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The Electric Screening Mass in Scalar Electrodynamics at High Temperature

We study the screening of static electric fields in massless scalar electrodynamics at high temperature and zero chemical potential. Effective field theory methods are used to separate the contributions from the momentum scales T and eT to the electric screening mass. The effects of the distance scale 1/T are encoded in the parameters of an effective three-dimensional field theory. The parameters of the effective Lagrangian can be written as a power series in e^2. The contribution to physical quantities from the scale 1/eT can be calculated from perturbation theory in the effective theory and is an expansion in e starting at e^3. The electric screening mass squared is computed to order e^4