A renormalization method for three-boson system with a triboson field

TL;DR

This paper introduces a renormalization approach using an auxiliary field for three-boson systems, demonstrating that different methods yield consistent results for key physical quantities despite the cyclic singularity.

Contribution

It presents a novel auxiliary field renormalization method for three-boson systems and compares it with the standard approach, confirming their equivalence in results.

Findings

Both methods successfully renormalize the system despite limit cycle behavior.

The counter term, scattering length, and wavefunction are consistent across methods.

The auxiliary field approach offers an alternative perspective for three-body renormalization.

Abstract

A renormalization method that introduces an auxiliary field to represent a three-body bound state is studied in a three-boson system with a triboson field. A cutoff dependence in the three-boson system emerges as a limit cycle, and the cyclic singularity is renormalized by employing two methods: a standard method and the auxiliary field method. For each method, different sets of diagrams are involved for renormalization, and thus we numerically study three quantities: counter term for renormalization, scattering length of $s$-wave boson-diboson scattering, and normalized wavefunction. We confirm that the two methods would lead to the same result.