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

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

INSPIRE   PDGID:

S014DP

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 + $\mathit a{}\mathit y$ + $\mathit b{}\mathit y{}^{2}$ + $\mathit c{}\mathit x$ + $\mathit d{}\mathit x{}^{2}$ + $\mathit e{}\mathit x{}\mathit y$ + $\mathit f{}\mathit y{}^{3}$ + $\mathit g{}\mathit x{}^{2}{}\mathit y$.

VALUE EVTS DOCUMENT ID TECN  COMMENT • • We do not use the following data for averages, fits, limits, etc. • • 4.7M 1 ANASTASI 2016 A KLOE ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \phi}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \gamma}}$ 79k ABLIKIM 2015 G BES3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \eta}}$ 174k ADLARSON 2014 A WASA ${{\mathit p}}$ ${{\mathit d}}$ $\rightarrow$ ${{\mathit \eta}}$ ${}^{3}\mathrm {He}$ 1.34M AMBROSINO 2008 D KLOE 3230 2 ABELE 1998 D CBAR ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \eta}}$ at rest 1077 3 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 1968 C WIRE 1300 CLPWY 1966 HBC 705 LARRIBE 1966 HBC 1  ANASTASI 2016A measure the Dalitz parameters $\mathit a$, $\mathit b$, $\mathit d$, $\mathit f$, and $\mathit g$. This is the first measurement of $\mathit g$. 2  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 $0.06$. 3  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:

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

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