skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Three-body Final State Interaction in η→3π

Abstract

We present an unitary dispersive model for the $$\eta \to 3 \pi$$ decay process based upon the Khuri-Treiman equations which are solved by means of the Pasquier inversion method. The description of the hadronic final-state interactions for the $$\eta \to 3\pi$$ decay is essential to reproduce the available data and to understand the existing discrepancies between Dalitz plot parameters from experiment and chiral perturbation theory. Our approach incorporates substraction constants that are fixed by fitting the recent high-statistics WASA-at-COSY data for $$\eta \to \pi^+ \pi^- \pi^0$$. Based on the parameters obtained we predict the slope parameter for the neutral channel to be $$\alpha=-0.022\pm 0.004$$. Through matching to next-to-leading order chiral perturbation theory we estimate the quark mass double ratio to be $$Q=21.4 \pm 0.4$$.

Authors:
 [1];  [2];  [3];  [2];  [4];  [1]
  1. Indiana Univ., Bloomington, IN (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
  2. Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
  3. Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); George Washington Univ., Washington, DC (United States)
  4. Indiana Univ., Bloomington, IN (United States)
Publication Date:
Research Org.:
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
Contributing Org.:
Joint Physics Analysis Center
OSTI Identifier:
1223489
Alternate Identifier(s):
OSTI ID: 1215457
Report Number(s):
JLAB-THY-15-2041; DOE/OR/23177-3343; arXiv:1505.01715
Journal ID: ISSN 1550-7998; PRVDAQ
Grant/Contract Number:  
PHY-1415459; PHY-1205019; AC05-06OR23177
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review. D, Particles, Fields, Gravitation and Cosmology
Additional Journal Information:
Journal Volume: 92; Journal Issue: 5; Journal ID: ISSN 1550-7998
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Guo, Peng, Danilkin, Igor V., Schott, Diane, Fernández-Ramírez, C., Mathieu, V., and Szczepaniak, Adam P. Three-body Final State Interaction in η→3π. United States: N. p., 2015. Web. doi:10.1103/PhysRevD.92.054016.
Guo, Peng, Danilkin, Igor V., Schott, Diane, Fernández-Ramírez, C., Mathieu, V., & Szczepaniak, Adam P. Three-body Final State Interaction in η→3π. United States. https://doi.org/10.1103/PhysRevD.92.054016
Guo, Peng, Danilkin, Igor V., Schott, Diane, Fernández-Ramírez, C., Mathieu, V., and Szczepaniak, Adam P. 2015. "Three-body Final State Interaction in η→3π". United States. https://doi.org/10.1103/PhysRevD.92.054016. https://www.osti.gov/servlets/purl/1223489.
@article{osti_1223489,
title = {Three-body Final State Interaction in η→3π},
author = {Guo, Peng and Danilkin, Igor V. and Schott, Diane and Fernández-Ramírez, C. and Mathieu, V. and Szczepaniak, Adam P.},
abstractNote = {We present an unitary dispersive model for the $\eta \to 3 \pi$ decay process based upon the Khuri-Treiman equations which are solved by means of the Pasquier inversion method. The description of the hadronic final-state interactions for the $\eta \to 3\pi$ decay is essential to reproduce the available data and to understand the existing discrepancies between Dalitz plot parameters from experiment and chiral perturbation theory. Our approach incorporates substraction constants that are fixed by fitting the recent high-statistics WASA-at-COSY data for $\eta \to \pi^+ \pi^- \pi^0$. Based on the parameters obtained we predict the slope parameter for the neutral channel to be $\alpha=-0.022\pm 0.004$. Through matching to next-to-leading order chiral perturbation theory we estimate the quark mass double ratio to be $Q=21.4 \pm 0.4$.},
doi = {10.1103/PhysRevD.92.054016},
url = {https://www.osti.gov/biblio/1223489}, journal = {Physical Review. D, Particles, Fields, Gravitation and Cosmology},
issn = {1550-7998},
number = 5,
volume = 92,
place = {United States},
year = {Fri Sep 11 00:00:00 EDT 2015},
month = {Fri Sep 11 00:00:00 EDT 2015}
}

