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 ,. . .,${\mathit{N}}_{\mathit{c}}$/2) in a manner fixed by large-${\mathit{N}}_{\mathit{c}}$ group theory. The solution involves surprisingly elegant interplay between the classical and quantum properties of a new configuration: the rotationally improved 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 \ensuremath{\Delta} decay width within a few MeV of its measured value, and, furthermore, the higher-spin baryons (I=J\ensuremath{\ge}5/2) with widths so large (\ensuremath{\Gamma}>800 MeV) that these undesirable large-${\mathit{N}}_{\mathit{c}}$ 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/${\mathit{N}}_{\mathit{c}}$ expansion. This approach elucidates the connection between Skyrmions on the one hand, and Feynman diagrams in an effective field theory on the other.