Chiral potential renormalized in harmonic-oscillator space

Abstract

We renormalize the chiral effective field theory potential in harmonic-oscillator (HO) model space. The low energy constants (LECs) are utilized to absorb not just the ultraviolet part of the physics due to the cutoff, but also the infrared part due to the truncation of model space. We use the inverse $J$-matrix method to reproduce the nucleon-nucleon scattering phase shifts in the given model space. We demonstrate that by including the NLO correction, the nucleon-nucleon scattering in the continuum could be well reproduced in the truncated HO trap space up to laboratory energy ${T}_{\mathrm{lab}}=100\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$ with number of HO basis ${n}_{\mathrm{max}}$ as small as 10. A perturbative power counting starts at subleading order is adopted in this work, and how to extract the perturbative contribution is demonstrated. This work serves as the input to perform ab initio calculations.