Three-particle finite-volume formalism for π + π + K + and related systems

Blanton, Tyler D.; Sharpe, Stephen R.

doi:10.1103/PhysRevD.104.034509

Title: Three-particle finite-volume formalism for $π^{+} π^{+} K^{+}$ and related systems

Journal Article · Mon Aug 30 00:00:00 EDT 2021 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.104.034509· OSTI ID:1817802

Blanton, Tyler D.;

We consider three-particle systems consisting of two identical particles and a third that is different, with all being spinless. Examples include π⁺π⁺K⁺ and K⁺K⁺π⁺. We derive the formalism necessary to extract two- and three-particle infinite-volume scattering amplitudes from the spectrum of such systems in finite volume. We use a relativistic formalism based on an all-orders diagrammatic analysis in generic effective field theory, adopting the methodology used recently to study the case of three nondegenerate particles. We present both a direct derivation, and also a cross-check based on an appropriate limit and projection of the fully nondegenerate formalism. We also work out the threshold expansions for the three-particle K matrix that will be needed in practical applications, both for systems with two identical particles plus a third, and also for the fully nondegenerate theory.

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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:: 1817802

Alternate ID(s):: OSTI ID: 1837903

Journal Information:: Physical Review D, Journal Name: Physical Review D Vol. 104 Journal Issue: 3; ISSN 2470-0010

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (35)

