The Nucleon-Nucleon Interaction in a Chiral Effective Field Theory

might be responsible for solving the Ay problem in the elastic nd scattering at low energies. For
more discussion on that see ref. [196J.
We also point out that problems related to renormalization of the effective Hamiltonian after
eliminating the pionic degrees of freedom have to be investigated more carefully than it has been
done in sec. 3.8.2. In particular, one should include also the zero- and one-body operators in order
to perform a complete renormalization at NLO and NNLO. Furthermore, it would be interesting
to study the problem of carrying out the renormalization at an arbitrary order in the moment um
expansion. As far as we know, the problem of renormalization within the Hamiltonian approach
has never been worked out in detail (also in the context of an effective field theory).
Last not least we have shown that isospin violation can be systematically included in the effective
field theory approach to the two-nucleon system in the KSW formulation. For that, one has to
construct the most general isospin violating effective Lagrangian and extend the power counting
sehe me accordingly. We have shown that this framework allows one to syste�atically classify
the various contributions to charge indepedence and charge symmetry breaking (CIB and CSB).
In particular, the power counting combined with dimensional analysis allows one to understand
the suppression of contributions from a possible charge-dependence in the pion-nucleon coupling
constants. It would be interesting to extend this formalism to other partial waves and to higher
energies so as to investigate e.g. isospin violation in pion production.
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