Skyrmion Quantization and the Decay of the Delta

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 $(I=J=3/2,5/2,\cdots ,N_c/2)$ in a manner fixed by large-$N_c$ group theory. The solution involves surprisingly elegant interplay between the classical and quantum properties of a new configuration, the ``new improved skyrmion''. This is the near-hedgehog obtained by minimizing the usual skyrmion mass functional augmented by an all-important isorotational kinetic term. The numerics are pleasing: a $\Delta$ decay width within a few MeV of its measured value, and furthermore, the higher-spin baryons $(I=J\ge 5/2)$ with widths so large ($\Gamma >800MeV$) that these undesirable large-$N_c$ 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 $1/N_c$ expansion. This approach elucidates the connection between skyrmions on the one hand, and Feynman diagrams in an effective field theory on the other.

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References in corpus (6)

• Baryon-Pion Couplings from Large-N QCD
• Dynamics of Moving and Spinning Skyrmions
• Soliton quantization and internal symmetry
• Solvability, Consistency and the Renormalization Group in Large-$N_c$ Models of Hadrons
• CP-Violating Yukawa Couplings in the Skyrme Model and the Neutron Electric Dipole Moment
• Scattering in Soliton Models and the Bosonic Exchange description

Cited by in corpus (24)

• Baryon Mass Splittings in the 1/N_c Expansion
• Chiral-Soliton Predictions for Exotic Baryons
• Quantum scattering of charged solitons in the complex sine-Gordon model
• Chiral Lagrangian for Baryons in the $1/N_c$ Expansion
• Spinning Skyrmions and the Skyrme Parameters
• Homotopy of Rational Maps and the Quantization of Skyrmions
• Bound State versus Collective Coordinate Approaches in Chiral Soliton Models and the Width of the ${\Theta }^{+}$ Pentaquark
• Stability and Representation Dependence of the Quantum Skyrmion
• The decay width of stringy hadrons
• Resolving Ordering Ambiguities in the Collective Quantization by Particle Conjugation Constraints
• Pion-Nucleon Scattering in a Large-N Sigma Model
• Covariant Quantization of the Skyrmion
• From Effective Lagrangians, to Chiral Bags, to Skyrmions with the Large-N_c Renormalization Group
• Oblate Skyrmions
• Topology and metastability in the lattice Skyrme model
• Skyrmions coupled with the electromagnetic field via the gauged Wess-Zumino term
• The 35-plet Baryons from Chiral Soliton Models
• Chiral Divergent Properties of Hadrons in the Large-N_c Limit
• Exotic Baryons in Chiral Soliton Models
• Can Plane Wave Modes be Physical Modes in Soliton Models?
• Collective Coordinates and the Absence of Yukawa Coupling in the Classical Skyrme Model
• Nonrigid chiral soliton for the octet and decuplet baryons
• On quantization of the SU(2) Skyrmions
• Representation Mixing and Exotic Baryons in the Skyrme Model