CP-VIOLATING YUKAWA COUPLINGS IN THE SKYRME MODEL AND THE NEUTRON ELECTRIC-DIPOLE MOMENT

We argue that the large-N(c) behaviour of the Yukawa couplings in the Skyrme model involves issues more subtle than the vanishing of linear fluctuations needed for classical stability of the skyrmion. The chira l fluctuations about the skyrmion must be quantized in order to reach a conclusion. An improved quantization procedure allows us to confront this question directly. The pion-nucleon coupling constants g(piNN) ( CP conserving) and g(piNN)BAR (CP violating) are calculated in the lar ge-N(c), three-flavour Skyrme model by direct evaluation of the leadin g matrix elements appearing in the LSZ reduction formula. We find that g(piNN) approximately N(c)3/2, but that, at most, g(piNN)BAR approxim ately m(pi)2N(c)-1/2. These results show that the leading contribution to the neutron electric dipole moment in large-N, Skyrme model is the direct one (D(n) approximately N(c)m(pi)2), rather than the pion loop contribution.