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

TL;DR

This paper precisely determines charge-dependent pion-nucleon-nucleon coupling constants using a comprehensive analysis of scattering data, accounting for charge symmetry breaking and systematic uncertainties, providing refined values with covariance error analysis.

Contribution

The study introduces a detailed covariance error analysis of coupling constants from extensive scattering data, including charge symmetry breaking effects and systematic uncertainties, improving precision over previous estimates.

Findings

Determined $f^2=0.0763(1)$ for the coupling constant.

Found charge-dependent coupling constants with specific values and anti-correlation.

Confirmed the normality of residuals in the fit.

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 $r_c=3 {\rm fm}$ we obtain $f^2=0.0763(1)$. The effects of charge symmetry breaking on the $^3P_0$, $^3P_1$ and $^3P_2$ 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.