Abstract
We study the vacuum structures for various invisible-axion models. We illustrate that the assignment of U(1)PQ charge for the Higgs-singlet field plays a very important role in determining the domain-wall number NDW. Especially, we find that the existence of trilinear terms in the Higgs potential would reduce NDW by a factor 2 compared with the usual quartic-type one. This factor is important in constructing domain-wall-free models. Several possibilities of constructing such models are pointed out. © 1990 The American Physical Society.