Few-Nucleon Systems in Chiral Effective Field Theory

Differential cross section for elastic nucleon - deuteron scattering at 10 MeV

Determining the nature of the interaction between nucleons is crucial for understanding nuclear reactions and the properties of nuclei. According to quantum chromodynamics (QCD), the nuclear force is a residual color force between the color-charge neutral hadrons. A direct derivation of the nuclear force from QCD is not yet possible due to its nonperturbative nature in the low-energy regime. Chiral effective field theory (EFT) provides a systematic and model-independent framework to study the properties of hadronic systems. It relies on the chiral symmetry of QCD that governs low-energy hadron dynamics. In the Goldstone boson and single-baryon sectors, this method allows the determination of the scattering amplitude based on the perturbative expansion in powers of the low external momenta and about the chiral limit, the so-called chiral expansion. As shown by Weinberg in the early 1990s, it can also be applied to derive nuclear forces and current operators which may then be used as input in few- and many-body calculations.

In the past few years, the two-nucleon system has been studied extensively in the framework of chiral EFT. The most advanced analyses at next-to-next-to-next-to-leading order (N³LO) in the chiral expansion demonstrate the ability of the novel chiral forces to provide an accurate description of the data in the low-energy region. The first promising results have also been obtained for three- and more-nucleon systems. The calculations up to next-to-leading order (NLO) are based entirely on the two-nucleon force and, therefore, yield parameter-free results in the case of three and more nucleons. The chiral three-nucleon force first needs to be accounted for at NNLO and depends on two unknown low-energy constants. Having fixed these two parameters from the triton binding energy and the doublet neutron-deuteron scattering length, we applied the resulting parameter-free 3N Hamiltonian to systems with up to 6 nucleons. As a typical example, the figure shows the results for the differential cross section for elastic nucleon-deuteron scattering at E_nucl = 10MeV at NLO and NNLO in comparison with the data. The uncertainty estimate is based on the cutoff variation. Further results and applications can be found in a recent review article.

References:
D. R. Entem, R. Machleidt, Phys. Rev. C68 (2003) 041001
E. Epelbaum, W. Glockle, U.-G. Meissner, Nucl. Phys. A747 (2005) 362
E. Epelbaum, nucl-th/0511025