  The scaling limit of the less than half filled attractive Hubbard chain is
studied. This is a continuum limit in which the particle number per lattice
site, n, is kept finite (0<n<1) while adjusting the interaction and bandwidth
in a such way that there is a finite mass gap. We construct this limit both for
the spectrum and the secular equations describing the excitations. We find,
that similarly to the half filled case, the limiting model has a massive and a
massless sector. The structure of the massive sector is closely analogous to
that of the half filled band and consequently to the chiral invariant SU(2)
Gross-Neveu (CGN) model. The structure of the massless sector differs from that
of the half filled band case: the excitations are of particle and hole type,
however they are not uniquely defined. The energy and the momentum of this
sector exhibits a tower structure corresponding to a conformal field theory
with c=1 and SU(2)xSU(2) symmetry. The energy-momentum spectrum and the zero
temperature free energy of the states with finite density coincides with that
of the half filled case supporting the identification of the limiting model
with the SU(2) symmetric CGN theory.
