Equivalence of relativistic three-particle quantization conditions

TL;DR

This paper demonstrates the equivalence between two formulations of relativistic three-particle quantization conditions, unifying different theoretical approaches and extending their applicability to arbitrary angular momenta.

Contribution

It shows that a new form of the three-particle quantization condition aligns with the R matrix approach, unifying existing methods and generalizing to all angular momenta.

Findings

Proves the equivalence of two relativistic three-particle quantization formalisms.

Extends the 'finite-volume unitarity' approach to arbitrary angular momenta.

Provides a unified framework for three-particle scattering analysis.

Abstract

We show that a recently derived alternative form of the relativistic three-particle quantization condition for identical particles can be rewritten in terms of the R matrix introduced to give a unitary representation of the infinite-volume three-particle scattering amplitude. Combined with earlier work, this shows the equivalence of the relativistic effective field theory approach of Hansen and Sharpe (Refs.[1,2]) and the "finite-volume unitarity" approach of Mai and D\"oring (Refs.[3,4]). It also provides a generalization of the latter approach to arbitrary angular momenta of two-particle subsystems.