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

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

doi:10.1103/PhysRevD.100.054508

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

Abstract

Hansen and Sharpe [Phys. Rev. D 92, 114509 (2015)PRVDAQ1550-799810.1103/PhysRevD.92.114509] derived a relation between the scattering amplitude of three identical bosons, M3, and a real function referred to as the divergence-free K matrix and denoted Kdf,3. The result arose in the context of a relation between finite-volume energies and Kdf,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 Kdf,3 and M3. We show that, for any real choice of Kdf,3, M3 satisfies the three-particle unitarity constraint to all orders. Given that Kdf,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).

Authors:

Briceño, Raúl A.; Hansen, Maxwell T.;

; Szczepaniak, Adam P.

Publication Date:: Wed Sep 18 00:00:00 EDT 2019

Research Org.:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Indiana Univ., Bloomington, IN (United States); Univ. of Washington, Seattle, WA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP); USDOE Office of Science (SC), High Energy Physics (HEP)

Contributing Org.:: Jefferson Lab, Indiana University

OSTI Identifier:: 1562572

Alternate Identifier(s):: OSTI ID: 1567050; OSTI ID: 1595125; OSTI ID: 1669366

Report Number(s):: JLAB-THY-19-2945; DOE/OR/23177-4684; arXiv:1905.11188
Journal ID: ISSN 2470-0010; PRVDAQ; 054508

Grant/Contract Number:: SC0011637; FG02-87ER40365; AC05-06OR23177; SC0019229; PHY-1415459

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 5; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 43 PARTICLE ACCELERATORS; Lattice QCD; Lattice field theory; Quantum field theory; Quantum field theory (low energy); Scattering amplitudes; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; lattice QCD, scattering

Citation Formats


                    Briceño, Raúl A., Hansen, Maxwell T., Sharpe, Stephen R., and Szczepaniak, Adam P. Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism.  United States: N. p., 2019. 
Web.  doi:10.1103/PhysRevD.100.054508.

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                    Briceño, Raúl A., Hansen, Maxwell T., Sharpe, Stephen R., & Szczepaniak, Adam P. Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism.  United States.  https://doi.org/10.1103/PhysRevD.100.054508

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                    Briceño, Raúl A., Hansen, Maxwell T., Sharpe, Stephen R., and Szczepaniak, Adam P. Wed .  
"Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism".  United States.  https://doi.org/10.1103/PhysRevD.100.054508.

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@article{osti_1562572,

  title        = {Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism},

  author       = {Briceño, Raúl A. and Hansen, Maxwell T. and Sharpe, Stephen R. and Szczepaniak, Adam P.},

  abstractNote = {Hansen and Sharpe [Phys. Rev. D 92, 114509 (2015)PRVDAQ1550-799810.1103/PhysRevD.92.114509] derived a relation between the scattering amplitude of three identical bosons, M3, and a real function referred to as the divergence-free K matrix and denoted Kdf,3. The result arose in the context of a relation between finite-volume energies and Kdf,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 Kdf,3 and M3. We show that, for any real choice of Kdf,3, M3 satisfies the three-particle unitarity constraint to all orders. Given that Kdf,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).},

  doi          = {10.1103/PhysRevD.100.054508},

  journal      = {Physical Review D},

  number       = 5,

  volume       = 100,

  place        = {United States},

  year         = {Wed Sep 18 00:00:00 EDT 2019},

  month        = {Wed Sep 18 00:00:00 EDT 2019}

}

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

Abstract

Citation Formats

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Modified Isobar Approximation for π − ρ Scattering journal, June 1965

Relativistic, model-independent, three-particle quantization condition journal, December 2014

Three particles in a finite volume journal, May 2012

A solvable three-body model in finite volume journal, November 2017

Coupled π π , K K ¯ scattering in P -wave and the ρ resonance from lattice QCD journal, November 2015

Three-particle scattering amplitudes from a finite volume formalism journal, May 2013

Lattice QCD and the Timelike Pion Form Factor journal, August 2011

Two-particle multichannel systems in a finite volume with arbitrary spin journal, April 2014

Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude journal, December 2015

Minimal three-body equations with finite-range effects journal, October 1975

Towards three-body unitarity in D + → K − π + π + journal, November 2011

Multichannel 1 → 2 transition amplitudes in a finite volume journal, February 2015

Multichannel 0 → 2 and 1 → 2 transition amplitudes for arbitrary spin particles in a finite volume journal, October 2015

Volume dependence of the energy spectrum in massive quantum field theories: II. Scattering states journal, June 1986

