU (3) rotations of the Skyrmion, leading to the exotic baryons that cannot be made of three quarks. It is shown that in the limit of large number of colours the lowest-mass exotic baryons can be studied from the kaon-Skyrmion scattering amplitudes, an approach known after Callan and Klebanov. We follow this approach and find, both analytically and numerically, a strong Θ + resonance in the scattering amplitude that is traced to the rotational mode. The Skyrme model does predict an exotic resonance Θ + but grossly overestimates the width. To understand better the factors affecting the width, it is computed by several methods giving, however, identical results. In particular, we show that insofar as the width is small, it can be found from the transition axial constant. The physics leading to a narrow Θ + resonance is briefly reviewed and affirmed.

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“…In this discussion, which is based on Refs. [1][2][3], we will examine and review their description in the framework of chiral soliton models; see Ref. [4] for a recent review on these models.…”

Section: Introductionmentioning

confidence: 99%

“…(2). For both BSA versions scattering phase shifts can be computed and their difference is the resonance phase shift δ R .The litmus test for the RVA is then whether or not lim N C →∞ δ E (N C ) ?…”

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confidence: 99%