  The masses of the low lying baryons are evaluated using two degenerate
flavors of twisted mass sea quarks corresponding to pseudo scalar masses in the
range of about 270-500 MeV. The strange valence quark mass is tuned to
reproduce the mass of the kaon in the physical limit. The tree-level Symanzik
improved gauge action is employed. We use lattices of spatial size 2.1 fm and
2.7 fm at two values of the lattice spacing with $r_0/a=5.22(2)$ and
$r_0/a=6.61(3)$. We check for both finite volume and cut-off effects on the
baryon masses. We performed a detailed study of the chiral extrapolation of the
octet and decuplet masses using SU(2) $\chi$PT. The lattice spacings determined
using the nucleon mass at the physical point are consistent with the values
extracted using the pion decay constant. We examine the issue of isospin
symmetry breaking for the octet and decuplet baryons and its dependence on the
lattice spacing. We show that in the continuum limit isospin breaking is
consistent with zero, as expected. The baryon masses that we find after taking
the continuum limit and extrapolating to the physical limit are in good
agreement with experiment.
