Chiral Theory Applied to Nucleon-Nucleon Systems
Forschungszentrum Jülich, Institut für Kernphysik
Chiral effective field theory offers a systematic and controlled method
to study the dynamics of few-nucleon systems. In the approach proposed
by Weinberg, one starts from an effective Lagrangian for nucleon and pion
fields as well as external sources, in harmony with chiral and gauge invariance.
Based on a systematic power counting and using the method of unitary transformation
one constructs energy independent and hermitean nucleon-nucleon potential .
To leading order, one has the one-pion exchange together with two four-nucleon
interaction terms accompanied by low-energy constants (LECs). At
next-to-leading order, renormalizations of the OPE, the leading two-pion
exchange diagrams and seven more 4N operators appear. At NNLO, we have in addition
dimension two pion-nucleon operators, whose LECs can in principle be determined from the
chiral analysis of scattering.
The potential is then used in a properly regularized
Lippmann-Schwinger equation (e.g. by a sharp or exponential
momentum cut-off) to generate the bound and scattering states
as detailed in ref. .
The iteration of the potential leads to a non-perturbative
treatment of the pion exchange which is of major importance to properly describe
the NN tensor force. The nine LECs can be determined from a fit to the
low partial waves.
Most partial waves are well reproduced, with some exceptions in the
D- and F-waves. Various static deuteron properties are mostly well described
without any fine tuning.
In the same framework, one can also include
charge symmetry breaking and charge dependence of the nuclear force
by including the light quark
mass difference and elecromagnetic corrections .
Phase shifts for
and scattering can be compared to what is obtained using the Nijmegen,
Argonne or CD-Bonn potentials. Elastic electron-deuteron
scattering has also been investigated to NNLO ,
leading to a good description
of the deuteron form factors and structure function up to photon virtualities
of 0.2 GeV.
The extension to three- and
four-nucleon systems has also been started, see [5,6].
In addition, we have shown, that the
numerical values of the LECs corresponding to the four-nucleon contact operators
can be understood on the basis of phenomenological
one-boson-exchange models .
We also extract these values from various modern
high accuracy nucleon-nucleon potentials and demonstrate their consistency and
remarkable agreement with the values in the chiral effective field theory approach.
This paves the way for estimating the low-energy constants of operators with
more nucleon fields and/or external probes. Furthermore, it can be demonstrated
that the highly singular chiral EFT potential exhibits a so-called limit
cycle behaviour in the limit of letting the cut-off go to infinity .
This allows to perform exact (cut-off independent) renormalization.
A further outlook
and discussion of outstanding problems will also ge given.
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 E. Epelbaum, W. Glöckle and Ulf-G. Meißner, Nucl. Phys.
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 M. Walzl, Ulf-G. Meißner and E. Epelbaum, Nucl. Phys. A (2001)
 M. Walzl and Ulf-G. Meißner , Phys. Lett. B (2001)
 E. Epelbaum et al., Phys. Rev. Lett. 86 (2001) 4787.
 E. Epelbaum et al., in preparation.
 E. Epelbaum et al., nucl-th/0106007.
 E. Epelbaum and Ulf-G. Meißner, in preparation.