Ultrasoft Fermionic Mode in Yukawa Theory at High Temperature

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.