Renormalization of many-body effective field theory

TL;DR

This paper proves that achieving renormalization group invariance in many-body effective field theories requires a universal momentum cutoff for all single-particle states, demonstrated through chiral force calculations that reproduce experimental data nearly independently of cutoff variations.

Contribution

The paper establishes a necessary and sufficient condition for RG invariance in non-relativistic EFTs, introducing a universal cutoff scheme and demonstrating its effectiveness in nuclear force calculations.

Findings

RG invariance requires a universal cutoff for all single-particle momenta.

Reproduces experimental binding energies nearly independently of cutoff.

Explains cutoff dependence issues in recent nuclear EFT calculations.

Abstract

The renormalization of the effective field theories (EFTs) in many-body systems is the most pressing and challenging problem in modern nuclear ab initio calculation. For general non-relativistic EFTs, we prove that the renormalization group (RG) invariance can be achieved if and only if all single-particle momenta are regulated with a universal cutoff \Lambda. For a numerical demonstration, we construct a series of N^{2}LO chiral forces with \Lambda varying from 250 MeV to 400 MeV. With all low energy constants fixed in two- and three-nucleon systems, we reproduce the experimental binding energies of ^{4}He and ^{16}O nearly independently of \Lambda. In contrast, all recent nuclear EFT constructions regulate the relative momenta for Galilean invariance, thus inherently break the RG invariance. This explains the unpleasantly strong cutoff-dependences observed in recent ab initio calculations. Our method can also be used to build RG-invariant EFTs with non-perturbative interactions.