Abstract
The three-particle quantization condition is derived, using the particle-dimer picture in the non-relativistic effective field theory. The procedure for the extraction of various observables in the three-particle sector (the particle-dimer scattering amplitudes, breakup amplitudes, etc.) from the finite-volume lattice spectrum is discussed in detail. As an illustration of the general formalism, the expression for the finite-volume energy shift of the three-body bound-state in the unitary limit is re-derived. The role of the threebody force, which is essential for the renormalization, is highlighted, and the extension of the result beyond the unitary limit is studied. Comparison with other approaches, known in the literature, is carried out.
Highlights
Recent years have seen an increased interest in the calculation of the scattering observables through lattice simulations
The procedure for the extraction of various observables in the three-particle sector from the finite-volume lattice spectrum is discussed in detail
Whereas in the two-body sector this became a pretty standard procedure based on the so-called Lüscher method [1] and the Lellouch-Lüscher formula [2], no comparable framework exists in the three-body sector so far, despite some activity in this field during the last few years [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18]
Summary
Recent years have seen an increased interest in the calculation of the scattering observables through lattice simulations. [8] a three-particle quantization condition has been derived, which determines the finite-volume spectrum in the three-particle sector in terms of the infinite-volume quantities. This condition has a rather complicated form and contains unconventional scattering matrix elements that explicitly depend on the introduced cutoff. In our approach, these couplings represent the only unknown quantities, which determine the three-particle dynamics both in a finite and in the infinite volume and which should be fitted to the lattice data (we remind the reader that the effective couplings in the two-particle sector can be determined separately from the two-particle simulations by using the conventional Lüscher approach). We clarify the role of the three-body force in these calculations
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