Nuclear Physics & RIKEN Theory Seminar

The systematics and reorganization of the perturbative loop expansion in high
temperature gauge theories is investigated. In addition to infrared divergences in the
bare loop expansion with massless fermions, further evidence for the necessity
of a systematic restructuring of perturbation theory comes from the explicit
gauge parameter dependence of the fermion damping rate at both one and
two-loops. The calculation of the two-loop fermion self-energy in QED
shows that the leading terms in the high temperature expansion arise from
an explicit hard-soft factorization pattern, in which one of the loop integrals
is hard (p ~ T), nested inside a second loop integral which is soft (p ~ eT).
There are no hard-hard contributions to the two-loop self-energy at leading
order at high T. This hard-soft factorization pattern is necessary for
the resummation over multiple loops to coincide with the one-loop self-energy
calculated with HTL dressed propagators and vertices, and to yield the
complete next-to-leading order correction to the self-energy at scales ~eT, which
is both infrared finite and gauge invariant. The gauge invariant effective action
corresponding to this resummation and possible extensions of the resummation
program to softer processes not captured in the HTL approach will also be discussed.