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Three-body unitarity in the finite volume

  • Regular Article - Theoretical Physics
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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 \( 3\rightarrow 3\) 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.

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Authors and Affiliations

  1. The George Washington University, 20052, Washington, DC, USA

    M. Mai & M. Döring

  2. Thomas Jefferson National Accelerator Facility, 23606, Newport News, VA, USA

    M. Döring

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  1. M. Mai
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Correspondence to M. Mai.

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Communicated by B. Ananthanarayan

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Mai, M., Döring, M. Three-body unitarity in the finite volume. Eur. Phys. J. A 53, 240 (2017). https://doi.org/10.1140/epja/i2017-12440-1

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