  We analyze the influence of quantum critical fluctuations on single-particle
excitations at the onset of incommensurate $2k_F$ charge or spin density wave
order in two-dimensional metals. The case of a single pair of hot spots at high
symmetry positions on the Fermi surface needs to be distinguished from the case
of two hot spot pairs. We compute the fluctuation propagator and the electronic
self-energy perturbatively in leading order. The energy dependence of the
single-particle decay rate at the hot spots obeys non-Fermi liquid power laws,
with an exponent 2/3 in the case of a single hot spot pair, and exponent one
for two hot spot pairs. The prefactors of the linear behavior obtained in the
latter case are not particle-hole symmetric.
