Dispersive approaches for three-particle final state interaction

Guo, Peng; Danilkin, Igor V.; Szczepaniak, Adam P.

doi:10.1140/epja/i2015-15135-7

Title: Dispersive approaches for three-particle final state interaction

Abstract

In this work, we presented different representations of Khuri-Treiman equation, the advantage and disadvantage of each representations are discussed. With a scattering amplitude toy model, we also studied the sensitivity of solution of KT equation to left-hand cut of toy model and to the different approximate methods. At last, we give a brief discussion of Watson's theorem when three particles in final states are involved.

Authors:

Guo, Peng ^[1]; Danilkin, Igor V. ^[2]; Szczepaniak, Adam P. ^[1]

Indiana Univ., Bloomington, IN (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Publication Date:: Fri Oct 30 00:00:00 EDT 2015

Research Org.:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP)

OSTI Identifier:: 1226147

Report Number(s):: JLAB-THY-14-1953; DOE/OR/23177-3181; arXiv:1409.8652
Journal ID: ISSN 1434-6001; PII: 318; NSF grant: PHY-1205019

Grant/Contract Number:: AC05-06OR23177; FG02-87ER40365

Resource Type:: Accepted Manuscript

Journal Name:: European Physical Journal. A

Additional Journal Information:: Journal Volume: 51; Journal Issue: 10; Journal ID: ISSN 1434-6001

Publisher:: Springer

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Guo, Peng, Danilkin, Igor V., and Szczepaniak, Adam P. Dispersive approaches for three-particle final state interaction.  United States: N. p., 2015. 
Web.  doi:10.1140/epja/i2015-15135-7.

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                    Guo, Peng, Danilkin, Igor V., & Szczepaniak, Adam P. Dispersive approaches for three-particle final state interaction.  United States.  https://doi.org/10.1140/epja/i2015-15135-7

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                    Guo, Peng, Danilkin, Igor V., and Szczepaniak, Adam P. Fri .  
"Dispersive approaches for three-particle final state interaction".  United States.  https://doi.org/10.1140/epja/i2015-15135-7.  https://www.osti.gov/servlets/purl/1226147.

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@article{osti_1226147,

  title        = {Dispersive approaches for three-particle final state interaction},

  author       = {Guo, Peng and Danilkin, Igor V. and Szczepaniak, Adam P.},

  abstractNote = {In this work, we presented different representations of Khuri-Treiman equation, the advantage and disadvantage of each representations are discussed. With a scattering amplitude toy model, we also studied the sensitivity of solution of KT equation to left-hand cut of toy model and to the different approximate methods. At last, we give a brief discussion of Watson's theorem when three particles in final states are involved.},

  doi          = {10.1140/epja/i2015-15135-7},

  journal      = {European Physical Journal. A},

  number       = 10,

  volume       = 51,

  place        = {United States},

  year         = {Fri Oct 30 00:00:00 EDT 2015},

  month        = {Fri Oct 30 00:00:00 EDT 2015}

}

Copy to clipboard

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https://doi.org/10.1140/epja/i2015-15135-7

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Link, J. M.; Yager, P. M.; Anjos, J. C.
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Works referencing / citing this record:

Three-body unitarity with isobars revisited
journal, September 2017

Mai, M.; Hu, B.; Döring, M.
The European Physical Journal A, Vol. 53, Issue 9
DOI: 10.1140/epja/i2017-12368-4

Dispersive analysis of $$\eta \rightarrow 3 \pi $$ η → 3 π
journal, November 2018

Colangelo, Gilberto; Lanz, Stefan; Leutwyler, Heinrich
The European Physical Journal C, Vol. 78, Issue 11
DOI: 10.1140/epjc/s10052-018-6377-9

Solving integral equations in $$\eta \rightarrow 3\pi $$ η → 3 π
journal, November 2018

Gasser, Jürg; Rusetsky, Akaki
The European Physical Journal C, Vol. 78, Issue 11
DOI: 10.1140/epjc/s10052-018-6378-8

Variational approach to $N$-body interactions in finite volume
text, January 2018

Guo, Peng; Döring, Michael; Szczepaniak, Adam P.
arXiv
DOI: 10.48550/arxiv.1810.01261

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Title: Dispersive approaches for three-particle final state interaction

