The Nucleon-Nucleon Interaction in a Chiral Effective Field Theory

8 1. Introduction
completely dominated by pion exchanges. That is why parameter-free predictions are possible,
since the 7r N low-energy coupling constants are known from pion-nucleon scattering processes.
Furt her , the interaction in these channels is much weaker than in the S- and P-waves. That
opens the possibility to use standard perturbation theory. Kaiser et al. have used the technique
of Feynman diagrams to define the two-nucleon T-matrix. They obtained renormalized expressions
for leading and subleading two-pion exchanges. It was found that the model-independent
27r-exchange corrections are too large for the D- and F-waves. This indicates the increasing
importance of shorter range effects in these channels. For G- and higher waves the 27r-exchange
corrections bring the chiral predictions close to empirical phase shifts. In a following publication
[109J also some two-loop diagrams were considered as weIl as the contributions from virtual
�-excitations and from exchange of vector p and w exchange. These corrections improved the
predictions for the F-waves and for the D-waves below 50-80 MeV laboratory energy. Quite
recently also so me classes of the two-loop diagrams have been ca1culated by Kaiser [110], [111].
Similar investigations for some peripheral partial waves but using a different technique were performed
by the Brazilian group [112]. Recently they also analyzed some three-pion exchange
contributions [113] and found quite surprisingly that they have a long range of about 1.5 fm and
tend to enhance the OPEP.
Instead of trying to describe many-body processes completely in terms of effective field theory
Weinberg proposed in 1992 to apply chiral perturbation theory to generate the irreducible kernel
and combine these with phenomenological external nuclear wave functions [114]. These ideas were
adopted by Beane et al. to ca1culate neutral pion photoproduction on deuterium [115]. The results
agree weIl with experiment and allowed for a first quite successful prediction from CHPT in the
two-nucleon sector . A similar formalism was applied recently to study Compton scattering on the
deuteron [116] and neutral pion electroproduction off deuterium [117].
Also many-body interactions became a subject of intense investigations in the context of effective
theories. While Friar et al. [118] tried to constrain the possible form of the three-nucleon force from
chiral symmetry, a different strategy has been chosen by Bedaque and collaborators. Motivated
by the successful application of the KSW approach to two-nucleon problems, they considered the
three-body system at very low energies with pions integrated out [119], [120], [121]. BasicaIly,
they found a good agreement with experiment in the J = 3/2 channel without having any free
parameter. Here, the three-body force does not play any significant rule since, due to the Pauli
principle, particles can not be very close to each other. The situation is different in the J = 1/2
channel. Here it was shown that a three-body short-range force is required in order to eliminate
the cut-off dependence of the amplitude. Recently the quartet S-wave phase shift in nd scattering
was ca1culated including perturbative pions [122].
The purpose of this thesis is to investigate in detail the two-nucleon system within a cut-off
effective theory. The pioneering ca1culations along this line performed by Ord6iiez et al. [78]
leave much room for improvements. First, as already stressed before, some of the parameters
corresponding to the contact interactions in this work are redundant. As we will show later, one
can eliminate them due to anti-symmetrization of the potential. Secondly, we will use the values of
the 7r N low-energy constants consistent with CHPT ca1culations in the one nucleon sector instead
of determining them from the fitting to the N N data. Thus, the number of free parameters in
calculations to the same order in the low-momentum expansion decreases dramatically from 26
as it was the case in ref. [78] to 9 in the present work. We hope that this will allow to make
clearer statements about the role of chiral symmetry in the N N dynamies. Thirdly, we will use
a different formalism for deriving the NN interaction, which leads to an energy-independent