Sphalerons and Electroweak Strings

We show that the sphaleron energy which identifies with the (instanton) potential barrier for B-violation is reduced in the presence (background) of an electroweak Z-string. We also show that for large enough Higgs coupling, $\lambda$, the sphaleron energy can go negative. For such $\lambda$, electroweak Z-strings can reduce their energy by accumulating sphaleron bound states. This further endows them with baryon number. Given our approximation, the value of $\lambda$ at which this occurs is rather large to be realistic for the standard electroweak model.