Khuri-Treiman equations for 3$π$ decays of particles with spin

Albaladejo, M.; Winney, D.; Danilkin, I. V.; Fernández-Ramírez, C.; Mathieu, V.; Mikhasenko, M.; Pilloni, A.; Silva-Castro, J. A.; Szczepaniak, A. P.

doi:10.1103/PhysRevD.101.054018

Title: Khuri-Treiman equations for 3$$π$$ decays of particles with spin

Abstract

Khuri-Treiman equations have proven to be a useful theoretical tool in the analysis of three-body decays, especially into the 3$$π$$ final state. In this work we present in full detail the necessary generalization of the formalism to study the decays of particles with arbitrary spin, parity, and charge conjugation. To this extent, we find it most convenient to work with helicity amplitudes instead of the so-called invariant amplitudes, especially when dealing with the unitarity relations. The isobar expansions in the three possible (s-, t-, and u-) final channels are related with the appropriate crossing matrices. We pay special attention to the kinematical singularities and constraints of the helicity amplitudes, showing that these can be derived by means of the crossing matrix.

Authors:: Albaladejo, M.; Winney, D.; Danilkin, I. V.; Fernández-Ramírez, C.; Mathieu, V.; Mikhasenko, M.; Pilloni, A.; Silva-Castro, J. A.; Szczepaniak, A. P.; JPAC Collaboration

Publication Date:: Fri Mar 13 00:00:00 EDT 2020

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

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP); National Science Foundation (NSF); Ministerio de Ciencia, Innovación y Universidades (Spain); National Autonomous University of Mexico (UNAM); Consejo Nacional de Ciencia y Tecnología (CONACYT); German Research Foundation (DFG); German Excellence Strategy; Comunidad Autónoma de Madrid

Contributing Org.:: JPAC Collaboration

OSTI Identifier:: 1604504

Alternate Identifier(s):: OSTI ID: 1604951

Report Number(s):: JLAB-THY-19-3066; DOE/OR/23177-4788
Journal ID: ISSN 2470-0010; PRVDAQ; 054018

Grant/Contract Number:: AC05-06OR23177; FG02-87ER40365; PHY-1415459; IA101819; 251817; 734789; A1-S-21389; 204404729—SFB 1044; FPA2016-77313-P; FPA2016-75654-C2-2-P; 39083149

Resource Type:: Published Article

Journal Name:: Physical Review. D.

Additional Journal Information:: Journal Name: Physical Review. D. Journal Volume: 101 Journal Issue: 5; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Albaladejo, M., Winney, D., Danilkin, I. V., Fernández-Ramírez, C., Mathieu, V., Mikhasenko, M., Pilloni, A., Silva-Castro, J. A., Szczepaniak, A. P., and JPAC Collaboration. Khuri-Treiman equations for 3$π$ decays of particles with spin.  United States: N. p., 2020. 
Web.  doi:10.1103/PhysRevD.101.054018.

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                    Albaladejo, M., Winney, D., Danilkin, I. V., Fernández-Ramírez, C., Mathieu, V., Mikhasenko, M., Pilloni, A., Silva-Castro, J. A., Szczepaniak, A. P., & JPAC Collaboration. Khuri-Treiman equations for 3$π$ decays of particles with spin.  United States.  https://doi.org/10.1103/PhysRevD.101.054018

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                    Albaladejo, M., Winney, D., Danilkin, I. V., Fernández-Ramírez, C., Mathieu, V., Mikhasenko, M., Pilloni, A., Silva-Castro, J. A., Szczepaniak, A. P., and JPAC Collaboration. Fri .  
"Khuri-Treiman equations for 3$π$ decays of particles with spin".  United States.  https://doi.org/10.1103/PhysRevD.101.054018.

