Abstract
Results of an exploratory study of the antinucleon-nucleon interaction within chiral effective field theory are reported. The antinucleon-nucleon potential is derived up to next-to-next-to-leading order, based on a modified Weinberg power counting, in close analogy to pertinent studies of the nucleon-nucleon interaction. The low-energy constants associated with the arising contact interactions are fixed by a fit to phase shifts and inelasticities provided by a recently published phase-shift analysis of antiproton-proton scattering data. The overall quality of the achieved description of the antinucleon-nucleon amplitudes is comparable to the one found in case of the nucleon-nucleon interaction at the same order. For most S-waves and several P-waves good agreement with the antinucleon-nucleon phase shifts and inelasticities is obtained up to laboratory energies of around 200 MeV.
Highlights
The success of chiral EFT in the N N sector provides a strong motivation to apply the same approach to the N N interaction
The numerical values of the low-energy constants (LECs) are compiled in tables 1 (NLO) and 2 (NNLO) for a selected combination of the cutoffs
In any case one has to keep in mind that, following ref. [36], we use a larger cutoff region at next-to-next-to-leading order (NNLO) than for the next-to-leading order (NLO) case
Summary
The contributions to the N N interaction up to NNLO are described in detail in refs. [18, 35, 36]. The contributions to the N N interaction up to NNLO are described in detail in refs. Where L is the number of loops in the diagram, di is the number of derivatives or pion mass insertions, and ni the number of internal nucleon fields at the vertex i under consideration. The LO potential corresponds to ν = 0 and consists of two four-nucleon contact terms without derivatives and of one-pion exchange. At NLO (ν = 2) seven new contact terms (with two derivatives) arise, together with loop contributions from (irreducible) two-pion exchange. At NNLO (ν = 3) there are additional contributions from two-pion exchange resulting from one insertion of dimension two pionnucleon vertices, see e.g. ref. The structure of the N N interaction is practically identical and, the potential given in refs. For the ease of the reader and for defining our potential uniquely we provide the explicit expressions below
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