Patterns of C P violation from mirror symmetry breaking in the η → π + π − π 0 Dalitz plot

Gardner, Susan; Shi, Jun

doi:10.1103/PhysRevD.101.115038

Title: Patterns of $C P$ violation from mirror symmetry breaking in the $η \to π^{+} π^{-} π^{0}$ Dalitz plot

Abstract

A violation of mirror symmetry in the $η → π^+π^–π^0$ Dalitz plot has long been recognized as a signal of $$\textit{C}$$ and $$\textit{CP}$$ violation. Here we show how the isospin of the underlying $$\textit{C}$$- and $$\textit{CP}$$-violating structures can be reconstructed from their kinematic representation in the Dalitz plot. Our analysis of the most recent experimental data reveals, for the first time, that the $$\textit{C}$$- and $$\textit{CP}$$-violating amplitude with total isospin $$\textit{I}$$ = 2 is much more severely suppressed than that with total isospin $$\textit{I}$$ = 0 .

Authors:: Gardner, Susan; Shi, Jun

Publication Date:: Mon Jun 29 00:00:00 EDT 2020

Research Org.:: Univ. of Kentucky, Lexington, KY (United States)

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

OSTI Identifier:: 1635321

Alternate Identifier(s):: OSTI ID: 1800857

Grant/Contract Number:: FG02-96ER40989

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 101 Journal Issue: 11; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Astronomy & Astrophysics; Physics

Citation Formats


                    Gardner, Susan, and Shi, Jun. Patterns of C P violation from mirror symmetry breaking in the η → π + π − π 0 Dalitz plot.  United States: N. p., 2020. 
Web.  doi:10.1103/PhysRevD.101.115038.

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                    Gardner, Susan, & Shi, Jun. Patterns of C P violation from mirror symmetry breaking in the η → π + π − π 0 Dalitz plot.  United States.  https://doi.org/10.1103/PhysRevD.101.115038

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                    Gardner, Susan, and Shi, Jun. Mon .  
"Patterns of C P violation from mirror symmetry breaking in the η → π + π − π 0 Dalitz plot".  United States.  https://doi.org/10.1103/PhysRevD.101.115038.

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@article{osti_1635321,

  title        = {Patterns of C P violation from mirror symmetry breaking in the η → π + π − π 0 Dalitz plot},

  author       = {Gardner, Susan and Shi, Jun},

  abstractNote = {A violation of mirror symmetry in the $η → π^+π^–π^0$ Dalitz plot has long been recognized as a signal of $\textit{C}$ and $\textit{CP}$ violation. Here we show how the isospin of the underlying $\textit{C}$- and $\textit{CP}$-violating structures can be reconstructed from their kinematic representation in the Dalitz plot. Our analysis of the most recent experimental data reveals, for the first time, that the $\textit{C}$- and $\textit{CP}$-violating amplitude with total isospin $\textit{I}$ = 2 is much more severely suppressed than that with total isospin $\textit{I}$ = 0 .},

  doi          = {10.1103/PhysRevD.101.115038},

  journal      = {Physical Review D},

  number       = 11,

  volume       = 101,

  place        = {United States},

  year         = {Mon Jun 29 00:00:00 EDT 2020},

  month        = {Mon Jun 29 00:00:00 EDT 2020}

}

Copy to clipboard

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Title: Patterns of C P violation from mirror symmetry breaking in the η → π + π − π 0 Dalitz plot

Abstract

Citation Formats

Electromagnetic corrections to the decays η → 3π journal, January 1996

ππ scattering journal, June 2001

Mesonic Low-Energy Constants journal, October 2014

New limits on T -odd, P -even interactions journal, June 1992

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

Erratum: Electric Dipole Moments and the Mass Scale of New T -Violating, P -Conserving Interactions [Phys. Rev. Lett. 83, 3997 (1999)] journal, June 2000

K→3π decays in chiral perturbation theory journal, January 2003

Test of C invariance in the 3π decay mode of the η meson journal, December 1966

Rho-omega mixing and the pion form factor in the timelike region journal, March 1998

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

Test Fundamental Symmetries via Precision Measurements of \(\pi ^{0}\), \(\eta \), and \(\eta '\) Decays conference, February 2017

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

The ratios of the light quark masses journal, June 1996

A measurement of the charge asymmetry in the decay η → π+π−πo journal, February 1974

