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Periodic Euclidean Solutions of SU(2)-Higgs Theory

We examine periodic, spherically symmetric, classical solutions of SU(2)-Higgs theory in four-dimensional Euclidean space. Classical perturbation theory is used to construct periodic time-dependent solutions in the neighborhood of the static sphaleron. The behavior of the action, as a function of period, changes character depending on the value of the Higgs mass. The required pattern of bifurcations of solutions as a function of Higgs mass is examined, and implications for the temperature dependence of the baryon number violation rate in the Standard Model are discussed.