Abstract
Using the three-particle quantization condition recently obtained in the particle-dimer framework, the finite-volume energy shift of the two lowest three-particle scattering states is derived up to and including order $L^{-6}$. Furthermore, assuming that a stable dimer exists in the infinite volume, the shift for the lowest particle-dimer scattering state is obtained up to and including order $L^{-3}$. The result for the lowest three-particle state agrees with the results from the literature, and the result for the lowest particle-dimer state reproduces the one obtained by using the Luescher equation.
Highlights
First and foremost, we provide closed analytic expressions for the energy shift of different levels in a finite volume, which can be fitted to the lattice data
This matrix identity can be used to produce a systematic expansion of the energy shift in powers of 1=L, as we shall see in the following
Note that deleting the entries corresponding to the first shell, makes the solution of the quantization condition easier—unlike the case with the irrep Aþ1, there is no need for the special treatment of the singular terms in the matrix A
Summary
Recent years have seen a rapid progress in developing the formalism for the analysis of the lattice data in the threeparticle sector [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28] (for a recent review, see Ref. [29]). In the presence of interactions, the energy levels are displaced from their free values In this case, the spectrum consists of the levels that in the infinite-volume limit end up in the continuum (we refer to these levels as to the scattering states), and the levels that are continuously transformed into the bound states in this limit. The expression for the energy shift of the lowest three-particle scattering state is known in the literature up to and including OðL−6Þ We derive the finite volume shift of the lowest three-particle and particle-dimer scattering states in a systematic expansion in powers of 1=L (including logarithms), using the approach of Ref.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
