Three-body unitarity in the finite volume
189 citations recorded by the source corpus.
Abstract.The physical interpretation of lattice QCD simulations, performed in a small volume, requires an extrapolation to the infinite volume. A method is proposed to perform such an extrapolation for three interacting particles at energies above threshold. For this, a recently formulated relativistic $ 3\rightarrow 3$3→3 amplitude based on the isobar formulation is adapted to the finite volume. The guiding principle is two- and three-body unitarity that imposes the imaginary parts of the amplitude in the infinite volume. In turn, these imaginary parts dictate the leading power-law finite-volume effects. It is demonstrated that finite-volume poles arising from the singular interaction, from the external two-body sub-amplitudes, and from the disconnected topology cancel exactly leaving only the genuine three-body eigenvalues. The corresponding quantization condition is derived for the case of three identical scalar-isoscalar particles and its numerical implementation is demonstrated.
Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/45d027608cd398c3652ba533b751cfb58be4811e
Citations in the corpus
- The XYZ states: Experimental and theoretical status and perspectives (2019, unknown): “[858–877].”