Samuel W. MacDowell | Searcharxiv

arXiv1995

INSTABILITY OF A NIELSEN-OLESEN VORTEX EMBEDDED IN THE ELECTROWEAK THEORY: II. ELECTROWEAK VORTICES AND GAUGE EQUIVALENCE

Vortex configurations in the electroweak gauge theory are investigated. Two gauge-inequivalent solutions of the field equations, the Z and W vortices, have previously been found. They correspond to embeddings of the abelian Nielsen-Olesen vortex solution into a U(1) subgroup of SU(2)xU(1). It is shown here that any electroweak vortex solution can be mapped into a solution of the same energy with a vanishing upper component of the Higgs field. The correspondence is a gauge equivalence for all vortex solutions except those for which the winding numbers of the upper and lower Higgs components add to zero. This class of solutions, which includes the W vortex, instead corresponds to a singular solution in the one-component gauge. The results, combined with numerical investigations, provide an argument against the existence of other vortex solutions in the gauge-Higgs sector of the Standard Model.

hep-ph↗

arXiv1994

Instability of a Nielsen-Olesen Vortex Embedded in the Electroweak Theory: I. the Single-Component Higgs Gauge

The stability of an abelian (Nielsen-Olesen) vortex embedded in the electroweak theory against W production is investigated in a gauge defined by the condition of a single-component Higgs field. The model is characterized by the parameters $β=({M_H\over M_Z})^2$ and $γ=\cos^2θ_{\rm w}$ where $θ_{\rm w}$ is the weak mixing angle. It is shown that the equations for W's in the background of the Nielsen-Olesen vortex have no solutions in the linear approximation. A necessary condition for the nonlinear equations to have a solution in the region of parameter space where the abelian vortex is classically unstable is that the W's be produced in a state of angular momentum $m$ such that $0>m>-2n$. The integer $n$ is defined by the phase of the Higgs field, $\exp(inφ)$. Solutions for a set of values of the parameters $β$ and $γ$ in this region were obtained numerically for the case $-m=n=1$. The possibility of existence of a stationary state for $n=1$ with W's in the state $m=-1$ was investigated. The boundary conditions for the Euler-Lagrange equations required to make the energy finite cannot be satisfied at $r=0$. For these values of $n$ and $m$ the possibility of a finite-energy stationary state defined in terms of distributions is discussed.

hep-ph↗