Determination of the chiral coupling constants $c_3$ and $c_4$ in new $\mathrm{pp}$ and $\mathrm{np}$ partial-wave analyses

As a first result of two new partial-wave analyses, one of the $\mathrm{pp}$ and another one of the $\mathrm{np}$ scattering data below 500 MeV, we report a study of the long-range chiral two-pion exchange interaction which contains the chiral coupling constants $c_1,$ $c_3,$ and $c_4.$ By using as input a theoretical value for $c_1$ we are able to determine in $\mathrm{pp}$ as well as in $\mathrm{np}$ scattering accurate values for $c_3$ and $c_4.$ The values determined from the $\mathrm{pp}$ data and independently from the $\mathrm{np}$ data are in very good agreement, indicating the correctness of the chiral two-pion exchange interaction. The weighted averages are $c_3=-4.78\left(10\right)/\mathrm{GeV}$ and $c_4=3.96\mathrm{}\left(22\right)/\mathrm{GeV},$ where the errors are statistical. The value of $c_3$ is best determined from the $\mathrm{pp}$ data and that of $c_4$ from the $\mathrm{np}$ data.