Dalitz-plot decomposition for three-body decays

Mikhasenko, M.; Albaladejo, M.; Bibrzycki, Ł.; Fernández-Ramírez, C.; Mathieu, V.; Mitchell, S.; Pappagallo, M.; Pilloni, A.; Winney, D.; Skwarnicki, T.; Szczepaniak, A. P.

doi:10.1103/PhysRevD.101.034033

Title: Dalitz-plot decomposition for three-body decays

Abstract

We present a general formalism to write the decay amplitude for multibody reactions with explicit separation of the rotational degrees of freedom, which are well controlled by the spin of the decay particle, and dynamic functions on the subchannel invariant masses, which require modeling. Using the three-particle kinematics we demonstrate the proposed factorization, named the Dalitz-plot decomposition. The Wigner rotations, which are subtle factors needed by the isobar modeling in the helicity framework, are simplified with the proposed decomposition. Consequently, we are able to provide them in an explicit form suitable for the general case of arbitrary spins. The only unknown model-dependent factors are the isobar line shapes that describe the subchannel dynamics. The advantages of the new decomposition are shown through three examples relevant for the recent discovery of the exotic charmonium candidate Z_c(4430), the pentaquarks P_c, and the intriguing Λ$$^+_c$$ → pK^– π⁺ decay.

Authors:

Mikhasenko, M.; Albaladejo, M.;

;

; Pappagallo, M.;

; Winney, D.;

; Szczepaniak, A. P.

Publication Date:: 2020-02-27

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)

OSTI Identifier:: 1602381

Alternate Identifier(s):: OSTI ID: 1602421

Report Number(s):: JLAB-THY-19-3070; DOE/OR/23177-4794
Journal ID: ISSN 2470-0010; PRVDAQ; 034033

Grant/Contract Number:: AC05-06OR23177; FG02-87ER40365; PHY-1415459; PHY-1803004; IA101819; 251817; A1-S-21389; 2018/29/B/ST2/02576; EXC-2094–390783311

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 101 Journal Issue: 3; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Hadron-hadron interactions; Particle decays; Particle production; Scattering amplitudes; Particle properties; Polarization

Citation Formats


                    Mikhasenko, M., Albaladejo, M., Bibrzycki, Ł., Fernández-Ramírez, C., Mathieu, V., Mitchell, S., Pappagallo, M., Pilloni, A., Winney, D., Skwarnicki, T., and Szczepaniak, A. P. Dalitz-plot decomposition for three-body decays.  United States: N. p., 2020. 
        Web.  doi:10.1103/PhysRevD.101.034033.

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                    Mikhasenko, M., Albaladejo, M., Bibrzycki, Ł., Fernández-Ramírez, C., Mathieu, V., Mitchell, S., Pappagallo, M., Pilloni, A., Winney, D., Skwarnicki, T., & Szczepaniak, A. P. Dalitz-plot decomposition for three-body decays.  United States.  doi:https://doi.org/10.1103/PhysRevD.101.034033

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                    Mikhasenko, M., Albaladejo, M., Bibrzycki, Ł., Fernández-Ramírez, C., Mathieu, V., Mitchell, S., Pappagallo, M., Pilloni, A., Winney, D., Skwarnicki, T., and Szczepaniak, A. P. Thu .  
        "Dalitz-plot decomposition for three-body decays".  United States.  doi:https://doi.org/10.1103/PhysRevD.101.034033.

