Precision determination of pion-nucleon coupling constants using effective field theory

The pion-nucleon ($\pi$N) coupling constants determine the strength of the long-range nuclear forces and play a fundamental part in our understanding of nuclear physics. While the charged- and neutral-pion couplings to protons and neutrons are expected to be very similar, owing to the approximate isospin symmetry of the strong interaction, the different masses of the up- and down-quarks and electromagnetic effects may result in their slightly different values. Despite previous attempts to extract the $\pi$N coupling constants from pion-nucleon scattering data, experimental data on pionic atoms as well as proton-antiproton and nucleon-nucleon scattering data, our knowledge of their values is still deficient, and their first-principles determination from lattice quantum-chromodynamics and quantum-electrodynamics calculations has so far been impractical. Here we use chiral effective field theory to describe the low-energy interactions of pions, protons, neutrons and photons and to determine the $\pi$N coupling constants from a combined Bayesian analysis of neutron-proton and proton-proton scattering data at the per-cent level with fully controlled uncertainties. Our results are consistent with no significant charge dependence of the coupling constants. These findings increase our understanding of low-energy nuclear physics and mark an important step towards developing a precision theory of nuclear forces and structure.