Three pion nucleon coupling constants

There exist four pion nucleon coupling constants, $f_{π^0, pp}$, $-f_{π^0, nn}$, $f_{π^+, pn} /\sqrt{2}$ and $f_{π^-, np} /\sqrt{2}$ which coincide when up and down quark masses are identical and the electron charge is zero. While there is no reason why the pion-nucleon-nucleon coupling constants should be identical in the real world, one expects that the small differences might be pinned down from a sufficiently large number of independent and mutually consistent data. Our discussion provides a rationale for our recent determination $f_p^2 = 0.0759(4) \, , \quad f_{0}^2 = 0.079(1) \,, \quad f_{c}^2 = 0.0763(6) \, ,$ based on a partial wave analysis of the $3σ$ self-consistent nucleon-nucleon Granada-2013 database comprising 6713 published data in the period 1950-2013.

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