Non-perturbative methods for NN singular interactions

Abstract

Chiral Effective Field Theory ($\chi$EFT) has been extensively used to study the $NN$ interaction during the last three decades. In Effective Field Theories (EFTs) the renormalization is performed order by order including the necessary counter terms. Due to the strong character of the $NN$ interaction a non-perturbative resummation is needed. In this work we will review some of the methods proposed to completely remove cutoff dependencies. The methods covered are renormalization with boundary conditions, renormalization with one counter term in momentum space (or equivalently substractive renormalization) and the exact $N/D$ method. The equivalence between the methods up to one renormalization condition will be checked showing results in the $NN$ system. The exact $N/D$ method allows to go beyond the others, and using a toy model it is shown how it can renormalize singular repulsive interactions.