Precise Determination of Charge Dependent Pion-Nucleon-Nucleon Coupling Constants

Abstract

We undertake a covariance error analysis of the pion-nucleon-nucleon coupling constants from the Granada-2013 np and pp database comprising a total of 6720 scattering data below LAB energy of 350 MeV. Assuming a unique pion-nucleon coupling constant in the One Pion Exchange potential above a boundary radius $r_c=3\mathrm{fm}$ we obtain $f^2=0.0763(1)$. The effects of charge symmetry breaking on the ${}^3{P}_0$, ${}^3{P}_1$ and ${}^3{P}_2$ partial waves are analyzed and we find $f_p^2=0.0761(4)$, $f_0^2=0.0790(9)$ and $f_c^2=0.0772(6)$ with a strong anti-correlation between $f_c^2$ and $f_0^2$. We successfully test normality for the residuals of the fit. Potential tails in terms of different boundary radii as well as chiral Two-Pion-Exchange contributions as sources of systematic uncertainty are also investigated.

Comments: 14 pages, 6 figures, 13 tables. Discussion on naturalness, Analysis of systematic errors, Inclusion of Two Pion Exchange and Tables with phases-shifts added