Publications
Publication Information
| Title | Three-body scattering and quantization conditions from S matrix unitarity |
| Authors | Andrew Jackura |
| JLAB number | JLAB-THY-22-3664 |
| LANL number | arXiv:2208.10587 |
| Other number | DOE/OR/23177-5542 |
| Document Type(s) | (Journal Article) |
| Associated with EIC: | No |
| Supported by Jefferson Lab LDRD Funding: | No |
| Funding Source: | Nuclear Physics (NP) |
|
Journal Compiled for Physical Review D Volume 108 Page(s) 034505 | |
| Publication Abstract: | Two methodologies have been presented in the literature which connect relativistic three-particle scattering amplitudes with lattice QCD spectra -- the ``relativistic effective field theory'' (RFT) approach and the ``finite-volume unitarity'' (FVU) method. While both methods have been shown to be equivalent in various works, it has not been shown how to arrive at the RFT results directly from $S$ matrix unitarity. In this work, we provide a simple proof of the RFT form of the scattering equations directly from unitarity. Motivated by the FVU approach, we then postulate a set of quantization conditions which relate the finite-volume energy spectra to the $K$ matrices which drive the short-distance physics in the scattering equations, obtaining all previously known results for three identical particles. This work also presents new relations which provide a clear pathway to easily generalize the results to arbitrary systems and the $n$-body problem. |
| Experiment Numbers: | other |
| Group: | THEORY CENTER |
| Document: | |
| DOI: | https://doi.org/10.1103/PhysRevD.108.034505 |
| Accepted Manuscript: | PhysRevD.108.034505.pdf |
| Supporting Documents: | |
| Supporting Datasets: | |