  Using the one-loop functional renormalization group technique we evaluate the
self-energy in the weak-coupling regime of the 2D t-t' Hubbard model. At van
Hove (vH) band fillings and at low temperatures the quasiparticle weight along
the Fermi surface (FS) continuously vanishes on approaching the (pi,0) point
where the quasiparticle concept is invalid. Away from vH band fillings the
quasiparticle peak is formed inside an anisotropic pseudogap and the
self-energy has the conventional Fermi-liquid characteristics near the Fermi
level. The spectral weight of the quasiparticle features is reduced on parts of
the FS between the near vicinity of hot spots and the FS points closest to
(pi,0) and (0,pi).
