The recoil retardation effect in the $K^-d$ scattering length is studied. Using the non-relativistic effective field theory approach, it is demonstrated that a systematic perturbative expansion of the recoil corrections in the parameter $xi=M_K/m_N$
is possible in spite of the fact that $K^-d$ scattering at low energies is inherently non-perturbative due to the large values of the $bar KN$ scattering lengths. The first order correction to the $K^-d$ scattering length due to single insertion of the retardation term in the multiple-scattering series is calculated. The recoil effect turns out to be reasonably small even at the physical value of $M_K/m_Nsimeq 0.5$.
In this review we present the recent advances for calculations of the reactions $NNto NNpi$ using chiral effective field theory. Discussed are the next-to-next-to leading order loop contributions with nucleon and Delta-isobar for near threshold s-wav
e pion production. Results of recent experimental pion-production data for energies close to the threshold are analyzed. Several particular applications are discussed: (i) it is shown how the measured charge symmetry violating pion-production reaction can be used to extract the strong-interaction contribution to the proton-neutron mass difference; (ii) the role of $NNto NNpi$ for the extraction of the pion-nucleon scattering lengths from pionic atoms data is illuminated.
In recent years, high-accuracy data for pionic hydrogen and deuterium have become the primary source of information on the pion-nucleon scattering lengths. Matching the experimental precision requires, in particular, the study of isospin-breaking cor
rections both in pion-nucleon and pion-deuteron scattering. We review the mechanisms that lead to the cancellation of potentially enhanced virtual-photon corrections in the pion-deuteron system, and discuss the subtleties regarding the definition of the pion-nucleon scattering lengths in the presence of electromagnetic interactions by comparing to nucleon-nucleon scattering. Based on the pi^{+/-} p channels we find for the virtual-photon-subtracted scattering lengths in the isospin basis a^{1/2}=(170.5 +/- 2.0) x 10^{-3} mpi^{-1} and a^{3/2}=(-86.5 +/- 1.8) x 10^{-3} mpi^{-1}.
We investigate the reaction pn -> dpipi in the framework of Chiral Perturbation Theory. For the first time a complete calculation of the leading order contributions is presented. We identify various diagrams that are of equal importance as compared t
o those recognized in earlier works. The diagrams at leading order behave as expected by the power counting. Also for the first time the nucleon-nucleon interaction in the initial, intermediate and final state is included consistently and found to be very important. This study provides a theoretical basis for a controlled evaluation of the non-resonant contributions in two-pion production reactions in nucleon-nucleon collisions.
We report about the recent results for s- and p-wave pion production in NN -> NNpi within effective field theory and discuss how the charge symmetry breaking in pn -> d pi^0 can be used to extract the strong contribution to the neutron-proton mass difference.
