Equivalence of relativistic three-particle quantization conditions

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 Döring (Refs.[3,4]). It also provides a generalization of the latter approach to arbitrary angular momenta of two-particle subsystems.

13 pages, 2 appendices; v2--added clarifications, corrected typos; v3--further clarifications added and typos corrected, results unchanged; matches published version

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Cited by in corpus (6)

• Relativistic three-particle quantization condition for nondegenerate scalars
• Finite-volume energy shift of the three-pion ground state
• Decay amplitudes to three hadrons from finite-volume matrix elements
• Interactions of $\pi K$, $\pi \pi K$ and $KK\pi$ systems at maximal isospin from lattice QCD
• Six-pion amplitude
• The isospin-3 three-particle $K$-matrix at NLO in ChPT