Spectrum of three-body bound states in a finite volume

Abstract

The spectrum of a bound state of three identical particles with a mass $m$ in a finite cubic box is studied. It is shown that in the unitary limit, the energy shift of a shallow bound state is given by $\Delta E=c({\kappa }^2/m)(\kappa L{)}^{-3/2}|A{|}^2\exp (-2\kappa L/\sqrt{3})$, where $\kappa$ is the bound-state momentum, $L$ is the box size, $|A{|}^2$ denotes the three-body analog of the asymptotic normalization coefficient of the bound state wave function and $c$ is a numerical constant. The formula is valid for $\kappa L\gg 1$.

An error in the calculation of the overlap integral in Eq. (11) is corrected. Our main result given in Eq. (26) remains the same, except the numerical value of the constant c, which changes approximately by 10%

References in corpus (11)

• A relativistic, model-independent, three-particle quantization condition
• Light Nuclei and Hypernuclei from Quantum Chromodynamics in the Limit of SU(3) Flavor Symmetry
• Nuclear Physics from Lattice QCD
• Scalar mesons in a finite volume
• Lattice Effective Field Theory for Medium-Mass Nuclei
• n-Boson Energies at Finite Volume and Three-Boson Interactions
• Efimov physics in a finite volume
• The triton in a finite volume
• A framework for the calculation of the $\Delta N{\gamma }^{\ast }$ transition form factors on the lattice
• Benchmark calculations for elastic fermion-dimer scattering
• Bound states on the lattice with partially twisted boundary conditions

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