Screening Masses in SU(N) from Wilson Renormalization Group

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We apply a gauge invariant formulation of Wilson Renormalization Group (RG) to the computation of the Debye and transverse gluon masses in pure gauge SU(N) at high temperature. Following the Hard Thermal Loop effective field theory as a guideline, we develop an approximation scheme to the exact evolution equations. The Debye mass receives sizable corrections compared to the leading order perturbative result, mainly due to the infrared singular behavior in the transverse gluon sector. A non-vanishing mass for the transverse gluons is found, which acts as an infrared regulator though not efficiently enough as to restore the validity of perturbation theory. Indeed, discussing the role of higher dimensional operators, we show that the gauge coupling for the transverse modes typically flows to non-perturbative values unless extremely high temperatures are reached. After comparing our results with recent lattice simulations, we comment on the possibility of using this formulation of the RG as a tool to construct an effective field theory for the non-perturbative, long wavelength, transverse modes.