η→3π: Study of the Dalitz plot and extraction of the Quark Mass Ratio Q [The decay η→3π: Study of the Dalitz plot and extraction of the quark mass ratio Q]

doi:10.1103/PhysRevLett.118.022001

Title: $η \to 3 π$ : Study of the Dalitz plot and extraction of the Quark Mass Ratio $Q$ [The decay $η \to 3 π$ : Study of the Dalitz plot and extraction of the quark mass ratio $Q$ ]

Abstract

The $$\eta\to 3\pi$$ amplitude is sensitive to the quark mass difference $$m_u-m_d$$ and offers a unique way to determine the quark mass ratio $$Q^2\equiv (m_s^2-m_{ud}^2)/(m_d^2-m_u^2)$$ from experiment. We calculate the amplitude dispersively and fit the KLOE data on the charged mode, varying the subtraction constants in the range allowed by chiral perturbation theory. The parameter-free predictions obtained for the neutral Dalitz plot and the neutral-to-charged branching ratio are in excellent agreement with experiment. Lastly, our representation of the transition amplitude implies $$Q = 22.0 \pm 0.7$$.

Authors:

Colangelo, Gilberto ^[1]; Lanz, Stefan ^[1]; Leutwyler, Heinrich ^[1]; Passemar, Emilie ^[2]

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

Publication Date:: 2017-01-09

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:: 1343881

Alternate Identifier(s):: OSTI ID: 1338658

Report Number(s):: JLAB-THY-16-2360; DOE/OR/23177-3959; arXiv:1610.03494
Journal ID: ISSN 0031-9007; PRLTAO; TRN: US1701022

Grant/Contract Number:: AC05-06OR23177

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review Letters

Additional Journal Information:: Journal Volume: 118; Journal Issue: 2; Journal ID: ISSN 0031-9007

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Colangelo, Gilberto, Lanz, Stefan, Leutwyler, Heinrich, and Passemar, Emilie. η→3π: Study of the Dalitz plot and extraction of the Quark Mass Ratio Q [The decay η→3π: Study of the Dalitz plot and extraction of the quark mass ratio Q].  United States: N. p., 2017. 
        Web.  doi:10.1103/PhysRevLett.118.022001.

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                    Colangelo, Gilberto, Lanz, Stefan, Leutwyler, Heinrich, & Passemar, Emilie. η→3π: Study of the Dalitz plot and extraction of the Quark Mass Ratio Q [The decay η→3π: Study of the Dalitz plot and extraction of the quark mass ratio Q].  United States.  doi:10.1103/PhysRevLett.118.022001.

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                    Colangelo, Gilberto, Lanz, Stefan, Leutwyler, Heinrich, and Passemar, Emilie. Mon .  
        "η→3π: Study of the Dalitz plot and extraction of the Quark Mass Ratio Q [The decay η→3π: Study of the Dalitz plot and extraction of the quark mass ratio Q]".  United States.  doi:10.1103/PhysRevLett.118.022001.  https://www.osti.gov/servlets/purl/1343881.

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@article{osti_1343881,

  title        = {η→3π: Study of the Dalitz plot and extraction of the Quark Mass Ratio Q [The decay η→3π: Study of the Dalitz plot and extraction of the quark mass ratio Q]},

  author       = {Colangelo, Gilberto and Lanz, Stefan and Leutwyler, Heinrich and Passemar, Emilie},

  abstractNote = {The $\eta\to 3\pi$ amplitude is sensitive to the quark mass difference $m_u-m_d$ and offers a unique way to determine the quark mass ratio $Q^2\equiv (m_s^2-m_{ud}^2)/(m_d^2-m_u^2)$ from experiment. We calculate the amplitude dispersively and fit the KLOE data on the charged mode, varying the subtraction constants in the range allowed by chiral perturbation theory. The parameter-free predictions obtained for the neutral Dalitz plot and the neutral-to-charged branching ratio are in excellent agreement with experiment. Lastly, our representation of the transition amplitude implies $Q = 22.0 \pm 0.7$.},

  doi          = {10.1103/PhysRevLett.118.022001},

  journal      = {Physical Review Letters},

  number       = 2,

  volume       = 118,

  place        = {United States},

  year         = {2017},

  month        = {1}

}

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DOI: 10.1103/PhysRevLett.118.022001

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Works referencing / citing this record:

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

Albaladejo, M.; Sherrill, N.; Fernández-Ramírez, C.
The European Physical Journal C, Vol. 78, Issue 7
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Constraints on low energy QCD parameters from $$\eta \rightarrow 3\pi $$ η → 3 π and $$\pi \pi $$ π π scattering
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Kolesár, Marián; Novotný, Jiří
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Khuri–Treiman equations for $$\pi \pi $$ π π scattering
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Albaladejo, M.; Sherrill, N.; Fernández-Ramírez, C.
The European Physical Journal C, Vol. 78, Issue 7
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Isospin splittings in the decuplet baryon spectrum from dynamical QCD + QED
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Horsley, R.; Koumi, Z.; Nakamura, Y.
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Theoretical analysis of the $γ γ \to π^{0} η$ process
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Isken, Tobias; Kubis, Bastian; Schneider, Sebastian P.
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Dispersive analysis of $$\eta \rightarrow 3 \pi $$ η → 3 π
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Colangelo, Gilberto; Lanz, Stefan; Leutwyler, Heinrich
The European Physical Journal C, Vol. 78, Issue 11
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Solving integral equations in $$\eta \rightarrow 3\pi $$ η → 3 π
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Gasser, Jürg; Rusetsky, Akaki
The European Physical Journal C, Vol. 78, Issue 11
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Title: η → 3 π : Study of the Dalitz plot and extraction of the Quark Mass Ratio Q [The decay η → 3 π : Study of the Dalitz plot and extraction of the quark mass ratio Q ]

Abstract

Citation Formats

Pion and Kaon Electromagnetic Masses in Chiral Perturbation Theory journal, December 1973

Phenomenological Model of Strong and Weak Interactions in Chiral U ( 3 ) ⊗ U ( 3 ) journal, September 1967

Resolution of the η → 3π problem journal, September 1981

ππ scattering journal, June 2001

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

Predictions for the cusp in η → 3 π 0 decay journal, February 2009

Rescattering effects in η → 3π decays journal, February 2011

Review of Particle Physics journal, August 2014

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

Chiral perturbation theory: Expansions in the mass of the strange quark journal, January 1985

η-X mixing, η→3π and chiral lagrangians journal, June 1970

Measurement of the slope parameter α for the η → 3 π 0 decay with the Crystal Ball detector at the Mainz Microtron (MAMI-C) journal, March 2009

Up and Down Quark Masses and Corrections to Dashen’s Theorem from Lattice QCD and Quenched QED journal, August 2016

Measurement of the η → π + π − π 0 Dalitz plot distribution journal, October 2014

Measurement of the matrix elements for the decays η → π + π − π 0 and η / η ′ → π 0 π 0 π 0 journal, July 2015

Pion-pion scattering amplitude. III. Improving the analysis with forward dispersion relations and Roy equations journal, March 2008

Analysis and interpretation of new low-energy $\pi\pi$ scattering data journal, July 2002

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

η → 3π to one loop journal, January 1985

Electromagnetic corrections in η→3π decays journal, February 2009

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

Precision measurement of the η → π + π − π 0 Dalitz plot distribution with the KLOE detector journal, May 2016

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

Current algebra and the decay η → 3 π journal, November 1966

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

A dispersive treatment of $$K_{\ell 4}$$ K ℓ 4 decays journal, April 2015

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

Constraints on low energy QCD parameters from $$\eta \rightarrow 3\pi $$ η → 3 π and $$\pi \pi $$ π π scattering journal, March 2018

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

Isospin splittings in the decuplet baryon spectrum from dynamical QCD + QED journal, September 2019

Theoretical analysis of the γ γ → π 0 η process journal, December 2017

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

η ′ and η mesons with connection to anomalous glue journal, February 2019

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

Title: $η \to 3 π$ : Study of the Dalitz plot and extraction of the Quark Mass Ratio $Q$ [The decay $η \to 3 π$ : Study of the Dalitz plot and extraction of the quark mass ratio $Q$ ]

Pion and Kaon Electromagnetic Masses in Chiral Perturbation Theory
journal, December 1973

Phenomenological Model of Strong and Weak Interactions in Chiral $U (3) \otimes U (3)$
journal, September 1967

Resolution of the η → 3π problem
journal, September 1981

ππ scattering
journal, June 2001

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

Predictions for the cusp in $η \to 3 π^{0}$ decay
journal, February 2009

Rescattering effects in η → 3π decays
journal, February 2011

Review of Particle Physics
journal, August 2014

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

Chiral perturbation theory: Expansions in the mass of the strange quark
journal, January 1985

η-X mixing, η→3π and chiral lagrangians
journal, June 1970

Measurement of the slope parameter $α$ for the $η \to 3 π^{0}$ decay with the Crystal Ball detector at the Mainz Microtron (MAMI-C)
journal, March 2009

Up and Down Quark Masses and Corrections to Dashen’s Theorem from Lattice QCD and Quenched QED
journal, August 2016

Measurement of the $η \to π^{+} π^{-} π^{0}$ Dalitz plot distribution
journal, October 2014

Measurement of the matrix elements for the decays $η \to π^{+} π^{-} π^{0}$ and $η / η^{'} \to π^{0} π^{0} π^{0}$
journal, July 2015

Pion-pion scattering amplitude. III. Improving the analysis with forward dispersion relations and Roy equations
journal, March 2008

Analysis and interpretation of new low-energy $\pi\pi$ scattering data
journal, July 2002

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

η → 3π to one loop
journal, January 1985

Electromagnetic corrections in η→3π decays
journal, February 2009

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

Precision measurement of the η → π + π − π 0 Dalitz plot distribution with the KLOE detector
journal, May 2016

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

Current algebra and the decay η → 3 π
journal, November 1966

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

A dispersive treatment of $$K_{\ell 4}$$ K ℓ 4 decays
journal, April 2015

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

Constraints on low energy QCD parameters from $$\eta \rightarrow 3\pi $$ η → 3 π and $$\pi \pi $$ π π scattering
journal, March 2018

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

Isospin splittings in the decuplet baryon spectrum from dynamical QCD + QED
journal, September 2019

Theoretical analysis of the $γ γ \to π^{0} η$ process
journal, December 2017

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

$η^{'}$ and $η$ mesons with connection to anomalous glue
journal, February 2019

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