Renormalization of the three-boson system with short-range interactions revisited

TL;DR

This paper revisits the renormalization of the three-boson system with short-range interactions using a Lorentz-invariant approach, showing it is perturbatively renormalizable and finite without needing a three-body counter term.

Contribution

It introduces a Lorentz-invariant formulation for three-boson renormalization that differs from non-relativistic methods by eliminating the need for a three-body counter term.

Findings

Leading-order equation is perturbatively renormalizable.

Equation is non-perturbatively finite.

No three-body counter term required.

Abstract

We consider renormalization of the three-body scattering problem in low-energy effective field theory of self-interacting scalar particles by applying time-ordered perturbation theory to the manifestly Lorentz-invariant formulation. The obtained leading-order equation is perturbatively renormalizable and non-perturbatively finite and does not require a three-body counter term in contrast to its non-relativistic approximation.