Stability of Z strings in strong magnetic fields

Abstract

We show that the Z-strings of the standard electroweak theory can be stabilized by strong external magnetic fields, provided that $\beta^{1/2} \equiv M_H/M_Z\leq 1$, where $M_H$ and $M_Z$ are the Higgs and Z masses. The magnetic fields needed are larger than $\beta^{1/2} B_c$ and smaller than $B_c$, where $B_c\equiv M^2_W/e$ is the critical magnetic field which causes W-condensation in the usual broken phase vacuum. If such magnetic fields were present after the electroweak transition, they would stabilize strings for a period comparable to the inverse Hubble rate at that time. Pair creation of monopoles and antimonopoles linked by segments of string is briefly considered.