Journal Article:

Citation Metrics:
Cited by: 62 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Review of Particle Physics
journal, July 2012


Present and Future of Hadron Spectroscopy at Jefferson lab
journal, June 2010


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


Roy equation analysis of ππ scattering
journal, November 2001


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


A new analysis of $\pi K$ scattering from Roy and Steiner type equations
journal, March 2004


A Model of Leptons
journal, November 1967


Chiral perturbation theory to one loop
journal, November 1984


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


Measurement of the slope parameter for the η 3 π 0 decay in the pp pp η reaction
journal, October 2007


Momentum dependence of the decay η→π+π−π0
journal, January 1998


Determination of the Quadratic Slope Parameter in η 3 π 0 Decay
journal, October 2001


Determination of η → π + π π 0 Dalitz plot slopes and asymmetries with the KLOE detector
journal, May 2008


Measurement of the <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>η</mml:mi><mml:mo>→</mml:mo><mml:mn>3</mml:mn><mml:msup><mml:mi>π</mml:mi><mml:mn>0</mml:mn></mml:msup></mml:math> slope parameter α with the KLOE detector
journal, October 2010


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


Current algebra and η → 3π
journal, January 1968


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


η → 3π to one loop
journal, January 1985


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


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


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


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


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


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


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


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


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


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


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


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


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


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


The low energy ππ amplitude to one and two loops
journal, December 1995


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


Study of Dalitz-Plot Distributions of the Decays η π + π π 0 and η π + π γ
journal, May 1973


Neutral decays of the ?-meson
journal, September 1984


Decay dynamics of the process η→3π0
journal, January 1998


Dynamics of η→3π0 decay
journal, May 2001


Measurement of the <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>η</mml:mi><mml:mo>→</mml:mo><mml:mn>3</mml:mn><mml:msup><mml:mi>π</mml:mi><mml:mn>0</mml:mn></mml:msup></mml:math> Dalitz plot distribution with the WASA detector at COSY
journal, June 2009


Determination of the Dalitz plot parameter $ \alpha$ for the decay $ \eta$ → 3 $ \pi^{0}_{}$ with the Crystal Ball at MAMI-B
journal, January 2009


Study of the Dalitz Plot of the $\eta \rightarrow \pi ^+ \pi ^- \pi ^0$ Decay with the KLOE Detector
journal, January 2015


QCD isospin breaking in meson masses, decay constants and quark mass ratios
journal, May 2001


Review of lattice results concerning low-energy particle physics
journal, September 2014


Leading isospin breaking effects on the lattice
journal, June 2013


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


Measurement of the <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">L</mml:mi></mml:msub><mml:mo>→</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>e</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:msup><mml:mi>e</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>e</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math> decay rate
journal, May 2005


Measurement of the ω → π+π−π0 Dalitz plot distribution
text, January 2017


Review of lattice results concerning low-energy particle physics
text, January 2017


Review of Particle Physics
text, January 2008


Measurement of the ω → π + π − π 0 Dalitz plot distribution
journal, July 2017


Review of lattice results concerning low-energy particle physics
text, January 2016


Review of Particle Physics
text, January 2018


Review of lattice results concerning low-energy particle physics
text, January 2014


Review of lattice results concerning low-energy particle physics
journal, July 2011


Review of Particle Physics
text, January 2012


Works referencing / citing this record:

Variational approach to N -body interactions in finite volume
journal, November 2018


Multiple-particle interaction in ( 1 + 1 )-dimensional lattice model
journal, January 2019


Three-body unitarity with isobars revisited
journal, September 2017


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


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


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


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


Theoretical analysis of the γγ (*)π 0 η process
journal, January 2019


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