Review of Particle Physics journal, August 2018

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

Anomalous decays of η ′ and η into four pions journal, January 2012

Second generation of “Miranda procedure” for C P violation in Dalitz studies of B (and D and τ ) decays journal, August 2012

Consequences of C -Violating Interactions in η 0 and X 0 Decays journal, January 1966

Experimental Determination of the Dalitz-Plot Distribution of the Decays η → π + π − π 0 and η → π + π − γ , and the Branching Ratio η → π + π − γ η → π + π − π 0 journal, August 1970

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

Direct CP-violation in untagged B-meson decays journal, February 2003

Some General Relations between the Photoproduction and Scattering of π Mesons journal, July 1954

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

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

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

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

Analysis of CP -Noninvariant Interactions and the K 1 0 , K 2 0 System journal, June 1965

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

Observing direct CP violation in untagged B -meson decays journal, February 2004

Possibility of CP violation in semi-strong interactions journal, March 1965

Measurement of the Charge Asymmetry in the Decay η → π + π − π 0 journal, July 1972

B -meson CP violation without flavor identification journal, January 1992

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

Experimental Test of C Invariance in η → π + π − π 0 journal, August 1968

Measuring CP asymmetry in B → ρ π decays without ambiguities journal, September 1993

New test for Δ I = 1 2 in K + Decay journal, June 1960

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

Physics beyond colliders at CERN: beyond the Standard Model working group report journal, December 2019

Effective lagrangian analysis of new interactions and flavour conservation journal, May 1986

New Test for Δ I = 1 2 in K + Decay journal, January 1960

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

Current algebra and η → 3π journal, January 1968

Constraints on T -odd, P -even interactions from electric dipole moments, reexamined journal, March 2001

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

ππ Phase-shift analysis from 600 to 1900 MeV journal, November 1973

Light-quark mass spectrum in quantum chromodynamics journal, April 1979

Penguin trapping with isospin analysis and CP asymmetries in B decays journal, September 1991

Roy equation analysis of ππ scattering journal, November 2001

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

The η → π+ π0 π− decay with C - violation journal, July 1965

What do we know in fact about T-odd, but P-even interactions? journal, March 1991

On a C P anisotropy measurement in the Dalitz plot journal, November 2009

Possible C -Noninvariant Effects in the 3 π Decay Modes of η 0 and ω 0 journal, September 1965

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

Strong CP-violation in an effective chiral lagrangian approach journal, December 1991

Dimension-six terms in the Standard Model Lagrangian journal, October 2010

C P -violating decays of the pseudoscalars η and η ′ and their connection to the electric dipole moment of the neutron journal, February 2017

Effective Lagrangians and parity-conserving time-reversal violation at low energies journal, May 1996

Erratum: Rho-omega mixing and the pion form factor in the timelike region [Phys. Rev. D 57 , 2716 (1998)] journal, June 2000

η → 3π to one loop journal, January 1985

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

Electric Dipole Moments and the Mass Scale of New T -Violating, P -Conserving Interactions journal, November 1999

Hunting for CP violation with untagged charm decays journal, June 2004

Light-quark masses and isospin violation journal, April 1979

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

Hadronic η and $ \eta{^\prime}$ decays journal, December 2005

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

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

Rescattering and chiral dynamics in B → ρ π decay journal, April 2002

Title: Patterns of $C P$ violation from mirror symmetry breaking in the $η \to π^{+} π^{-} π^{0}$ Dalitz plot

Electromagnetic corrections to the decays η → 3π
journal, January 1996

ππ scattering
journal, June 2001

Mesonic Low-Energy Constants
journal, October 2014

New limits on T -odd, P -even interactions
journal, June 1992

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

Erratum: Electric Dipole Moments and the Mass Scale of New $T$ -Violating, $P$ -Conserving Interactions [Phys. Rev. Lett. 83, 3997 (1999)]
journal, June 2000

K→3π decays in chiral perturbation theory
journal, January 2003

Test of C invariance in the 3π decay mode of the η meson
journal, December 1966

Rho-omega mixing and the pion form factor in the timelike region
journal, March 1998

Chiral perturbation theory: Expansions in the mass of the strange quark
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Test Fundamental Symmetries via Precision Measurements of \(\pi ^{0}\), \(\eta \), and \(\eta '\) Decays
conference, February 2017

