  In the low-energy region far below the chiral symmetry breaking scale (which
is of the order of 1 GeV) chiral perturbation theory provides a
model-independent approach for quantitative description of nuclear processes.
In the two- and more-nucleon sector perturbation theory is applicable only at
the level of an effective potential which serves as input in the corresponding
dynamical equation. To deal with the resulting many-body problem we put chiral
effective field theory (EFT) on the lattice. Here we present the results of our
lattice EFT study up to next-to-next-to-leading order in the chiral expansion.
Accurate description of two-nucleon phase-shifts and ground state energy ratio
of dilute neutron matter up to corrections of higher orders shows that lattice
EFT is a promising tool for a quantitative description of low-energy few- and
many-body systems.
