Three pion nucleon coupling constants

TL;DR

This paper investigates the small differences among four pion-nucleon coupling constants, providing a rationale and precise determination based on a comprehensive analysis of nucleon-nucleon scattering data from 1950-2013.

Contribution

It offers a new, consistent determination of the four pion-nucleon coupling constants using a large, self-consistent nucleon-nucleon scattering database and discusses their expected small differences.

Findings

Determined coupling constants: f_p^2=0.0759(4), f_0^2=0.079(1), f_c^2=0.0763(6).

Analysis based on 6713 data points from 1950-2013.

Provides rationale for small differences among the coupling constants.

Abstract

There exist four pion nucleon coupling constants, $f_{\pi^0, pp}$, $-f_{\pi^0, nn}$, $f_{\pi^+, pn} /\sqrt{2}$ and $ f_{\pi^-, 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 $3\sigma$ self-consistent nucleon-nucleon Granada-2013 database comprising 6713 published data in the period 1950-2013.