Fun with Electroweak Solitons

Abstract

We consider a variant of the standard electroweak theory in which the Higgs sector has been modified so that there is a classically stable weak scale soliton. We explore fermion number violating processes which involve soliton decay. A soliton can decay by tunneling under the sphaleron barrier, or the decay can be collision-induced if the energy is sufficient for the barrier to be traversed. We discuss classical solutions to the Minkowski space equations of motion in which a soliton is kicked over the barrier by an incoming pulse. We then consider a limit in which we can reliably estimate the amplitude for soliton decay induced by collision with a single W-boson. This amplitude depends on g like exp(−cg −1/3), and is larger than that for spontaneous decay via tunneling in the same limit. Finally we show that in soliton decays, light SU(2) L doublet fermions are anomalously produced. Thus we have a calculation of a two body process with energy above the sphaleron barrier in which fermion number is violated.