Static solutions of SU(2)-Higgs theory

The structure and stability of static spherically symmetric solutions in the SU(2)-Higgs theory are examined using both analytic and numerical methods. Accurate results are presented for the energy and instability growth rates of the "sphaleron" solution as a function of the Higgs-boson mass. The sphaleron is shown to undergo an infinite sequence of bifurcations as the Higgs-boson mass is increased, starting at $M_H=12\mathrm{}{M}_W$. New "deformed sphaleron" solutions emerge from each of these bifurcations. These deformed sphalerons are not charge-conjugation invariant, have non-half-integral winding numbers, and are lower in energy than the original sphaleron. Hence, for sufficiently large Higgs-boson mass, minimal-energy paths connecting inequivalent vacuum states do not pass through the original sphaleron configuration.