Energy barrier in the two-Higgs model

The electroweak model is extended by a second Higgs doublet and a numerical investigation of static, finite energy classical solutions is performed. The results indicate that for a large domain of the parameters of the Higgs potential, the energy barrier between topologically distinct vacua of the Lagrangian is constituted by a bisphaleron.Comment: 19 pages, including 4 eps figures, LaTex format, new results include

On Axially Symmetric Solutions in the Electroweak Theory

We present the general ansatz, the energy density and the Chern-Simons charge for static axially symmetric configurations in the bosonic sector of the electroweak theory. Containing the sphaleron, the multisphalerons and the sphaleron-antisphaleron pair at finite mixing angle, the ansatz further allows the construction of the sphaleron and multisphaleron barriers and of the bisphalerons at finite mixing angle. We conjecture that further solutions exist.Comment: 17 pages, latex, THU-94/0

Sphalerons with CP-Violating Higgs Potentials

We investigate the effect on the sphaleron in the two Higgs doublet electroweak theory of including CP violation in the Higgs potential. To have better control over the relation between the sphaleron energy and the physical quantities in the theory, we show how to parametrize the Higgs potential in terms of physical masses and mixing angles, one of which causes CP violation. By altering this CP violating angle (and keeping the other physical quantities fixed) the sphaleron energy increases by up to 10%. We also calculate the static minimum energy path between adjacent vacua as a function of Chern-Simons number, using the method of gradient flow. The only effect CP violation has on the barrier is the change in height. As a by-product of our work on parametrization of the potential, we demonstrate that CP violation in the Higgs sector favours nearly degenerate light Higgs masses.Comment: 13pp LaTeX2e, 2 eps figs, uses graphicx, a

Yang--Mills sphalerons in all even spacetime dimensions d=2kd=2k, k>2k>2 : kk=3,4

The classical solutions to higher dimensional Yang--Mills (YM) systems, which are integral parts of higher dimensional Einstein--YM (EYM) systems, are studied. These are the gravity decoupling limits of the fully gravitating EYM solutions. In odd spacetime dimensions, depending on the choice of gauge group, these are either topologically stable or unstable. Both cases are analysed, the latter numerically only. In even spacetime dimensions they are always unstable, describing saddle points of the energy, and can be described as {\it sphalerons}. This instability is analysed by constructing the noncontractible loops and calculating the Chern--Simons (CS) charges, and also perturbatively by numerically constructing the negative modes. This study is restricted to the simplest YM system in spacetime dimensions $d=6,7,8$, which is amply illustrative of the generic case.Comment: 16 pages, 3 figures ; comments added, to appear in J. Phys.