ENERGY DEPENDENCE OF ${{\mathit \eta}}$ $\rightarrow$ 3 ${{\mathit \pi}}$ DALITZ PLOTS

PARAMETERS FOR ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ INSPIRE search

See the “Note on ${{\mathit \eta}}$ Decay Parameters,” page 1454, in our 1994 edition (Physical Review D50 1173 (1994)). The following experiments fit to one or more of the coefficients $\mathit a$, $\mathit b$, $\mathit c$, $\mathit d$, $\mathit e$, $\mathit f$ or $\mathit g$ for $\vert $matrix element$\vert ^2$ = 1 + $\mathit a{}\mathit y$ + $\mathit b{}\mathit y{}^{2}$ + $\mathit c{}\mathit x$ + $\mathit d{}\mathit x{}^{2}$ + $\mathit e{}\mathit x{}\mathit y$ + $\mathit f{}\mathit y{}^{3}$ + $\mathit g{}\mathit x{}^{2}{}\mathit y$.
S014DP
VALUE EVTS DOCUMENT ID TECN  COMMENT
• • • We do not use the following data for averages, fits, limits, etc. • • •
631k 1
ABLIKIM
2023AN
 BES3 ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \eta}}$
4.7M 2
ANASTASI
2016A
 KLOE ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \phi}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \gamma}}$
79k
ABLIKIM
2015G
 BES3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \eta}}$
174k
ADLARSON
2014A
 WASA ${{\mathit p}}$ ${{\mathit d}}$ $\rightarrow$ ${{\mathit \eta}}{}^{3}\mathrm {He}$
1.34M
AMBROSINO
2008D
 KLOE
3230 3
ABELE
1998D
 CBAR ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \eta}}$ at rest
1077 4
AMSLER
1995
CBAR ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \eta}}$ at rest
81k
LAYTER
1973
ASPK
220k
LAYTER
1972
ASPK
1138
CARPENTER
1970
HBC
349
DANBURG
1970
DBC
7250
GORMLEY
1970
WIRE
526
BAGLIN
1969
HLBC
7170
CNOPS
1968
OSPK
37k
GORMLEY
1968C
 WIRE
1300
CLPWY
1966
HBC
705
LARRIBE
1966
HBC
1  ABLIKIM 2023AN fit the Dalitz plot density distribution with two parameter sets ($\mathit a,~b,~d,~f$), and ($\mathit a,~b,~d,~f,~g$).
2  ANASTASI 2016A measure the Dalitz parameters $\mathit a$, $\mathit b$, $\mathit d$, $\mathit f$, and $\mathit g$. This is the first measurement of $\mathit g$.
3  ABELE 1998D obtains $\mathit a$ =$-1.22$ $\pm0.07$ and $\mathit b$ = $0.22$ $\pm0.11$ when $\mathit c$ (or$~\mathit d$) is fixed at $0.06$.
4  AMSLER 1995 fits to (1$+\mathit ay+\mathit by{}^{2}$) and obtains $\mathit a=-0.94$ $\pm0.15$ and $\mathit b=0.11$ $\pm0.27$.
  References:
ABLIKIM 2023AN
PR D107 092007 Precision measurement of the matrix elements for ???+?-?0 and ???0?0?0 decays
ANASTASI 2016A
JHEP 1605 019 Precision Measurement of the ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ Dalitz Plot Distribution with the KLOE Detector
ABLIKIM 2015G
PR D92 012014 Measurement of the Matrix Elements for the Decays ${{\mathit \eta}}$ $\rightarrow$ ${+}$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ and ${{\mathit \eta}}$ $/$ ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$
ADLARSON 2014A
PR C90 045207 Measurement of the ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ Dalitz Plot Distribution
AMBROSINO 2008D
JHEP 0805 006 Determination of ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ Dalitz Plot Slopes and Asymmetries with the KLOE Detector
ABELE 1998D
PL B417 197 Momentum Dependence of the Decay ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$
AMSLER 1995
PL B346 203 ${{\mathit \eta}}$-Decays into Three Pion
LAYTER 1973
PR D7 2565 Study of Dalitz Plot Distributions of the Decays ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ and ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}}$
LAYTER 1972
PRL 29 316 Measurement of the Charge Asymmetry in the Decay ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$
CARPENTER 1970
PR D1 1303 ${{\mathit \pi}^{+}}$ ${{\mathit \pi}^{-}}$ ${{\mathit \pi}^{0}}$ Decay of 1138 ${{\mathit \eta}}$ Mesons Produced in ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \Lambda}}{{\mathit \eta}}$ near Threshold
DANBURG 1970
PR D2 2564 Production and Decay of ${{\mathit \eta}}$ and ${{\mathit \omega}}$ Mesons in the Reaction ${{\mathit \pi}^{+}}$ ${{\mathit d}}$ $\rightarrow$ ( ${{\mathit p}}$) ${{\mathit p}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ between 1.1 and 2.4 ${\mathrm {GeV/}}\mathit c$
GORMLEY 1970
PR D2 501 Experimental Determination of the Dalitz-Plot Distribution of the Decays ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ and ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}}$, and the Branching ratio ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}}$ $/$ ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$
Also
Thesis Nevis 181 Dalitz Plot Analysis of the Decays of ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ and ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}}$. The Branching Ratio ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}}$/ ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$
BAGLIN 1969
PL 29B 445 Heavy Liquid Chamber Analysis of ${{\mathit \eta}}$ $\rightarrow$ 3 ${{\mathit \pi}}$ and ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$ Decay Modes
Also
NP B22 66 Heavy Liquid Bubble Chamber Analysis of ${{\mathit \eta}}$ Neutral Decay Modes ${{\mathit \eta}}$ $\rightarrow$ 3 ${{\mathit \pi}^{0}}$ and ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}}$
CNOPS 1968
PRL 21 1609 Coherent Production of ${{\mathit \pi}^{+}}$ ${{\mathit \pi}^{+}}$ ${{\mathit \pi}^{-}}$ in Deuterium by 8 ${\mathrm {GeV/}}\mathit c$ ${{\mathit \pi}^{+}}$
GORMLEY 1968C
PRL 21 402 Experimental Test of $\mathit C$ Invariance in ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$
CLPWY 1966
PR 149 1044 Search for $\mathit C$ Violation in ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ (CLPWY: Columbia-Berkeley-Purdue-Wisconsin-Yale Collaboration)
LARRIBE 1966
PL 23 600 Test of $\mathit C$ Invariance in the 3${{\mathit \pi}}$ Decay Mode of the ${{\mathit \eta}}$ Meson