Contact operators in renormalization of attractive singular potentials

TL;DR

This paper examines the renormalization process of chiral nuclear forces in the 3P0 channel, highlighting issues with contact potential dependencies at certain cutoffs and proposing a strategy to resolve this within chiral effective field theory.

Contribution

It introduces a new approach to adjust the extraction of low-energy constants, improving the renormalization process for singular potentials in nuclear physics.

Findings

Dependence of contact potentials on ultraviolet cutoff can be mitigated

Adjusting the data fitting strategy resolves the cutoff dependency issue

Enhances the applicability of chiral EFT to nuclear force renormalization

Abstract

We discuss renormalization of chiral nuclear forces in the 3P0 channel of N N scattering at next- to-next-to leading order (N2LO) if the one-pion exchange is treated nonperturbatively at leading order. The matrix elements of the subleading contact potentials become nearly dependent of each other for the so-called exceptional ultraviolet momentum cutoff, making it difficult to determine the strengths of those contact potentials from the empirical phase shifts, as reported in Ref. [1]. We argue that this issue can be resolved by adjusting the strategy by which the low-energy constants are deduced from the data, thus making those exceptional cutoffs amenable to chiral effective field theory.