Testing the threshold expansion for three-particle energies at fourth order in Φ4 theory

Sharpe, Stephen R.

doi:10.1103/PhysRevD.96.054515

Title: Testing the threshold expansion for three-particle energies at fourth order in $Φ^{4}$ theory

Journal Article · Tue Sep 26 00:00:00 EDT 2017 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.96.054515· OSTI ID:1595791

Sharpe, Stephen R. ^[1]

Univ. of Washington, Seattle, WA (United States)

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.

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Research Organization:: Univ. of Washington, Seattle, WA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: SC0011637

OSTI ID:: 1595791

Alternate ID(s):: OSTI ID: 1394865

Journal Information:: Physical Review D, Vol. 96, Issue 5; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 33 works

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References (16)

Erratum: Threshold expansion of the three-particle quantization condition [Phys. Rev. D 93 , 096006 (2016)] Hansen, Maxwell T.; Sharpe, Stephen R. Physical Review D, Vol. 96, Issue 3 https://doi.org/10.1103/PhysRevD.96.039901	journal	August 2017
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Threshold expansion of the three-particle quantization condition Hansen, Maxwell T.; Sharpe, Stephen R. Physical Review D, Vol. 93, Issue 9 https://doi.org/10.1103/PhysRevD.93.096006	journal	May 2016
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Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude Hansen, Maxwell T.; Sharpe, Stephen R. arXiv https://doi.org/10.48550/arxiv.1504.04248	text	January 2015
Perturbative results for two and three particle threshold energies in finite volume Hansen, Maxwell T.; Sharpe, Stephen R. arXiv https://doi.org/10.48550/arxiv.1509.07929	text	January 2015
Relating the finite-volume spectrum and the two-and-three-particle $S$ matrix for relativistic systems of identical scalar particles Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R. arXiv https://doi.org/10.48550/arxiv.1701.07465	text	January 2017
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Opportunities for Lattice QCD in quark and lepton flavor physics Lehner, Christoph; Meinel, Stefan; Blum, Tom The European Physical Journal A, Vol. 55, Issue 11 https://doi.org/10.1140/epja/i2019-12891-2	journal	November 2019
Two- and three-body interactions in $$\varphi ^4$$ φ 4 theory from lattice simulations Romero-López, F.; Rusetsky, A.; Urbach, C. The European Physical Journal C, Vol. 78, Issue 10 https://doi.org/10.1140/epjc/s10052-018-6325-8	journal	October 2018
Three-body spectrum in a finite volume: the role of cubic symmetry Döring, M.; Hammer, H. -W.; Mai, M. GSI Helmholtzzentrum fuer Schwerionenforschung, GSI, Darmstadt https://doi.org/10.15120/gsi-2019-00687	text	January 2018
Three-body Unitarity in the Finite Volume Mai, M.; Döring, M. arXiv https://doi.org/10.48550/arxiv.1709.08222	text	January 2017
Three-particle bound states in a finite volume: unequal masses and higher partial waves Meng, Yu; Liu, Chuan; Meißner, Ulf-G. arXiv https://doi.org/10.48550/arxiv.1712.08464	text	January 2017
Three-body spectrum in a finite volume: the role of cubic symmetry Döring, M.; Hammer, H. -W.; Mai, M. arXiv https://doi.org/10.48550/arxiv.1802.03362	text	January 2018
Numerical study of the relativistic three-body quantization condition in the isotropic approximation Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R. arXiv https://doi.org/10.48550/arxiv.1803.04169	text	January 2018
Energy shift of the three-particle system in a finite volume Pang, Jin-Yi; Wu, Jia-Jun; Hammer, H. -W. arXiv https://doi.org/10.48550/arxiv.1902.01111	text	January 2019
Opportunities for lattice QCD in quark and lepton flavor physics Lehner, Christoph; Meinel, Stefan; Blum, Tom arXiv https://doi.org/10.48550/arxiv.1904.09479	text	January 2019

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Title: Testing the threshold expansion for three-particle energies at fourth order in $Φ^{4}$ theory