arXiv : Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism

Briceño, Raúl A.; Szczepaniak, Adam P.; Sharpe, Stephen R.; Hansen, Maxwell T.

doi:10.1103/PhysRevD.100.054508

Article
Report number	arXiv:1905.11188 ; JLAB-THY-19-2945 ; CERN-TH-2019-078
Title	Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism
Author(s)	Briceño, Raúl A. (Jefferson Lab ; Old Dominion U.) ; Hansen, Maxwell T. (CERN) ; Sharpe, Stephen R. (Washington U., Seattle) ; Szczepaniak, Adam P. (Indiana U., Bloomington (main) ; Indiana U., CEEM ; Jefferson Lab)
Publication	2019-09-19
Imprint	2019-05-27
Number of pages	19
Note	19 pages, 4 figures, JLAB-THY-19-2945, CERN-TH-2019-078
In:	Phys. Rev. D 100 (2019) 054508
DOI	10.1103/PhysRevD.100.054508
Subject category	hep-ph ; Particle Physics - Phenomenology ; hep-lat ; Particle Physics - Lattice
Abstract	In a previous publication, two of us derived a relation between the scattering amplitude of three identical bosons, $\mathcal M_3$, and a real function referred to as the {divergence-free} K matrix and denoted $\mathcal K_{\text{df},3}$. The result arose in the context of a relation between finite-volume energies and $\mathcal K_{\text{df},3}$, derived to all orders in the perturbative expansion of a generic low-energy effective field theory. In this work we set aside the role of the finite volume and focus on the infinite-volume relation between $\mathcal K_{\text{df},3}$ and $\mathcal M_3$. We show that, for any real choice of $\mathcal K_{\text{df},3}$, $\mathcal M_3$ satisfies the three-particle unitarity constraint to all orders. Given that $\mathcal K_{\text{df},3}$ is also free of a class of kinematic divergences, the function may provide a useful tool for parametrizing three-body scattering data. Applications include the phenomenological analysis of experimental data (where the connection to the finite volume is irrelevant) as well as calculations in lattice quantum chromodynamics (where the volume plays a key role).
Copyright/License	preprint: (License: arXiv nonexclusive-distrib 1.0) publication: © 2019-2025 authors (License: CC-BY-4.0)

$Diagrammatic representation of the right-hand side of Eq.~(\ref{eq:desired}), which gives the imaginary part of $\mathcal D^\uu$. Squares with rounded corners depict $\mathcal D^\uu$, and for simplicity we do not distinguish between $\mathcal D^\uu$ and its conjugate. The two types of cut, defined in the text, are distinguished by the shapes of the adjacent lines.$ $Diagrammatic representation of the right-hand side of Eq.~(\ref{eq:desired}), which gives the imaginary part of $\mathcal D^\uu$. Squares with rounded corners depict $\mathcal D^\uu$, and for simplicity we do not distinguish between $\mathcal D^\uu$ and its conjugate. The two types of cut, defined in the text, are distinguished by the shapes of the adjacent lines.$ $Schematic representation of the definition of symmetrization given in Eq.~(\ref{eq:M3symm}), using the example of the leading term in $\cD^{(u,u)}$. (a) Basis transformation from the $k, \ell,m$ to the on in terms of three momenta; (b) Summing over permutations of assignments of external momenta. Open circles represent $\mathcal M_2$, which is itself symmetric under particle interchange. The third momentum on the left-hand side is given by $\vec b_{ka}= \vec P-\vec k - \vec a$, with $\vec b_{pa'}$ defined similarly. See main text for further explanation.$ Show more plots

Corresponding record in: Inspire

Back to search

Record created 2019-05-29, last modified 2022-08-10

Similar records

Article from SCOAP3: