https://doi.org/10.1140/epja/i2017-12440-1
Regular Article - Theoretical Physics
Three-body unitarity in the finite volume
1
The George Washington University, 20052, Washington, DC, USA
2
Thomas Jefferson National Accelerator Facility, 23606, Newport News, VA, USA
* e-mail: maximmai@gwu.edu
Received:
11
October
2017
Accepted:
9
November
2017
Published online:
18
December
2017
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 
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.
© SIF, Springer-Verlag GmbH Germany, part of Springer Nature, 2017
