  We present results on the mass of the nucleon and the Delta using two
dynamical degenerate twisted mass quarks and the tree-level Symanzik improved
gauge action. The evaluation is performed at four quark masses corresponding to
a pion mass in the range of about 300-600 MeV on lattices of 2.1-2.7 fm. We
check for cut-off effects by evaluating these baryon masses on lattices of
spatial size 2.1 fm at beta=3.9 and beta=4.05 and on a lattice of 2.4 fm at
beta=3.8. The values we find are compatible within our statistical errors.
Lattice results are extrapolated to the physical limit using continuum chiral
perturbation theory. Performing a combined fit to our lattice data at beta=3.9
and beta=4.05 we find a nucleon mass of 964\pm 28 (stat.) \pm 8 (syst.) MeV.
The nucleon mass at the physical point provides an independent determination of
the lattice spacing. Using heavy baryon chiral perturbation theory at O(p^3) we
find a_{\beta=3.9}=0.0890\pm 0.0039(stat.) \pm 0.0014(syst.) fm, and
a_{\beta=4.05}= 0.0691\pm 0.0034(stat.) \pm 0.0010(syst.) fm, in good agreement
with the values determined from the pion decay constant. Isospin violating
lattice artifacts in the Delta-system are found to be compatible with zero for
the values of the lattice spacings used in this work. Performing a combined fit
to our lattice data at beta=3.9 and beta=4.05 we find for the masses of the
Delta^{++,-} and Delta^{+,0} 1316 \pm 60 (stat.) MeV and 1330 \pm 74 (stat.)
MeV respectively. We confirm that in the continuum limit they are also
degenerate.