Three-particle quantization condition in a finite volume: 1. The role of the three-particle force Hammer, Hans-Werner; Pang, Jin-Yi; Rusetsky, Akaki Journal of High Energy Physics, Vol. 2017, Issue 9, 23 p. https://doi.org/10.1007/JHEP09(2017)109	journal	September 2017
Energy shift of the three-particle system in a finite volume Pang, Jin-Yi; Wu, Jia-Jun; Hammer, Hans-Werner Physical Review D, Vol. 99, Issue 7 https://doi.org/10.1103/PhysRevD.99.074513	journal	April 2019
Scattering of two and three physical pions at maximal isospin from lattice QCD: Extended Twisted Mass Collaboration Fischer, Matthias; Kostrzewa, Bartosz; Liu, Liuming The European Physical Journal C, Vol. 81, Issue 5 https://doi.org/10.1140/epjc/s10052-021-09206-5	journal	May 2021
Finite-volume energy spectrum of the $K^{-} K^{-} K^{-}$ system Alexandru, Andrei; Brett, Ruairí; Culver, Chris Physical Review D, Vol. 102, Issue 11 https://doi.org/10.1103/PhysRevD.102.114523	journal	December 2020
Finite-Volume Spectrum of $π^{+} π^{+}$ and $π^{+} π^{+} π^{+}$ Systems Mai, M.; Döring, M. Physical Review Letters, Vol. 122, Issue 6 https://doi.org/10.1103/PhysRevLett.122.062503	journal	February 2019
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. Physical Review D, Vol. 95, Issue 7 https://doi.org/10.1103/PhysRevD.95.074510	journal	April 2017
Three-body unitarity in the finite volume Mai, M.; Döring, M. The European Physical Journal A, Vol. 53, Issue 12 https://doi.org/10.1140/epja/i2017-12440-1	journal	December 2017
Generalizing the relativistic quantization condition to include all three-pion isospin channels Hansen, Maxwell T.; Romero-López, Fernando; Sharpe, Stephen R. Journal of High Energy Physics, Vol. 2020, Issue 7 https://doi.org/10.1007/JHEP07(2020)047	journal	July 2020
Equivalence of three-particle scattering formalisms Jackura, A. W.; Dawid, S. M.; Fernández-Ramírez, C. Physical Review D, Vol. 100, Issue 3 https://doi.org/10.1103/PhysRevD.100.034508	journal	August 2019
Relativistic N-particle energy shift in finite volume Romero-López, Fernando; Rusetsky, Akaki; Schlage, Nikolas Journal of High Energy Physics, Vol. 2021, Issue 2 https://doi.org/10.1007/JHEP02(2021)060	journal	February 2021
Lattice QCD and Three-Particle Decays of Resonances Hansen, Maxwell T.; Sharpe, Stephen R. Annual Review of Nuclear and Particle Science, Vol. 69, Issue 1 https://doi.org/10.1146/annurev-nucl-101918-023723	journal	October 2019
Equivalence of relativistic three-particle quantization conditions Blanton, Tyler D.; Sharpe, Stephen R. Physical Review D, Vol. 102, Issue 5 https://doi.org/10.1103/PhysRevD.102.054515	journal	September 2020
Two- and Three-Pion Finite-Volume Spectra at Maximal Isospin from Lattice QCD Hörz, Ben; Hanlon, Andrew Physical Review Letters, Vol. 123, Issue 14 https://doi.org/10.1103/PhysRevLett.123.142002	journal	October 2019
Three-particle quantization condition in a finite volume: 2. General formalism and the analysis of data Hammer, Hans-Werner; Pang, Jin-Yi; Rusetsky, Akaki Journal of High Energy Physics, Vol. 2017, Issue 10, 31 p. https://doi.org/10.1007/JHEP10(2017)115	journal	October 2017
Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states Romero-López, Fernando; Sharpe, Stephen R.; Blanton, Tyler D. Journal of High Energy Physics, Vol. 2019, Issue 10 https://doi.org/10.1007/JHEP10(2019)007	journal	October 2019
Three pion spectrum in the $I = 3$ channel from lattice QCD Culver, C.; Mai, M.; Brett, R. Physical Review D, Vol. 101, Issue 11 https://doi.org/10.1103/PhysRevD.101.114507	journal	June 2020
Three-body unitarity versus finite-volume $π^{+} π^{+} π^{+}$ spectrum from lattice QCD Mai, M.; Döring, M.; Culver, C. Physical Review D, Vol. 101, Issue 5 https://doi.org/10.1103/PhysRevD.101.054510	journal	March 2020
Energy-Dependent $π^{+} π^{+} π^{+}$ Scattering Amplitude from QCD Hansen, Maxwell T.; Briceño, Raul A.; Edwards, Robert G. Physical Review Letters, Vol. 126, Issue 1 https://doi.org/10.1103/PhysRevLett.126.012001	journal	January 2021
Numerical study of the relativistic three-body quantization condition in the isotropic approximation Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R. Physical Review D, Vol. 98, Issue 1 https://doi.org/10.1103/PhysRevD.98.014506	journal	July 2018
Implementing the three-particle quantization condition including higher partial waves Blanton, Tyler D.; Romero-López, Fernando; Sharpe, Stephen R. Journal of High Energy Physics, Vol. 2019, Issue 3 https://doi.org/10.1007/JHEP03(2019)106	journal	March 2019
Relativistic, model-independent, three-particle quantization condition Hansen, Maxwell T.; Sharpe, Stephen R. Physical Review D, Vol. 90, Issue 11 https://doi.org/10.1103/PhysRevD.90.116003	journal	December 2014
Multi-particle systems on the lattice and chiral extrapolations: a brief review Mai, Maxim; Döring, Michael; Rusetsky, Akaki The European Physical Journal Special Topics, Vol. 230, Issue 6 https://doi.org/10.1140/epjs/s11734-021-00146-5	journal	June 2021
Three particles in a finite volume Polejaeva, K.; Rusetsky, A. The European Physical Journal A, Vol. 48, Issue 5 https://doi.org/10.1140/epja/i2012-12067-8	journal	May 2012
Three-particle scattering amplitudes from a finite volume formalism Briceño, Raúl A.; Davoudi, Zohreh Physical Review D, Vol. 87, Issue 9 https://doi.org/10.1103/PhysRevD.87.094507	journal	May 2013
Three-body unitarity with isobars revisited Mai, M.; Hu, B.; Döring, M. The European Physical Journal A, Vol. 53, Issue 9 https://doi.org/10.1140/epja/i2017-12368-4	journal	September 2017
Phenomenology of relativistic $$\mathbf {3}\rightarrow \mathbf {3}$$ 3 → 3 reaction amplitudes within the isobar approximation Jackura, A.; Fernández-Ramírez, C.; Mathieu, V. The European Physical Journal C, Vol. 79, Issue 1 https://doi.org/10.1140/epjc/s10052-019-6566-1	journal	January 2019
Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude Hansen, Maxwell T.; Sharpe, Stephen R. Physical Review D, Vol. 92, Issue 11 https://doi.org/10.1103/PhysRevD.92.114509	journal	December 2015
Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R. Physical Review D, Vol. 100, Issue 5 https://doi.org/10.1103/PhysRevD.100.054508	journal	September 2019
Finite-volume energy shift of the three-pion ground state Müller, Fabian; Yu, Tiansu; Rusetsky, Akaki Physical Review D, Vol. 103, Issue 5 https://doi.org/10.1103/PhysRevD.103.054506	journal	March 2021
Relativistic three-particle quantization condition for nondegenerate scalars Blanton, Tyler D.; Sharpe, Stephen R. Physical Review D, Vol. 103, Issue 5 https://doi.org/10.1103/PhysRevD.103.054503	journal	March 2021
Three-body interactions from the finite-volume QCD spectrum Brett, Ruairí; Culver, Chris; Mai, Maxim Physical Review D, Vol. 104, Issue 1 https://doi.org/10.1103/PhysRevD.104.014501	journal	July 2021
$D D K$ system in finite volume Pang, Jin-Yi; Wu, Jia-Jun; Geng, Li-Sheng Physical Review D, Vol. 102, Issue 11 https://doi.org/10.1103/PhysRevD.102.114515	journal	December 2020
$I = 3$ Three-Pion Scattering Amplitude from Lattice QCD Blanton, Tyler D.; Romero-López, Fernando; Sharpe, Stephen R. Physical Review Letters, Vol. 124, Issue 3 https://doi.org/10.1103/PhysRevLett.124.032001	journal	January 2020
Alternative derivation of the relativistic three-particle quantization condition Blanton, Tyler D.; Sharpe, Stephen R. Physical Review D, Vol. 102, Issue 5 https://doi.org/10.1103/PhysRevD.102.054520	journal	September 2020
Three-particle systems with resonant subprocesses in a finite volume Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R. Physical Review D, Vol. 99, Issue 1 https://doi.org/10.1103/PhysRevD.99.014516	journal	January 2019

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