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Title: Lattice QCD and Three-Particle Decays of Resonances

Abstract

The majority of strong-interaction resonances have decay channels involving three or more particles, including many of the recently discovered X, Y, and Z resonances. In order to study such resonances from first principles using lattice QCD, one must understand finite-volume effects for three particles in the cubic box used in calculations. Here, we review efforts to develop a three-particle quantization condition that relates finite-volume energies to infinite-volume scattering amplitudes. We describe in detail the three approaches that have been followed, and present new results on the relationship between the corresponding results. Furthermore, we show examples of the numerical implementation of all three approaches and point out the important issues that remain to be resolved.

Authors:
 [1];  [2]
  1. European Organization for Nuclear Research (CERN), Geneva (Switzerland)
  2. Univ. of Washington, Seattle, WA (United States)
Publication Date:
Research Org.:
Univ. of Washington, Seattle, WA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP)
OSTI Identifier:
1595798
Grant/Contract Number:  
SC0011637
Resource Type:
Accepted Manuscript
Journal Name:
Annual Review of Nuclear and Particle Science
Additional Journal Information:
Journal Volume: 69; Journal Issue: 1; Journal ID: ISSN 0163-8998
Publisher:
Annual Reviews
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; finite-volume quantum field theory; lattice QCD; three-particle quantization condition; resonances

Citation Formats

Hansen, Maxwell T., and Sharpe, Stephen R. Lattice QCD and Three-Particle Decays of Resonances. United States: N. p., 2019. Web. doi:10.1146/annurev-nucl-101918-023723.
Hansen, Maxwell T., & Sharpe, Stephen R. Lattice QCD and Three-Particle Decays of Resonances. United States. https://doi.org/10.1146/annurev-nucl-101918-023723
Hansen, Maxwell T., and Sharpe, Stephen R. Sat . "Lattice QCD and Three-Particle Decays of Resonances". United States. https://doi.org/10.1146/annurev-nucl-101918-023723. https://www.osti.gov/servlets/purl/1595798.
@article{osti_1595798,
title = {Lattice QCD and Three-Particle Decays of Resonances},
author = {Hansen, Maxwell T. and Sharpe, Stephen R.},
abstractNote = {The majority of strong-interaction resonances have decay channels involving three or more particles, including many of the recently discovered X, Y, and Z resonances. In order to study such resonances from first principles using lattice QCD, one must understand finite-volume effects for three particles in the cubic box used in calculations. Here, we review efforts to develop a three-particle quantization condition that relates finite-volume energies to infinite-volume scattering amplitudes. We describe in detail the three approaches that have been followed, and present new results on the relationship between the corresponding results. Furthermore, we show examples of the numerical implementation of all three approaches and point out the important issues that remain to be resolved.},
doi = {10.1146/annurev-nucl-101918-023723},
journal = {Annual Review of Nuclear and Particle Science},
number = 1,
volume = 69,
place = {United States},
year = {2019},
month = {10}
}

Journal Article:
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Cited by: 66 works
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Figures / Tables:

Figure 1 Figure 1: Representations of the scattering amplitude, $\mathcal{M}$2 and its finite-volume correspondent, $\mathcal{M}$2$L$. (a) First- and second-order contributions to $\mathcal{M}$2$L$ in $λ\phi$4 theory, with the dashed rectangles indicating that the spatial momenta are summed over the discrete finite-volume values. (b) The set of diagrams that must be summed in ordermore » to calculate the leading order energy shift in $λ\phi$4 theory. (c) Bethe-Salpeter (BS) equation for the infinite-volume amplitude, with $B$2 being the BS kernel. (d) Iterated version of the BS equation. (e) BS equation for the finite-volume amplitude, with $S$ and the dashed rectangle both indicating a sum over finite-volume three-momenta. (f) Iterated version of finite-volume BS equation.« less

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Works referencing / citing this record:

Scattering amplitudes and contour deformations
text, January 2019


Consistency checks for two-body finite-volume matrix elements: I. Conserved currents and bound states
text, January 2019


Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.