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

The ratios of the light quark masses
journal, June 1996

A measurement of the charge asymmetry in the decay η → π+π−πo
journal, February 1974

Review of Particle Physics
journal, August 2018

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

Anomalous decays of $η^{'}$ and $η$ into four pions
journal, January 2012

Second generation of “Miranda procedure” for $C P$ violation in Dalitz studies of $B$ (and $D$ and $τ$ ) decays
journal, August 2012

Consequences of $C$ -Violating Interactions in $η^{0}$ and $X^{0}$ Decays
journal, January 1966

Experimental Determination of the Dalitz-Plot Distribution of the Decays $η \to π^{+} π^{-} π^{0}$ and $η \to π^{+} π^{-} γ$ , and the Branching Ratio $\frac{η \to π^{+} π^{-} γ}{η \to π^{+} π^{-} π^{0}}$
journal, August 1970

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

Direct CP-violation in untagged B-meson decays
journal, February 2003

Some General Relations between the Photoproduction and Scattering of $π$ Mesons
journal, July 1954

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

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

Study of Dalitz-Plot Distributions of the Decays $η \to π^{+} π^{-} π^{0}$ and $η \to π^{+} π^{-} γ$
journal, May 1973

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

Analysis of $CP$ -Noninvariant Interactions and the $K_{1}^{0}$ , $K_{2}^{0}$ System
journal, June 1965

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

Observing direct CP violation in untagged B -meson decays
journal, February 2004

Possibility of CP violation in semi-strong interactions
journal, March 1965

Measurement of the Charge Asymmetry in the Decay $η \to π^{+} π^{-} π^{0}$
journal, July 1972

$B$ -meson $CP$ violation without flavor identification
journal, January 1992

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

Experimental Test of $C$ Invariance in $η \to π^{+} π^{-} π^{0}$
journal, August 1968

Measuring $CP$ asymmetry in $B \to ρ π$ decays without ambiguities
journal, September 1993

New test for $Δ I = \frac{1}{2}$ in $K^{+}$ Decay
journal, June 1960

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

Physics beyond colliders at CERN: beyond the Standard Model working group report
journal, December 2019

Effective lagrangian analysis of new interactions and flavour conservation
journal, May 1986

New Test for $Δ I = \frac{1}{2}$ in $K^{+}$ Decay
journal, January 1960

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

Current algebra and η → 3π
journal, January 1968

Constraints on T -odd, P -even interactions from electric dipole moments, reexamined
journal, March 2001

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

ππ Phase-shift analysis from 600 to 1900 MeV
journal, November 1973

Light-quark mass spectrum in quantum chromodynamics
journal, April 1979

Penguin trapping with isospin analysis and $CP$ asymmetries in $B$ decays
journal, September 1991

Roy equation analysis of ππ scattering
journal, November 2001

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

The η → π+ π0 π− decay with C - violation
journal, July 1965

What do we know in fact about T-odd, but P-even interactions?
journal, March 1991

On a $C P$ anisotropy measurement in the Dalitz plot
journal, November 2009

Possible $C$ -Noninvariant Effects in the $3 π$ Decay Modes of $η^{0}$ and $ω^{0}$
journal, September 1965

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

Strong CP-violation in an effective chiral lagrangian approach
journal, December 1991

Dimension-six terms in the Standard Model Lagrangian
journal, October 2010

$C P$ -violating decays of the pseudoscalars $η$ and $η^{'}$ and their connection to the electric dipole moment of the neutron
journal, February 2017

Effective Lagrangians and parity-conserving time-reversal violation at low energies
journal, May 1996

Erratum: Rho-omega mixing and the pion form factor in the timelike region [Phys. Rev. D 57 , 2716 (1998)]
journal, June 2000

η → 3π to one loop
journal, January 1985

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

Electric Dipole Moments and the Mass Scale of New $T$ -Violating, $P$ -Conserving Interactions
journal, November 1999

Hunting for CP violation with untagged charm decays
journal, June 2004

Light-quark masses and isospin violation
journal, April 1979

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

Hadronic η and $ \eta{^\prime}$ decays
journal, December 2005

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

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

Rescattering and chiral dynamics in $\vec{B} ρ π$ decay
journal, April 2002