The leading three-pion exchange nucleon-nucleon potential is scheme dependent, and this paper provides the version consistent with the method of unitary transformation, which differs from Kaiser's S-matrix results for three classes of diagrams.
Three-pion exchange: a gap in the nucleon-nucleon potential
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abstract
The leading contribution to the three-pion exchange nucleon-nucleon potential is calculated in the framework of chiral symmetry. It has pseudoscalar and axial components and is dominated by the former, which has a range of about 1.5 fm and tends to enhance the OPEP. The strength of this force does not depend on the pion mass and hence it survives in the chiral limit.
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Chiral $3\pi$-exchange potential using the method of unitary transformation
The leading three-pion exchange nucleon-nucleon potential is scheme dependent, and this paper provides the version consistent with the method of unitary transformation, which differs from Kaiser's S-matrix results for three classes of diagrams.