| The idea of effective field theory (EFT) was developed decades ago in low-energy strong-interaction---hadronic and nuclear---physics. After introducing chiral perturbation theory (ChPT), we focus in this thesis on three non-perturbative cases that standard ChPT cannot deal with by itself.;First, we investigate pion-nucleon (piN) scattering around the delta resonance, which is an important non-perturbative feature of low-energy nuclear physics. We show that in order to describe pi N scattering around the delta peak, a power counting is necessary that goes beyond the power counting of ChPT. Using this new power counting, we calculate the phase shifts in the spin-3/2 P-wave channel up to next-to-next-to-leading order (NNLO).;Second, in order to clarify the issue of renormalization and power counting of nucleon-nucleon potentials, we use a toy model to illustrate how to build effective theories for singular potentials, which some nuclear potentials belong to. We consider a central attractive 1/r2 potential perturbed by a 1/r4 correction. We show that leading-order counterterms are needed in all partial waves where the potential overcomes the centrifugal barrier, and that the additional counterterms at next-to-leading order are the ones expected on the basis of dimensional analysis.;Finally, we illustrate how non-perturbative EFT can be used to study neutron-antineutron oscillation inside the deuteron. We build an EFT for a model-independent, systematic study of two-unit baryon-number (|Delta B|=2) violation in the context of nuclear physics. To cope with the non-perturbative deuteron structure, we apply the pionless version of this EFT to calculate deuteron decay. The decay width is obtained up to next-to-leading order. We show that the contribution of direct two-nucleon annihilation to the deuteron decay appears only at NNLO. |