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@article{osti_1602381,

  title        = {Dalitz-plot decomposition for three-body decays},

  author       = {Mikhasenko, M. and Albaladejo, M. and Bibrzycki, Ł. and Fernández-Ramírez, C. and Mathieu, V. and Mitchell, S. and Pappagallo, M. and Pilloni, A. and Winney, D. and Skwarnicki, T. and Szczepaniak, A. P.},

  abstractNote = {We present a general formalism to write the decay amplitude for multibody reactions with explicit separation of the rotational degrees of freedom, which are well controlled by the spin of the decay particle, and dynamic functions on the subchannel invariant masses, which require modeling. Using the three-particle kinematics we demonstrate the proposed factorization, named the Dalitz-plot decomposition. The Wigner rotations, which are subtle factors needed by the isobar modeling in the helicity framework, are simplified with the proposed decomposition. Consequently, we are able to provide them in an explicit form suitable for the general case of arbitrary spins. The only unknown model-dependent factors are the isobar line shapes that describe the subchannel dynamics. The advantages of the new decomposition are shown through three examples relevant for the recent discovery of the exotic charmonium candidate Zc(4430), the pentaquarks Pc, and the intriguing Λ$^+_c$ → pK– π+ decay.},

  doi          = {10.1103/PhysRevD.101.034033},

  journal      = {Physical Review D},

  number       = 3,

  volume       = 101,

  place        = {United States},

  year         = {2020},

  month        = {2}

}

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DOI: https://doi.org/10.1103/PhysRevD.101.034033

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Title: Dalitz-plot decomposition for three-body decays

Abstract

Citation Formats

On the search for the electric dipole moment of strange and charm baryons at LHC journal, March 2017

Partial-Wave Analysis of the Deck Amplitude for π N → π π π N journal, December 1973

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

Erratum: Helicity-coupling amplitudes in tensor formalism [Phys. Rev. D 48 , 1225 (1993)] journal, October 1997

Λ 0 Hyperon Polarization in Inclusive Production by 300-GeV Protons on Beryllium journal, May 1976

Model-Independent Observation of Exotic Contributions to B 0 → J / ψ K + π − Decays journal, April 2019

Covariant spin tensors in meson spectroscopy journal, March 1995

Beyond the isobar model: Rescattering in the system of three particles. conference, December 2016

Nonstandard heavy mesons and baryons: Experimental evidence journal, February 2018

Observation of a new charged charmoniumlike state in B ¯ 0 → J / ψ K − π + decays journal, December 2014

Helicity-coupling amplitudes in tensor formalism journal, August 1993

Dalitz analysis of B → K π + ψ ′ decays and the Z ( 4430 ) + journal, August 2009

Observation of the Resonant Character of the Z ( 4430 ) − State journal, June 2014

Covariant helicity-coupling amplitudes: A new formulation journal, October 2008

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

Observation of a Narrow Pentaquark State, P c ( 4312 ) + , and of the Two-Peak Structure of the P c ( 4450 ) + journal, June 2019

Feasibility of beauty baryon polarization measurement in the Lambda 0 J/psi decay channel with the pp collider experiment journal, May 1995

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

Measurements of the branching fractions of Λ c + → pπ−π+, Λ c + → pK−K+, and Λ c + → pπ−K+ journal, March 2018

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

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

Production, decay, and polarization of excited heavy hadrons journal, April 1994

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

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

Model-Independent Evidence for J / ψ p Contributions to Λ b 0 → J / ψ p K − Decays journal, August 2016

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

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

Review of Particle Physics journal, August 2018

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

Experimental constraints on the spin and parity of the Z ( 4430 ) + journal, October 2013

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

Multidimensional resonance analysis of Λc+→pK−π+ journal, January 2000

Model-independent confirmation of the Z ( 4430 ) − state journal, December 2015

Observation of J / ψ p Resonances Consistent with Pentaquark States in Λ b 0 → J / ψ K − p Decays journal, August 2015

Multiquark resonances journal, January 2017

Partial decay widths of baryons in the spin-momentum operator expansion method journal, October 2006

Kinematical singularities in cross-sections and density matrices journal, May 1968

Are there important unitarity corrections to the isobar model? journal, July 1979

Towards the experimental clarification of quarkonium polarization journal, September 2010

First Observation of the Doubly Cabibbo-Suppressed Decay of a Charmed Baryon: Λ c + → p K + π − journal, June 2016

