Skyrmion quantization and the decay of the [Delta]

doi:https://doi.org/10.1103/PhysRevD.50.5816

Title: Skyrmion quantization and the decay of the [Delta]

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Abstract

We present the complete solution to the so-called Yukawa problem'' of the Skyrme model. This refers to the perceived difficulty of reproducing, purely from soliton physics, the usual pseudovector pion-nucleon coupling, echoed by pion coupling to the higher-spin/isospin baryons ([ital I]=[ital J]=3/2, 5) / 2 ,. . .,([ital N][sub [ital c]]/2) in a manner fixed by large-[ital N][sub [ital c]] group theory. The solution involves surprisingly elegant interplay between the classical and quantum properties of a new configuration: the [ital rotationally] [ital improved] [ital Skyrmion]. This is the near-hedgehog solution obtained by minimizing the usual Skyrmion mass functional augmented by an all-important (iso)rotational kinetic term. The numerics are pleasing: a [Delta] decay width within a few MeV of its measured value, and, furthermore, the higher-spin baryons ([ital I]=[ital J][ge]5/2) with widths so large ([Gamma][gt]800 MeV) that these undesirable large-[ital N][sub [ital c]] artifacts effectively drop out of the spectrum, and pose no phenomenological problem. Beyond these specific results, we ground the Skyrme model in the Feynman path integral, and set up a transparent collective coordinate formalism that makes maximal use of the 1/[ital N][sub [ital c]] expansion. This approach elucidates the connection between Skyrmions on the one hand, and Feynmanmore »« less

Authors:

Dorey, N ^[1]; Hughes, J ^[2]; Mattis, M P ^[3]

Physics Department, University College of Swansea, Swansea SA2 8PP (United Kingdom)
Physics Department, Michigan State University, East Lansing, Michigan 48823 (United States)
Theoretical Division T-8, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

Publication Date:: 1994-11-01

OSTI Identifier:: 6924202

Resource Type:: Journal Article

Journal Name:: Physical Review, D (Particles Fields); (United States)

Additional Journal Information:: Journal Volume: 50:9; Journal ID: ISSN 0556-2821

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; DELTA BARYONS; PARTICLE DECAY; SKYRME POTENTIAL; QUANTIZATION; BARYONS; COUPLING; FEYNMAN DIAGRAM; FEYNMAN PATH INTEGRAL; HIGH SPIN STATES; PION-NUCLEON INTERACTIONS; SOLITONS; SPECTRA; DECAY; DIAGRAMS; ELEMENTARY PARTICLES; ENERGY LEVELS; FERMIONS; HADRON-HADRON INTERACTIONS; HADRONS; INTEGRALS; INTERACTIONS; MESON-BARYON INTERACTIONS; MESON-NUCLEON INTERACTIONS; N BARYONS; NUCLEON-NUCLEON POTENTIAL; PARTICLE INTERACTIONS; POTENTIALS; QUASI PARTICLES; 662240* - Models for Strong Interactions- (1992-); 662110 - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-); 662360 - Decays of Baryons- (1992-); 662410 - Properties of Baryons & Baryon Resonances- (1992-)

Citation Formats


                    Dorey, N, Hughes, J, and Mattis, M P. Skyrmion quantization and the decay of the [Delta].  United States: N. p., 1994. 
        Web.  doi:10.1103/PhysRevD.50.5816.

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                    Dorey, N, Hughes, J, & Mattis, M P. Skyrmion quantization and the decay of the [Delta].  United States.  https://doi.org/10.1103/PhysRevD.50.5816

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                    Dorey, N, Hughes, J, and Mattis, M P. Tue .  
        "Skyrmion quantization and the decay of the [Delta]".  United States.  https://doi.org/10.1103/PhysRevD.50.5816.

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@article{osti_6924202,

  title        = {Skyrmion quantization and the decay of the [Delta]},

  author       = {Dorey, N and Hughes, J and Mattis, M P},

  abstractNote = {We present the complete solution to the so-called Yukawa problem'' of the Skyrme model. This refers to the perceived difficulty of reproducing, purely from soliton physics, the usual pseudovector pion-nucleon coupling, echoed by pion coupling to the higher-spin/isospin baryons ([ital I]=[ital J]=3/2, 5) / 2 ,. . .,([ital N][sub [ital c]]/2) in a manner fixed by large-[ital N][sub [ital c]] group theory. The solution involves surprisingly elegant interplay between the classical and quantum properties of a new configuration: the [ital rotationally] [ital improved] [ital Skyrmion]. This is the near-hedgehog solution obtained by minimizing the usual Skyrmion mass functional augmented by an all-important (iso)rotational kinetic term. The numerics are pleasing: a [Delta] decay width within a few MeV of its measured value, and, furthermore, the higher-spin baryons ([ital I]=[ital J][ge]5/2) with widths so large ([Gamma][gt]800 MeV) that these undesirable large-[ital N][sub [ital c]] artifacts effectively drop out of the spectrum, and pose no phenomenological problem. Beyond these specific results, we ground the Skyrme model in the Feynman path integral, and set up a transparent collective coordinate formalism that makes maximal use of the 1/[ital N][sub [ital c]] expansion. This approach elucidates the connection between Skyrmions on the one hand, and Feynman diagrams in an effective field theory on the other.},

  doi          = {10.1103/PhysRevD.50.5816},

  url          = {https://www.osti.gov/biblio/6924202},
  journal      = {Physical Review, D (Particles Fields); (United States)},

  issn         = {0556-2821},

  number       = ,

  volume       = 50:9,

  place        = {United States},

  year         = {1994},

  month        = {11}

}

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