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@article{osti_1604504,

  title        = {Khuri-Treiman equations for 3$π$ decays of particles with spin},

  author       = {Albaladejo, M. and Winney, D. and Danilkin, I. V. and Fernández-Ramírez, C. and Mathieu, V. and Mikhasenko, M. and Pilloni, A. and Silva-Castro, J. A. and Szczepaniak, A. P. and JPAC Collaboration},

  abstractNote = {Khuri-Treiman equations have proven to be a useful theoretical tool in the analysis of three-body decays, especially into the 3$π$ final state. In this work we present in full detail the necessary generalization of the formalism to study the decays of particles with arbitrary spin, parity, and charge conjugation. To this extent, we find it most convenient to work with helicity amplitudes instead of the so-called invariant amplitudes, especially when dealing with the unitarity relations. The isobar expansions in the three possible (s-, t-, and u-) final channels are related with the appropriate crossing matrices. We pay special attention to the kinematical singularities and constraints of the helicity amplitudes, showing that these can be derived by means of the crossing matrix.},

  doi          = {10.1103/PhysRevD.101.054018},

  journal      = {Physical Review. D.},

  number       = 5,

  volume       = 101,

  place        = {United States},

  year         = {Fri Mar 13 00:00:00 EDT 2020},

  month        = {Fri Mar 13 00:00:00 EDT 2020}

}

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Title: Khuri-Treiman equations for 3$$π$$ decays of particles with spin

Abstract

Citation Formats

Three-body final state interaction in η→ 3π updated journal, August 2017

Pole position of the a 1 ( 1260 ) from τ -decay journal, November 2018

On kinematical constraints in boson-boson systems journal, September 2012

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

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

Kinematical constraints in fermion-antifermion systems journal, December 2011

Pion-pion scattering amplitude. IV. Improved analysis with once subtracted Roy-like equations up to 1100 MeV journal, April 2011

Dispersion-theoretical analysis of the D + → K − π + π + Dalitz plot journal, October 2015

Consistent Dalitz plot analysis of Cabibbo-favored D + → K ¯ π π + decays journal, May 2018

On the General Theory of Collisions for Particles with Spin journal, April 2000

Kinematical singularities, crossing matrix and kinematical constraints for two-body helicity amplitudes journal, February 1968

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Analyticity Properties of Helicity Amplitudes and Construction of Kinematical Singularity-Free Amplitudes for Any Spin journal, October 1964

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

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Review of Particle Physics journal, August 2018

A Master Formula for Chiral Symmetry Breaking journal, May 1996

Resonance production and π π S -wave in π − + p → π − π − π + + p recoil at 190 GeV / c journal, February 2017

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

Dalitz plot analysis of the decay ω → π + π − π 0 journal, December 2018

η→3π at two loops in Chiral Perturbation Theory journal, November 2007

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

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

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

Final-state interaction and current algebra in K3π and η3π decays journal, March 1970

Extended chiral Khuri–Treiman formalism for $$\eta \rightarrow 3\pi $$ η → 3 π and the role of the $$a_0(980)$$ a 0 ( 980 ) , $$f_0(980)$$ f 0 ( 980 ) resonances journal, August 2017

Dispersive approach to chiral perturbation theory journal, December 2008

Dispersive analysis of ω→3π and ϕ→3π decays journal, May 2012

Kinematic Singularities of Partial-Wave Scattering Amplitudes journal, December 1966

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

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

Final-state interactions in a system of three pions journal, March 1981

Khuri–Treiman equations for $$\pi \pi $$ π π scattering journal, July 2018

What π − π scattering tells us about chiral perturbation theory journal, May 1993

Crossing relations for helicity amplitudes journal, February 1964

η → 3 π : Study of the Dalitz Plot and Extraction of the Quark Mass Ratio Q journal, January 2017

Dispersion relations for $$\eta '\rightarrow \eta \pi \pi $$ η ′ → η π π journal, July 2017

Equivalence of three-particle scattering formalisms journal, August 2019

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

Khuri-Treiman Representation and Perturbation Theory journal, December 1963

Amplitude analysis and the nature of the Z c (3900) journal, September 2017

General Method of Constructing Helicity Amplitudes Free from Kinematic Singularities and Zeros journal, February 1966

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

Roy equation analysis of ππ scattering journal, November 2001

What is the right formalism to search for resonances? II. The pentaquark chain: Joint Physics Analysis Center journal, September 2018

What is the right formalism to search for resonances? journal, March 2018

Observation of a J PC = 1 − + Exotic Resonance in Diffractive Dissociation of 190 GeV / c π − into π − π − π + journal, June 2010

Kinematic Singularities and Threshold Relations for Helicity Amplitudes journal, May 1968

On the general theory of collisions for particles with spin journal, August 1959

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

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

Kinematics of General Scattering Processes and the Mandelstam Representation journal, February 1960