Abstract

Citation Formats

Pion-Pion Scattering and K ± → 3 π Decay journal, August 1960

Khuri-Treiman Representation and Perturbation Theory journal, December 1963

Final-state interactions among three particles journal, January 1965

Dispersion Theory Model of Three-Body Production and Decay Processes journal, February 1965

Dispersion Theory of Three-Body Production and Decay Processes journal, February 1967

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

Khuri-Treiman-Type Equations for Three-Body Decay and Production Processes journal, June 1968

Khuri-Treiman-Type Equations for Three-Body Decay and Production Processes. II journal, January 1969

Final state interactions and Khuri-Treiman equations in,ν → 3π decays journal, April 1996

Dispersive analysis of the decay η → 3π journal, May 1996

Analytical dispersive construction of η → 3 π amplitude: First order in isospin breaking journal, December 2011

Analyticity of $$\eta \pi $$ η π isospin-violating form factors and the $$\tau \rightarrow \eta \pi \nu $$ τ → η π ν second-class decay journal, July 2014

Eta Decays at and Beyond p4 in Chiral Perturbation Theory journal, January 2002

Dispersive analysis of ω / ϕ → 3 π , π γ * journal, May 2015

Three-body final state interaction in η → 3 π journal, September 2015

On the solution of certain singular integral equations of quantum field theory journal, April 1958

Theory of the Low-Energy Pion-Pion Interaction journal, July 1960

Analysis of Partial-Wave Dispersion Relations journal, April 1963

Unitarity Condition Below Physical Thresholds in the Normal and Anomalous Cases journal, January 1960

Effect of a Pion-Pion Scattering Resonance on Nucleon Structure journal, April 1959

Mass and Width of the Lowest Resonance in QCD journal, April 2006

Precise Determination of the f 0 ( 600 ) and f 0 ( 980 ) Pole Parameters from a Dispersive Data Analysis journal, August 2011

Photon– and pion–nucleon interactions in a unitary and causal effective field theory based on the chiral Lagrangian journal, December 2010

Dynamical light vector mesons in low-energy scattering of Goldstone bosons journal, September 2011

Unitary analytic isobar model for the reaction nucleon-meson to nucleon-meson-meson journal, June 1978

The Effect of Final State Interactions on Reaction Cross Sections journal, December 1952

Rescattering effects in three-particle final states. I.—The Model journal, September 1967

Coherence in Three-Body Final States journal, June 1967

Watson's Theorem When There Are Three Strongly Interacting Particles in the Final State journal, September 1968

Regge theory for multiparticle amplitudes journal, December 1974

Construction of Unitary Scattering Amplitudes journal, May 1961

Unitarity and Production Amplitudes journal, July 1962

ω → π 0 γ * and ϕ → π 0 γ * transition form factors in dispersion theory journal, September 2012

Constraints on the $$\mathbf {\omega \pi }$$ ω π form factor from analyticity and unitarity journal, December 2014

Testing the consistency of the ω π transition form factor with unitarity and analyticity journal, July 2015

Model-independent measurement of S -wave K − π + systems using D + → K π π decays from Fermilab E791 journal, February 2006

Dalitz plot analysis of the D + → K − π + π + decay journal, September 2008

Rescattering effects and the σ pole in hadronic decays journal, July 2006

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

Diffractive Dissociation into π[sup −]π[sup −]π[sup +] Final States at COMPASS conference, January 2011

Some Experimental Consequences of Triangle Singularities in Production Processes journal, July 1962

Puzzle of Anomalously Large Isospin Violations in η ( 1405 / 1475 ) → 3 π journal, February 2012

Systematic study of the singularity mechanism in heavy quarkonium decays journal, August 2013

Decoding the Riddle of Y ( 4260 ) and Z c ( 3900 ) journal, September 2013

Three-body unitarity with isobars revisited journal, September 2017

Dispersive analysis of $$\eta \rightarrow 3 \pi $$ η → 3 π journal, November 2018

Solving integral equations in $$\eta \rightarrow 3\pi $$ η → 3 π journal, November 2018

Variational approach to $N$-body interactions in finite volume text, January 2018

