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Low-energy pion–nucleon scattering is relevant for many areas in nuclear and hadronic physics, ranging from the scalar couplings of the nucleon to the long-range part of two-pion-exchange potentials and three-nucleon forces in Chiral Effective Field Theory. In this talk, we show how the fruitful combination of dispersion-theoretical methods, in particular in the form of Roy–Steiner equations, with modern high-precision data on hadronic atoms allows one to determine the pion–nucleon scattering amplitudes at low energies with unprecedented accuracy. Special attention will be paid to the extraction of the pion–nucleon σ-term, and we discuss in detail the current tension with recent lattice results, as well as the determination of the low-energy constants of chiral perturbation theory.c

We present recent results for 4He and 6Li obtained with improved NN interactions derived from chiral effective field theory up to N4LO. The many-body calculations are performed order-by-order in the chiral expansion. At N3LO and N4LO additional renormalization using the Similarity Renormalization Group is adopted to improve numerical convergence of the many-body calculations. We discuss results for the ground state energies, as well as the magnetic moment and the low-lying spectrum of 6Li.

In this talk, we present a coupled system of integral equations for the πN → πN (s-channel) and ππ → N̅N (t-channel) lowest partial waves, derived from Roy–Steiner equations for pion–nucleon scattering. After giving a brief overview of this system of equations, we present the solution of the t-channel sub-problem by means of Muskhelishvili–Omnès techniques, and solve the s-channel sub-problem after finding a set of phase shifts and subthreshold parameters which satisfy the Roy–Steiner equations.

We discuss the role of non-perturbative pion dynamics on the near-threshold resonant X(3872) charmonium state, which is assumed to be an S-wave DD̄* bound system. We calculate the contribution to the width of the X(3872) from the DD̄π intermediate state treated non-perturbatively and compare it with different approximate approaches. Further, we explore the quark-mass dependence of the pole position of the X(3872) state. We find that the trajectory of the X(3872) depends strongly on the assumed quark-mass dependence of the short-range interactions which can be determined in lattice QCD calculations.

We review recent progress on nuclear lattice simulations using chiral effective field theory. We discuss lattice results for dilute neutron matter at next-to-leading order, three-body forces at next-to-next-toleading order, isospin-breaking and Coulomb effects, and the binding energy of light nuclei.

The two- and three-nucleon interaction derived in chiral effective field theory is used to obtain the binding energy of nuclear matter for small densities at next-to-leading (NLO) and next-to-next-to-leading orders (N2LO). The order N2LO is not yet sufficient to push the range of validity of the expansion beyond the empirical Fermi momentum of nuclear matter. A phenomenological extension of the interaction suggests that both effective three- and four-nucleon interactions are required for a description of the bulk properties of nuclear mater.

Nuclear forces are considered based on chiral perturbation theory with and without explicit ∆-isobar degrees of freedom. We discuss the subleading corrections to chiral three-nucleon forces in the ∆-less formalism which contain no additional free parameters. In the formalism with explicit ∆-isobar we present the complete next-to-next-to-leading order analysis of isospin-conserving and next-to-leading order analysis of isospinviolating nuclear forces. The perturbative expansion of nuclear forces in the ∆-full case is shown to have much better convergence compared with the ∆-less theory where the ∆-resonance is integrated out and is encoded in certain low-energy constants.

We review on a novel chiral power counting scheme for in-medium chiral perturbation theory with nucleons and pions as degrees of freedom. It allows for a systematic expansion taking into account local as well as pion-mediated inter-nucleon interactions. Based on this power counting, one can identify classes of nonperturbative diagrams that require a resummation. As a method for performing those resummations we review on the techniques of Unitary Chiral Pertubation Theory for nucleon-nucleon interactions. We then apply both power counting and non-perturbative methods to the example of calculating the pion self-energy in asymmetric nuclear matter up-to-and-including next-to-leading order. It is shown that the leading corrections involving in-medium nucleon-nucleon interactions cancel between each other at given chiral orders.

The neutron-proton mass difference in (isospin asymmetric) nuclear matter and finite nuclei is studied in the framework of a medium-modified Skyrme model. The proposed effective Lagrangian incorporates both the medium influence of the surrounding nuclear environment on the single nucleon properties and an explicit isospin-breaking effect in the mesonic sector. Energy-dependent charged and neutral pion optical potentials in the s- and p-wave channels are included as well. The present approach predicts that the neutron-proton mass difference is mainly dictated by its strong part and that it markedly decreases in neutron matter. Furthermore, the possible interplay between the effective nucleon mass in finite nuclei and the Nolen-Schiffer anomaly is discussed. In particular, we find that a correct description of the properties of mirror nuclei leads to a stringent restriction of possible modifications of the nucleon’s effective mass in nuclei.