Crossing Relations for Helicity Amplitudes journal, February 1971

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

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

Exact integral equation for pion-pion scattering involving only physical region partial waves journal, September 1971

Dalitz-plot decomposition for three-body decays journal, February 2020

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journal, August 2017

Pole position of the $a_{1} (1260)$ from $τ$ -decay
journal, November 2018

On kinematical constraints in boson-boson systems
journal, September 2012

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

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

Kinematical constraints in fermion-antifermion systems
journal, December 2011

Pion-pion scattering amplitude. IV. Improved analysis with once subtracted Roy-like equations up to 1100 MeV
journal, April 2011

Dispersion-theoretical analysis of the D + → K − π + π + Dalitz plot
journal, October 2015

Consistent Dalitz plot analysis of Cabibbo-favored D + → K ¯ π π + decays
journal, May 2018

On the General Theory of Collisions for Particles with Spin
journal, April 2000

Kinematical singularities, crossing matrix and kinematical constraints for two-body helicity amplitudes
journal, February 1968

Kinematic Singularities of Helicity and Transversity Amplitudes and Asymptotic Regge‐Pole Contributions
journal, November 1968

Analyticity Properties of Helicity Amplitudes and Construction of Kinematical Singularity-Free Amplitudes for Any Spin
journal, October 1964

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

Coupled-channel approach in hadron–hadron scattering
journal, January 2020

Review of Particle Physics
journal, August 2018

A Master Formula for Chiral Symmetry Breaking
journal, May 1996

Resonance production and $π π$ $S$ -wave in $π^{-} + p \to π^{-} π^{-} π^{+} + p_{recoil}$ at $190 GeV / c$
journal, February 2017

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

Dalitz plot analysis of the decay $ω \to π^{+} π^{-} π^{0}$
journal, December 2018

η→3π at two loops in Chiral Perturbation Theory
journal, November 2007

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

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

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

Final-state interaction and current algebra in K3π and η3π decays
journal, March 1970

Extended chiral Khuri–Treiman formalism for $$\eta \rightarrow 3\pi $$ η → 3 π and the role of the $$a_0(980)$$ a 0 ( 980 ) , $$f_0(980)$$ f 0 ( 980 ) resonances
journal, August 2017

Dispersive approach to chiral perturbation theory
journal, December 2008

Dispersive analysis of ω→3π and ϕ→3π decays
journal, May 2012

Kinematic Singularities of Partial-Wave Scattering Amplitudes
journal, December 1966

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

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

Final-state interactions in a system of three pions
journal, March 1981

Khuri–Treiman equations for $$\pi \pi $$ π π scattering
journal, July 2018

What $π - π$ scattering tells us about chiral perturbation theory
journal, May 1993

Crossing relations for helicity amplitudes
journal, February 1964

$η \to 3 π$ : Study of the Dalitz Plot and Extraction of the Quark Mass Ratio $Q$
journal, January 2017

Dispersion relations for $$\eta '\rightarrow \eta \pi \pi $$ η ′ → η π π
journal, July 2017

Equivalence of three-particle scattering formalisms
journal, August 2019

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

Khuri-Treiman Representation and Perturbation Theory
journal, December 1963

Amplitude analysis and the nature of the Z c (3900)
journal, September 2017

General Method of Constructing Helicity Amplitudes Free from Kinematic Singularities and Zeros
journal, February 1966

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

Roy equation analysis of ππ scattering
journal, November 2001

What is the right formalism to search for resonances? II. The pentaquark chain: Joint Physics Analysis Center
journal, September 2018

What is the right formalism to search for resonances?
journal, March 2018

Observation of a $J^{PC} = 1^{- +}$ Exotic Resonance in Diffractive Dissociation of $190 GeV / c$ $π^{-}$ into $π^{-} π^{-} π^{+}$
journal, June 2010

Kinematic Singularities and Threshold Relations for Helicity Amplitudes
journal, May 1968

On the general theory of collisions for particles with spin
journal, August 1959

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

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

Kinematics of General Scattering Processes and the Mandelstam Representation
journal, February 1960

Crossing Relations for Helicity Amplitudes
journal, February 1971

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

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

Exact integral equation for pion-pion scattering involving only physical region partial waves
journal, September 1971

Dalitz-plot decomposition for three-body decays
journal, February 2020