Asymptotic thermal quark masses and the entropy of QCD in the large-N_f limit

We study the thermodynamics of QCD in the limit of large flavor number (N_f) and test the proposal to resum the physics of hard thermal loops (HTL) through a nonperturbative expression for the entropy obtained from a Φ-derivable two-loop approximation. The fermionic contribution to the entropy involves a full next-to-leading order evaluation of the asymptotic thermal quark mass, which is nonlocal, and for which only a weighted average value was known previously. For a natural choice of renormalization scale we find remarkably good agreement of the next-to-leading order HTL results for the fermion self-energy and in turn for the entropy with the respective exact large-N_f results, even at very large coupling.