We derive the sub-subleading two-pion exchange contributions to the three-nucleon force which appear at next-to-next-to-next-to-next-to-leading order in chiral effective field theory. In order to determine the low-energy constants, a complete analysis of pion-nucleon scattering at the subleading-loop order in the heavy-baryon expansion is carried out utilizing the power counting scheme employed in the derivation of the nuclear forces. We discuss the convergence of the chiral expansion for this particular three-nucleon force topology and give the values of the low-energy constants which provide the most realistic description of the three-nucleon force when the chiral expansion is truncated at next-to-next-to-leading order.

The N interaction is studied within a meson-exchange model and in a coupled-channels approach which includes the channels N, N, as well as three effective N channels, namely, N, ⌬, and N. Starting out from an earlier model of the Jülich group systematic improvements in the dynamics and in some technical aspects are introduced. With the new model an excellent quantitative reproduction of the N phase shifts and inelasticity parameters in the energy region up to 1.9 GeV and for total angular momenta Jഛ3/2 is achieved. Simultaneously, good agreement with data for the total and differential N→N transition cross sections is obtained. The connection of the N dynamics in the S 11 partial wave with the reaction N→N is discussed.

A dispersion integral is derived that allows one to relate directly (spin dependent) ΛN invariant mass spectra, measured in a large-momentum transfer reaction such as pp → K + pΛ or γd → K + nΛ, to the scattering length for elastic ΛN scattering. The involved systematic uncertainties are estimated to be smaller than 0.3 fm. This estimate is confirmed by comparing results of the proposed formalism with those of microscopic model calculations. We also show, for the specific reaction pp → K + Λp, how polarization observables can be used to separate the two spin states of the ΛN system.

Nucleon-nucleon scattering in the 1 S 0 partial wave is considered in chiral effective field theory within the renormalizable formulation of Ref.[1] beyond the leading-order approximation. By applying subtractive renormalization, the subleading contact interaction in this channel is taken into account non-perturbatively. For a proper choice of renormalization conditions, the predicted energy dependence of the phase shift and the coefficients in the effective range expansion are found to be in a good agreement with the results of the Nijmegen partial wave analysis.

We present and apply a novel scheme for studying photon-and pion-nucleon scattering beyond the threshold region. Partial-wave amplitudes for the γ N and π N states are obtained by an analytic extrapolation of subthreshold reaction amplitudes computed in chiral perturbation theory, where the constraints set by electromagneticgauge invariance, causality and unitarity are used to stabilize the extrapolation. Based on the chiral Lagrangian we recover the empirical s-and p-wave amplitudes up to energies √ s 1300 MeV in terms of the parameters relevant at order Q 3 .

We derive the subleading contributions to the two-pion-one-pion exchange and ring three-nucleon force topologies emerging at next-to-next-to-next-to-next-to-leading order in chiral effective field theory. The resulting expressions do not involve any unknown parameters. To study convergence of the chiral expansion we work out the most general operator structure of a local isospin-invariant three-nucleon force. Using the resulting operator basis with 22 independent structures, we compare the strength of the corresponding potentials in configuration space for individual topologies at various orders in the chiral expansion. As expected, the subleading contributions from the two-pionone-pion-exchange and ring diagrams are large which can be understood in terms of intermediate excitation of the ∆(1232) isobar.

We present the results of a third order calculation of the pion-nucleon scattering amplitude in a chiral effective field theory with pions, nucleons and delta resonances as explicit degrees of freedom. We work in a manifestly Lorentz invariant formulation of baryon chiral perturbation theory using dimensional regularization and the extended on-mass-shell renormalization scheme. In the delta resonance sector, the on mass-shell renormalization is realized as a complex-mass scheme. By fitting the low-energy constants of the effective Lagrangian to the S-and P -partial waves a satisfactory description of the phase shifts from the analysis of the Roy-Steiner equations is obtained. We predict the phase shifts for the D and F waves and compare them with the results of the analysis of the George Washington University group. The threshold parameters are calculated both in the delta-less and delta-full cases. Based on the determined low-energy constants, we discuss the pion-nucleon sigma term. Additionally, in order to determine the strangeness content of the nucleon, we calculate the octet baryon masses in the presence of decuplet resonances up to next-to-next-to-leading order in SU(3) baryon chiral perturbation theory. The octet baryon sigma terms are predicted as a byproduct of this calculation.

Elastic pion-nucleon scattering is analyzed in the framework of chiral perturbation theory up to fourth order within the heavy-baryon expansion and a covariant approach based on an extended on-mass-shell renormalization scheme. We discuss in detail the renormalization of the various low-energy constants and provide explicit expressions for the relevant β-functions and the finite subtractions of the power-counting breaking terms within the covariant formulation. To estimate the theoretical uncertainty from the truncation of the chiral expansion, we employ an approach which has been successfully applied in the most recent analysis of the nuclear forces. This allows us to reliably extract the relevant low-energy constants from the available scattering data at low energy. The obtained results provide a clear evidence that the breakdown scale of the chiral expansion for this reaction is related to the ∆-resonance. The explicit inclusion of the leading contributions of the ∆-isobar is demonstrated to substantially increase the range of applicability of the effective field theory. The resulting predictions for the phase shifts are in an excellent agreement with the ones from the recent Roy-Steiner-equation analysis of pion-nucleon scattering. * dmitrij.siemens@rub.de †