The Nucleon-Nucleon Interaction in a Chiral Effective Field Theory

4 1. Introduction
the Thcson-Melbourne 3NF does not lead to a significant improvement. This problem still remains
unsolved [196].
In spite of a very successful description of most of the experimental data the modern realistic
N N potentials are quite phenomenological approaches. For instance, one of the basic ingredients
of these models is a fictitious (J' (550 MeV) boson, which is needed to produce the rather strong
attraction in the central part of the potential. This attraction is evident from the N N scattering
data, see also discussion in ref. [48]. Such a (J'-meson, however, has never been observed experimentally.
For a recent discussion about the experimental evidence of the (J'-meson see ref. [49].
Another common feature of the boson-exchange models is the ad hoc introduction of the strong
form-factors4 at each meson-nucleon vertex in order to correct the large momentum behavior of
the potential and to allow for practical calculations. Such form-factors are usually interpreted
in terms of higher-order (in a coupling constant) meson-nucleon and meson-meson interactions,
dressing each vertex. Because of the non-perturbative nature of such interactions one is not able to
directly calculate these form-factors and approximates them typically by some smooth functions
of momenta. Only in the case of the so-called Ruhr-potential (RuhrPot) [50] the form-factors
are generated dynamically by solving the corresponding integral equations. Another interesting
feature of this potential is its manifest energy independence resulting from the method of unitary
transformation [51], [53] which has been used to define the nuclear force. On the contrary, the
standard approach based on the time-ordered perturbation theory leads necessarily to an effective
Hamiltonian which depends on the initial energy of the nucleons (i.e. to an operator which
depends explicitly on its own eigenvalue). Such an energy dependence of the nuclear forces causes
many complications in practical calculations for more than two nucleons. Another problem of the
various meson-exchange potentials is how to systematicaHy improve these models and whether
the one-boson exchange approximation is well justified. Indeed, if one takes the meson-exchange
picture of the nuclear force seriously, one would expect that two- and more-meson exchanges are
also important (because of the strong meson-nucleon coupling). Usually one argues at this point
that the force based on the two- and more-meson exchanges are, in general, of shorter range than
the one-meson exchange force and thus are less relevant for the energy region of nuclear physics
(with exception of pion-exchange interactions). Although quite plausible, such arguments should
be considered more qualitative than quantitative.
The main conceptual problem of the OBE models, however, can be illustrated in terms of the
following "classical" picture [54]: ass urne that hadrons are hard spheres. The charge radius of the
proton is .J(rI) rv 0.6 fm, while the typical size of light mesons is about 0.5 fm. Then mesons
can not mediate the nuclear force at distances below rv 2 x 0.6 fm + 2 x 0.5 fm = 2.2 fm. Even if
this picture is very much simplified and does not take into account quantum mechanical effects,
it becomes clear that the traditional meson-exchange picture should not be adequate to describe
the nuclear matter phenomena at distances below 2 fm.
One hopes that quantum chromodynamics (QCD), the fundamental theory of the strong interaction,
can help to avoid these problems of the OBE models and provide us with a deeper understanding
of the nature of the nuclear forces. QCD is a SU(3)color gauge theory of the strong
interaction, formulated in terms of quarks and gluons. The structure of nucleons as weH as interactions
between them are, in principle, completely determined by QCD. Direct calculations of the
nuclear force from QCD are not possible up to now. This is because at low energies the interaction
is too strong to apply the usual perturbative methods. However, many attempts were made
to incorporate more information from QCD in models of the N N interactions. In the so-called
4 Such form-factors are anyway not well-defined in quantum field theory.