Renormalization in various schemes of nucleon-nucleon chiral EFT

Renormalizability of an effective field theory allows one to perform a systematic expansion of the calculated observable quantities in terms of some small parameter in accordance with a certain power counting. We consider chiral effective field theory in application to the nucleon-nucleon interaction at next-to-leading order in the chiral expansion as an example of the renormalizability of a theory with a nonperturbative leading-order interaction. The requirement of the renormalizability imposes nontrivial constraints on a choice of such interaction. Two different approaches are discussed: the finite- and the infinite-cutoff schemes. Another considered example is the quantum mechanical problem of the inverse-square potential, which is often regarded as a toy model for various physical systems.