Nuclear forces can be systematically derived using effective chiral Lagrangians consistent with the symmetries of QCD. I review the status of the calculations for two- and three-nucleon forces and their applications in few-nucleon systems. I also address issues like the quark mass dependence of the nuclear forces and resonance saturation for four-nucleon operators.

/pdf/modern-theory-of-nuclear-forces-436h635pm0.pdf

Modern theory of nuclear forces

The hidden-charm pentaquark and tetraquark states

We review the implications of the spontaneous chiral symmetry breaking in QCD for processes involving one, two, or more nucleons.

Chiral dynamics in nucleons and nuclei

We review how nuclear forces emerge from low-energy QCD via chiral effective field theory. The presentation is accessible to the non-specialist. At the same time, we also provide considerable detailed information (mostly in appendices) for the benefit of researchers who wish to start working in this field.

Chiral effective field theory and nuclear forces

Aspects of chiral pion - nucleon physics

The next-to-leading order chiral pion-nucleon Lagrangian contains seven finite low-energy constants. Two can be fixed from the nucleon anomalous magnetic moments and another one from the quark mass contribution to the neutron-proton mass splitting. We find a set of nine observables, which to one loop order do only depend on the remaining four dimension two couplings. These are then determined from a best fit. We also show that their values can be understood in terms of resonance exchange related to $\Delta$ excitation as well as vector and scalar meson exchange. In particular, we discuss the role of the fictitious scalar-isoscalar meson. We also investigate the chiral expansion of the two P-wave scattering volumes $P_1^-$ and $P_2^+$ as well as the isovector S-wave effective range parameter $b^-$. The one-loop calculation is in good agreement with the data. The difference $P_1^- - P_2^+$ signals chiral loop effects in the $\pi N$ P-waves. The calculated D- and F-wave threshold parameters compare well with the empirical values.

Aspects of chiral pion-nucleon physics

Chiral corrections to the S-wave pion-nucleon scattering lengths

We investigate threshold pion photoproduction in the framework of heavy baryon chiral perturbation theory. We give the expansion of the electric dipole amplitude E
 0+ to three orders in μ the ratio of the pion to nucleon mass, and show that it is slowly converging. We argue that this observable is not a good testing ground for the chiral dynamics of QCD. In contrast, we exhibit new and fastly converging low-energy theorems in the P-waves which should be used to constrain the data analysis. We also discuss the importance of polarization observables to accurately pin down certain multipoles and give predictions for the reaction γ
 n → π0
 n.

N. Kaiser

Papers

Chiral dynamics in nucleons and nuclei

Aspects of chiral pion - nucleon physics

Aspects of chiral pion-nucleon physics

Chiral corrections to the S-wave pion-nucleon scattering lengths

Neutral pion photoproduction off nucleons revisited