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.
Charge-Independence Breaking in the Two-Pion-Exchange Nucleon-Nucleon Force
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abstract
Charge-independence breaking due to the pion-mass difference in the (chiral) two-pion-exchange nucleon-nucleon force is investigated. A general argument based on symmetries is presented that relates the charge-symmetric part of that force to the proton-proton case. The static potential linear in that mass difference is worked out as an explicit example by means of Feynman diagrams, and this confirms the general argument.
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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.