Testing the threshold expansion for three-particle energies at fourth order in theory
Abstract
We report that a relativistic formalism for relating the the energies of the states of three scalar particles in finite volume to infinite volume scattering amplitudes has recently been developed. This formalism has been used to predict the energy of the state closest to threshold in an expansion in powers of 1/L, with L the box length. This expansion has been tested previously by a perturbative calculation of the threshold energy in λφ4 theory, working to third order in λ and up to O(1/L6) in the volume expansion. However, several aspects of the predicted threshold behavior do not enter until fourth (three-loop) order in perturbation theory. Here I extend the perturbative calculation to fourth order and find agreement with the general prediction. This check also requires a two-loop calculation of the infinite-volume off-shell two-particle scattering amplitude near threshold. As a spin-off, I check the threshold expansion for two particles to the same order, finding agreement with the result that follows from Lüscher's formalism.
- Authors:
-
- 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:
- 1595791
- Alternate Identifier(s):
- OSTI ID: 1394865
- Grant/Contract Number:
- SC0011637
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review D
- Additional Journal Information:
- Journal Volume: 96; Journal Issue: 5; Journal ID: ISSN 2470-0010
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Few-body systems; Lattice field theory; Perturbation theory
Citation Formats
Sharpe, Stephen R. Testing the threshold expansion for three-particle energies at fourth order in Φ4 theory. United States: N. p., 2017.
Web. doi:10.1103/PhysRevD.96.054515.
Sharpe, Stephen R. Testing the threshold expansion for three-particle energies at fourth order in Φ4 theory. United States. https://doi.org/10.1103/PhysRevD.96.054515
Sharpe, Stephen R. Tue .
"Testing the threshold expansion for three-particle energies at fourth order in Φ4 theory". United States. https://doi.org/10.1103/PhysRevD.96.054515. https://www.osti.gov/servlets/purl/1595791.
@article{osti_1595791,
title = {Testing the threshold expansion for three-particle energies at fourth order in Φ4 theory},
author = {Sharpe, Stephen R.},
abstractNote = {We report that a relativistic formalism for relating the the energies of the states of three scalar particles in finite volume to infinite volume scattering amplitudes has recently been developed. This formalism has been used to predict the energy of the state closest to threshold in an expansion in powers of 1/L, with L the box length. This expansion has been tested previously by a perturbative calculation of the threshold energy in λφ4 theory, working to third order in λ and up to O(1/L6) in the volume expansion. However, several aspects of the predicted threshold behavior do not enter until fourth (three-loop) order in perturbation theory. Here I extend the perturbative calculation to fourth order and find agreement with the general prediction. This check also requires a two-loop calculation of the infinite-volume off-shell two-particle scattering amplitude near threshold. As a spin-off, I check the threshold expansion for two particles to the same order, finding agreement with the result that follows from Lüscher's formalism.},
doi = {10.1103/PhysRevD.96.054515},
journal = {Physical Review D},
number = 5,
volume = 96,
place = {United States},
year = {Tue Sep 26 00:00:00 EDT 2017},
month = {Tue Sep 26 00:00:00 EDT 2017}
}
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Numerical study of the relativistic three-body quantization condition in the isotropic approximation
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