Pion-Pion Scattering and $K^{\pm} \to 3 π$ Decay
journal, August 1960

Khuri-Treiman Representation and Perturbation Theory
journal, December 1963

Final-state interactions among three particles
journal, January 1965

Dispersion Theory Model of Three-Body Production and Decay Processes
journal, February 1965

Dispersion Theory of Three-Body Production and Decay Processes
journal, February 1967

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

Khuri-Treiman-Type Equations for Three-Body Decay and Production Processes
journal, June 1968

Khuri-Treiman-Type Equations for Three-Body Decay and Production Processes. II
journal, January 1969

Final state interactions and Khuri-Treiman equations in,ν → 3π decays
journal, April 1996

Dispersive analysis of the decay η → 3π
journal, May 1996

Analytical dispersive construction of $η \to 3 π$ amplitude: First order in isospin breaking
journal, December 2011

Analyticity of $$\eta \pi $$ η π isospin-violating form factors and the $$\tau \rightarrow \eta \pi \nu $$ τ → η π ν second-class decay
journal, July 2014

Eta Decays at and Beyond p4 in Chiral Perturbation Theory
journal, January 2002

Dispersive analysis of $ω / ϕ \to 3 π, π γ^{*}$
journal, May 2015

Three-body final state interaction in $η \to 3 π$
journal, September 2015

On the solution of certain singular integral equations of quantum field theory
journal, April 1958

Theory of the Low-Energy Pion-Pion Interaction
journal, July 1960

Analysis of Partial-Wave Dispersion Relations
journal, April 1963

Unitarity Condition Below Physical Thresholds in the Normal and Anomalous Cases
journal, January 1960

Effect of a Pion-Pion Scattering Resonance on Nucleon Structure
journal, April 1959

Mass and Width of the Lowest Resonance in QCD
journal, April 2006

Precise Determination of the $f_{0} (600)$ and $f_{0} (980)$ Pole Parameters from a Dispersive Data Analysis
journal, August 2011

Photon– and pion–nucleon interactions in a unitary and causal effective field theory based on the chiral Lagrangian
journal, December 2010

Dynamical light vector mesons in low-energy scattering of Goldstone bosons
journal, September 2011

Unitary analytic isobar model for the reaction nucleon-meson to nucleon-meson-meson
journal, June 1978

The Effect of Final State Interactions on Reaction Cross Sections
journal, December 1952

Rescattering effects in three-particle final states. I.—The Model
journal, September 1967

Coherence in Three-Body Final States
journal, June 1967

Watson's Theorem When There Are Three Strongly Interacting Particles in the Final State
journal, September 1968

Regge theory for multiparticle amplitudes
journal, December 1974

Construction of Unitary Scattering Amplitudes
journal, May 1961

Unitarity and Production Amplitudes
journal, July 1962

$ω \to π^{0} γ^{}$ and $ϕ \to π^{0} γ^{}$ transition form factors in dispersion theory
journal, September 2012

Constraints on the $$\mathbf {\omega \pi }$$ ω π form factor from analyticity and unitarity
journal, December 2014

Testing the consistency of the $ω π$ transition form factor with unitarity and analyticity
journal, July 2015

Model-independent measurement of $S$ -wave $K^{-} π^{+}$ systems using $D^{+} \to K π π$ decays from Fermilab E791
journal, February 2006

Dalitz plot analysis of the $D^{+} \to K^{-} π^{+} π^{+}$ decay
journal, September 2008

Rescattering effects and the σ pole in hadronic decays
journal, July 2006

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

Diffractive Dissociation into π[sup −]π[sup −]π[sup +] Final States at COMPASS
conference, January 2011

Some Experimental Consequences of Triangle Singularities in Production Processes
journal, July 1962

Puzzle of Anomalously Large Isospin Violations in $η (1405 / 1475) \to 3 π$
journal, February 2012

Systematic study of the singularity mechanism in heavy quarkonium decays
journal, August 2013

Decoding the Riddle of $Y (4260)$ and $Z_{c} (3900)$
journal, September 2013

Three-body unitarity with isobars revisited
journal, September 2017

Dispersive analysis of $$\eta \rightarrow 3 \pi $$ η → 3 π
journal, November 2018

Solving integral equations in $$\eta \rightarrow 3\pi $$ η → 3 π
journal, November 2018

Variational approach to $N$-body interactions in finite volume
text, January 2018