Relativistic, model-independent, three-particle quantization condition
By M. Hansen, Stephen R. Sharpe. 2013
210 citations recorded by the source corpus.
We present a generalization of Luescher's relation between the finite-volume spectrum and scattering amplitudes to the case of three particles. We consider a relativistic scalar field theory in which the couplings are arbitrary aside from a Z2 symmetry that removes vertices with an odd number of particles. The theory is assumed to have two-particle phase shifts that are bounded by \pi/2 in the regime of elastic scattering. We determine the spectrum of the finite-volume theory from the poles in the odd-particle-number finite-volume correlator, which we analyze to all orders in perturbation theory. We show that it depends on the infinite-volume two-to-two K-matrix as well as a nonstandard infinite-volume three-to-three K-matrix. A key feature of our result is the need to subtract physical singularities in the three-to-three amplitude and thus deal with a divergence-free quantity. This allows our initial, formal result to be truncated to a finite dimensional determinant equation. At present, the relation of the three-to-three K-matrix to the corresponding scattering amplitude is not known, although previous results in the non-relativistic limit suggest that such a relation exists.
Subfields: Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/dce44709df9be0d11aa4a166574120275f981aba
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In Nuclear and High Energy Physics
Citations in the corpus
- Nuclear effective field theory: Status and perspectives (2019, methodology): “An alternative formulation was given by Hansen and Sharpe (2014).”
- Hadronic molecules (2017, background): “For the discussion of hadronic molecules (or most other hadron resonances), this method needs to be extended in various directions, such as considering higher partial waves and spins (Bernard et al., 2008; Briceño and Davoudi, 2013a; Göckeler et al., 2012; König et al., 2011, 2012; Luu and Savage”
- Scattering processes and resonances from lattice QCD (2017, methodology): “In (Hansen and Sharpe, 2014, 2015) it was shown that poles in the K-matrix can lead to power-law finite-volume effects which have thus far not been accounted for.”