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Numerical study of plasmon properties in the SU(2)-Higgs model

Using the (effective) classical approximation, we compute numerically time-dependent correlation functions in the SU(2)-Higgs model around the electroweak phase transition, for $m_H \approx m_W$. The parameters of the classical model have been determined previously by the dimensional reduction relations for time-independent correlators. The $H$ and $W$ correlation functions correspond to gauge invariant fields. They show damped oscillatory behavior from which we extract frequencies $\om$ and damping rates $\gm$. In the Higgs phase the damping rates have roughly the values obtained in analytic calculations in the quantum theory. In the plasma phase (where analytic estimates for gauge invariant fields are not available), the damping rate associated with $H$ is an order of magnitude larger than in the Higgs phase, while the $W$ correlator appears to be overdamped, with a small rate. The frequency $\om_H$ shows a clear dip at the transition. The results are approximately independent of the lattice spacing, but this appears to be compatible with the lattice spacing dependence expected from perturbation theory.