On the three-particle analog of the Lellouch-Lüscher formula

Abstract

Using non-relativistic effective field theory, we derive a three-particle analog of the Lellouch-Lüscher formula at the leading order. This formula relates the three-particle decay amplitudes in a finite volume with their infinite-volume counterparts and, hence, can be used to study the three-particle decays on the lattice. The generalization of the approach to higher orders is briefly discussed.

15 pages, 3 figures

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• Three-body resonances in the ${\phi }^4$ theory
• Particle-dimer approach for the Roper resonance in a finite volume
• Spurious poles in a finite volume
• Rediscovery of Numerical Lüscher's Formula from the Neural Network
• Emergence of the $\pi (1300)$ Resonance from Lattice QCD
• Lellouch-Lüscher relation for ultracold few-atom systems under confinement