Ultrasoft Fermionic Mode in Yukawa Theory at High Temperature

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Abstract

We explore whether an ultrasoft fermionic mode exists at extremely high temperature in Yukawa theory with massless fermion (coupling constant is g). We find that the fermion propagator has a pole at \omega = \pm p/3-i\zeta, for ultrasoft momentum p, where \zeta \sim g^4T ln 1/g, and the residue is Z \sim g^2. It is shown that one needs to take into account the asymptotic masses and the damping rate of hard particles to get a sensible result for such an ultrasoft fermionic mode; possible vertex correction turns out unnecessary for the scalar coupling in contrast to the gauge coupling.