Dynamically-coupled partial-waves in ρπ isospin-2 scattering from lattice QCD journal, July 2018

Form factors of two-hadron states from a covariant finite-volume formalism journal, August 2019

Tetraquark operators in lattice QCD and exotic flavour states in the charm sector journal, November 2017

Minimal Three-Body Scattering Theory journal, July 1974

Three-particle systems with resonant subprocesses in a finite volume journal, January 2019

Two particle states and the S -matrix elements in multi-channel scattering journal, July 2005

Matrix elements of unstable states journal, September 2012

Three-body unitarity in the finite volume journal, December 2017

Scattering phases for meson and baryon resonances on general moving-frame lattices journal, November 2012

Isoscalar π π Scattering and the σ Meson Resonance from QCD journal, January 2017

Resonances in Coupled π K − η K Scattering from Quantum Chromodynamics journal, October 2014

Finite volume corrections to the two-particle decay of states with nonzero momentum journal, December 2005

Scattering processes and resonances from lattice QCD journal, April 2018

Three-Body Unitarity and Khuri-Treiman Amplitudes journal, December 1966

Extraction of isoscalar π π phase shifts from lattice QCD journal, July 2018

Elastic I = 3 / 2 p -wave nucleon-pion scattering amplitude and the Δ ( 1232 ) resonance from N f = 2 + 1 lattice QCD journal, January 2018

Numerical study of the relativistic three-body quantization condition in the isotropic approximation journal, July 2018

Implementing the three-particle quantization condition including higher partial waves journal, March 2019

Light nuclei and hypernuclei from quantum chromodynamics in the limit of SU(3) flavor symmetry journal, February 2013

An a 0 resonance in strongly coupled π η , K K ¯ scattering from lattice QCD journal, May 2016

Two-particle states on a torus and their relation to the scattering matrix journal, May 1991

Three-body spectrum in a finite volume: The role of cubic symmetry journal, June 2018

Unitarity and the evaluation of discontinuities journal, October 1962

Construction of Coupled Scattering and Production Amplitudes Satisfying Analyticity and Unitarity journal, May 1960

Determination of s- and p-wave I = 1/2 Kπ scattering amplitudes in Nf = 2 + 1 lattice QCD journal, July 2018

Three-body unitarity with isobars revisited journal, September 2017

Baryon masses at nonzero isospin/kaon density journal, October 2013

Unitary states for three pions journal, July 1975

Unitarity and Production Amplitudes journal, July 1962

Finite-volume effects for two-hadron states in moving frames journal, October 2005

Phenomenology of relativistic $$\mathbf {3}\rightarrow \mathbf {3}$$ 3 → 3 reaction amplitudes within the isobar approximation journal, January 2019

Scattering and Production Amplitudes with Unstable Particles journal, October 1962

Determination of s - and p -wave I = 1/2 Kπ scattering amplitudes in N f = 2 + 1 lattice QCD text, January 2018

Scattering phases for meson and baryon resonances on general moving-frame lattices text, January 2012

Three-particle quantization condition in a finite volume: 1. The role of the three-particle force
journal, September 2017

Rummukainen-Gottlieb formula on a two-particle system with different masses
journal, January 2012

Recoupling Effects in the Isobar Model. I. General Formalism for Three-Pion Scattering
journal, July 1964

Finite-Volume Spectrum of $π^{+} π^{+}$ and $π^{+} π^{+} π^{+}$ Systems
journal, February 2019

Multiple-channel generalization of Lellouch-Lüscher formula
journal, July 2012

Relating the finite-volume spectrum and the two-and-three-particle $S$ matrix for relativistic systems of identical scalar particles
journal, April 2017

Analysis of Three-Hadron Final States
journal, October 1973

The three-boson system with short-range interactions
journal, February 1999

Renormalization of the Three-Body System with Short-Range Interactions
journal, January 1999

A method to measure the antikaon–nucleon scattering length in lattice QCD
journal, November 2009

Moving multichannel systems in a finite volume with application to proton-proton fusion
journal, November 2013

Timelike pion form factor in lattice QCD
journal, March 2015

Weak Transition Matrix Elements¶from Finite-Volume Correlation Functions
journal, May 2001

Three-particle quantization condition in a finite volume: 2. General formalism and the analysis of data
journal, October 2017

Resonance scattering phase shifts on a non-rest-frame lattice
journal, September 1995

Relativistic, model-independent, multichannel $2 \to 2$ transition amplitudes in a finite volume
journal, July 2016

