RIBBONS AROUND MEXICAN HATS

We analyze quasi-topological solitons winding around a Mexican-hat pot ential in two space-time dimensions. They are prototypes for a large n umber of physical excitations, including skyrmions of the Higgs sector of the standard electroweak model, magnetic bubbles in thin ferromagn etic films, and strings in certain non-trivial backgrounds. We present explicit solutions, derive the conditions for classical stability, an d show that contrary to the naive expectation these can be satisfied i n the weak-coupling limit. In this limit we can calculate the soliton properties reliably, and estimate their lifetime semiclassically. We e xplain why gauge interactions destabilize these solitons, unless the s calar sector is extended.