Chiral potential renormalized in harmonic-oscillator space

TL;DR

This paper develops a method to renormalize chiral EFT potentials within harmonic oscillator space, enabling accurate nucleon-nucleon scattering predictions up to 100 MeV with small basis sizes, facilitating ab-initio nuclear calculations.

Contribution

It introduces a renormalization approach in harmonic-oscillator space that incorporates both UV and IR physics, improving scattering predictions with minimal basis size.

Findings

NLO correction improves scattering predictions up to 100 MeV

Effective renormalization absorbs cutoff and truncation effects

Perturbative power counting is successfully implemented

Abstract

We renormalize the chiral effective field theory (EFT) potential in harmonic-oscillator (HO) model space. The low energy constants (LECs) are utilized to absorb not just the ultra-violet 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 (NN) 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 $T_{lab}=100$ MeV with number of HO basis $n_{max}$ 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. Our work serves as the input to perform ab-initio calculations.