Skyrmion Quantization and the Decay of the Delta

Details Skyrmion Quantization and the Decay of the Delta Skyrmion Quantization and the Decay of the Delta

1994-04-16

arxiv.org/abs/hep-ph/9404274v2

Phys.Rev. D50 (1994) 5816-5833

Physics

High Energy Physics

High Energy Physics - Phenomenology

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Scientific paper

10.1103/PhysRevD.50.5816

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 ($\Gamma > 800 MeV$) 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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