Centrifugal-Barrier Effects in Resonance Partial Decay Widths, Shapes, and Production Amplitudes journal, February 1972

Use of Angular-Momentum Tensors journal, October 1965

Determination of the b → c handedness using nonleptonic Λ c decays journal, March 1994

Visible narrow cusp structure in Λ c + → p K − π + enhanced by triangle singularity journal, September 2019

On the search for the electric dipole moment of strange and charm baryons at LHC
journal, March 2017

Partial-Wave Analysis of the Deck Amplitude for $π N \to π π π N$
journal, December 1973

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

Erratum: Helicity-coupling amplitudes in tensor formalism [Phys. Rev. D 48 , 1225 (1993)]
journal, October 1997

$Λ^{0}$ Hyperon Polarization in Inclusive Production by 300-GeV Protons on Beryllium
journal, May 1976

Model-Independent Observation of Exotic Contributions to $B^{0} \to J / ψ K^{+} π^{-}$ Decays
journal, April 2019

Covariant spin tensors in meson spectroscopy
journal, March 1995

Beyond the isobar model: Rescattering in the system of three particles.
conference, December 2016

Nonstandard heavy mesons and baryons: Experimental evidence
journal, February 2018

Observation of a new charged charmoniumlike state in ${\bar{B}}^{0} \to J / ψ K^{-} π^{+}$ decays
journal, December 2014

Helicity-coupling amplitudes in tensor formalism
journal, August 1993

Dalitz analysis of $B \to K π^{+} ψ^{'}$ decays and the $Z (4430)^{+}$
journal, August 2009

Observation of the Resonant Character of the $Z (4430)^{-}$ State
journal, June 2014

Covariant helicity-coupling amplitudes: A new formulation
journal, October 2008

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

Observation of a Narrow Pentaquark State, $P_{c} (4312)^{+}$ , and of the Two-Peak Structure of the $P_{c} (4450)^{+}$
journal, June 2019

Feasibility of beauty baryon polarization measurement in the Lambda ⁰ J/psi decay channel with the pp collider experiment
journal, May 1995

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

Measurements of the branching fractions of Λ c + → pπ−π+, Λ c + → pK−K+, and Λ c + → pπ−K+
journal, March 2018

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

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

Production, decay, and polarization of excited heavy hadrons
journal, April 1994

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

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

Model-Independent Evidence for $J / ψ p$ Contributions to $Λ_{b}^{0} \to J / ψ p K^{-}$ Decays
journal, August 2016

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

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

Review of Particle Physics
journal, August 2018

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

Experimental constraints on the spin and parity of the $Z (4430)^{+}$
journal, October 2013

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

Multidimensional resonance analysis of Λc+→pK−π+
journal, January 2000

Model-independent confirmation of the $Z (4430)^{-}$ state
journal, December 2015

Observation of $J / ψ p$ Resonances Consistent with Pentaquark States in $Λ_{b}^{0} \to J / ψ K^{-} p$ Decays
journal, August 2015

Multiquark resonances
journal, January 2017

Partial decay widths of baryons in the spin-momentum operator expansion method
journal, October 2006

Kinematical singularities in cross-sections and density matrices
journal, May 1968

Are there important unitarity corrections to the isobar model?
journal, July 1979

Towards the experimental clarification of quarkonium polarization
journal, September 2010

First Observation of the Doubly Cabibbo-Suppressed Decay of a Charmed Baryon: $Λ_{c}^{+} \to p K^{+} π^{-}$
journal, June 2016

Centrifugal-Barrier Effects in Resonance Partial Decay Widths, Shapes, and Production Amplitudes
journal, February 1972

Use of Angular-Momentum Tensors
journal, October 1965

Determination of the $b \to c$ handedness using nonleptonic $Λ_{c}$ decays
journal, March 1994

Visible narrow cusp structure in $Λ_{c}^{+} \to p K^{-} π^{+}$ enhanced by triangle singularity
journal, September 2019