The I = 1 pion–pion scattering amplitude and timelike pion form factor from Nf = 2 + 1 lattice QCD
journal, February 2019

Modified Isobar Approximation for $π - ρ$ Scattering
journal, June 1965

Relativistic, model-independent, three-particle quantization condition
journal, December 2014

Three particles in a finite volume
journal, May 2012

A solvable three-body model in finite volume
journal, November 2017

Coupled $π π$ , $K \bar{K}$ scattering in $P$ -wave and the $ρ$ resonance from lattice QCD
journal, November 2015

Three-particle scattering amplitudes from a finite volume formalism
journal, May 2013

Lattice QCD and the Timelike Pion Form Factor
journal, August 2011

Two-particle multichannel systems in a finite volume with arbitrary spin
journal, April 2014

Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
journal, December 2015

Minimal three-body equations with finite-range effects
journal, October 1975

Towards three-body unitarity in $D^{+} \to K^{-} π^{+} π^{+}$
journal, November 2011

Multichannel $1 \to 2$ transition amplitudes in a finite volume
journal, February 2015

Multichannel $0 \to 2$ and $1 \to 2$ transition amplitudes for arbitrary spin particles in a finite volume
journal, October 2015

Volume dependence of the energy spectrum in massive quantum field theories: II. Scattering states
journal, June 1986

Dynamically-coupled partial-waves in ρπ isospin-2 scattering from lattice QCD
journal, July 2018

Form factors of two-hadron states from a covariant finite-volume formalism
journal, August 2019

Tetraquark operators in lattice QCD and exotic flavour states in the charm sector
journal, November 2017

Minimal Three-Body Scattering Theory
journal, July 1974

Three-particle systems with resonant subprocesses in a finite volume
journal, January 2019

Two particle states and the S -matrix elements in multi-channel scattering
journal, July 2005

Matrix elements of unstable states
journal, September 2012

Three-body unitarity in the finite volume
journal, December 2017

Scattering phases for meson and baryon resonances on general moving-frame lattices
journal, November 2012

Isoscalar $π π$ Scattering and the $σ$ Meson Resonance from QCD
journal, January 2017

Resonances in Coupled $π K − η K$ Scattering from Quantum Chromodynamics
journal, October 2014

Finite volume corrections to the two-particle decay of states with nonzero momentum
journal, December 2005

Scattering processes and resonances from lattice QCD
journal, April 2018

Three-Body Unitarity and Khuri-Treiman Amplitudes
journal, December 1966

Extraction of isoscalar $π π$ phase shifts from lattice QCD
journal, July 2018

Elastic $I = 3 / 2$ $p$ -wave nucleon-pion scattering amplitude and the $Δ (1232)$ resonance from $N_{f} = 2 + 1$ lattice QCD
journal, January 2018

Numerical study of the relativistic three-body quantization condition in the isotropic approximation
journal, July 2018

Implementing the three-particle quantization condition including higher partial waves
journal, March 2019

Light nuclei and hypernuclei from quantum chromodynamics in the limit of SU(3) flavor symmetry
journal, February 2013

An $a_{0}$ resonance in strongly coupled $π η$ , $K \bar{K}$ scattering from lattice QCD
journal, May 2016

Two-particle states on a torus and their relation to the scattering matrix
journal, May 1991

Three-body spectrum in a finite volume: The role of cubic symmetry
journal, June 2018

Unitarity and the evaluation of discontinuities
journal, October 1962

Construction of Coupled Scattering and Production Amplitudes Satisfying Analyticity and Unitarity
journal, May 1960

Determination of s- and p-wave I = 1/2 Kπ scattering amplitudes in Nf = 2 + 1 lattice QCD
journal, July 2018

Three-body unitarity with isobars revisited
journal, September 2017

Baryon masses at nonzero isospin/kaon density
journal, October 2013

Unitary states for three pions
journal, July 1975

Unitarity and Production Amplitudes
journal, July 1962

Finite-volume effects for two-hadron states in moving frames
journal, October 2005

Phenomenology of relativistic $$\mathbf {3}\rightarrow \mathbf {3}$$ 3 → 3 reaction amplitudes within the isobar approximation
journal, January 2019

Scattering and Production Amplitudes with Unstable Particles
journal, October 1962

Determination of s - and p -wave I  = 1/2 Kπ scattering amplitudes in N f  = 2 + 1 lattice QCD
text, January 2018

Scattering phases for meson and baryon resonances on general moving-frame lattices
text, January 2012