Renormalization in the Three-Body Sector with Singular Potentials

Despite the success of chiral effective field theory (EFT) in describing the nuclear interaction, there remains a significant debate over the power-counting scheme used to systematize the contributions. One-pion exchange (OPE) is part of the leading-order chiral EFT nucleon-nucleon potential, so we study the case of the attractive, inverse-cube potential, whose wave functions should have the same short-distance behavior. In principle, the renormalization at large cutoffs of two- and three-body observables found with this potential should mimic the cutoff dependence of those same observables calculated with OPE. I will present results that demonstrate the sufficiency of a two-body contact term to renormalize three-body binding energies and scattering observables. I will also discuss a rigorous analysis of the higher-order corrections that finds two-body corrections subleading to three-body corrections, suggesting that a three-body counterterm may be required at next-to-leading order.