  We analyze the particle-hole symmetric two-dimensional Hubbard model on a
square lattice starting from weak-to-moderate couplings by means of the
field-theoretical renormalization group (RG) approach up to two-loop order.
This method is essential in order to evaluate the effect of the
momentum-resolved anomalous dimension $\eta(\textbf{p})$ which arises in the
normal phase of this model on the corresponding low-energy single-particle
excitations. As a result, we find important indications pointing to the
existence of a non-Fermi liquid (NFL) regime at temperature $T\to 0$ displaying
a truncated Fermi surface (FS) for a doping range exactly in between the
well-known antiferromagnetic insulating and the $d_{x^2-y^2}$-wave singlet
superconducting phases. This NFL evolves as a function of doping into a
correlated metal with a large FS before the $d_{x^2-y^2}$-wave pairing
susceptibility finally produces the dominant instability in the low-energy
limit.
