  We consider a U(1) gauge theory, minimally coupled to a massless Dirac field,
where a higher-derivative term is added to the pure gauge sector, as in the
Lee-Wick models. We find that this term can trigger chiral symmetry breaking at
low energy in the weak coupling regime. Then, the fermion field acquires a mass
that turns out to be a function of both the energy scale associated to the
higher-derivative term and the gauge coupling. The dependence of the fermion
mass on the gauge coupling is non-perturbative. Extensions to SU(N) gauge
theories and fermion-scalar interactions are also analyzed, as well as to
theories with massive gauge fields. A few implications of these results in the
framework of quark-mass generation are discussed.
