# ${{\boldsymbol \eta}^{\,'}{(958)}}$ $\rightarrow$ ${{\boldsymbol \eta}}{{\boldsymbol \pi}}{{\boldsymbol \pi}}$ DECAY PARAMETERS $\vert$MATRIX ELEMENT$\vert ^2$ = $\vert$1 + $\alpha {}\boldsymbol Y\vert ^2$ + $\boldsymbol C{}\boldsymbol X$ + $\boldsymbol D{}\boldsymbol X{}^{2}$

$\mathit X$ and $\mathit Y$ are Dalitz variables; $\alpha$ is complex and $\mathit C$, and $\mathit D$ are real-valued. Parameters $\mathit C$ and $\mathit D$ are not necessarily equal to $\mathit c$ and $\mathit d$, respectively, in the generalized parameterization following this one. May be different for ${{\mathit \eta}^{\,'}{(958)}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ and ${{\mathit \eta}^{\,'}{(958)}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ decays. Because of different initial assumptions and strong correlations of the parameters we do not average the parameters in the section below.

# $\boldsymbol Re(\alpha$) decay parameter INSPIRE search

VALUE EVTS DOCUMENT ID TECN  COMMENT
• • • We do not use the following data for averages, fits, limits, etc. • • •
$-0.034$ $\pm0.002$ $\pm0.002$ 351k
 2018
BES3 ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$
$-0.054$ $\pm0.004$ $\pm0.001$ 56k
 2018
BES3 ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$
$-0.033$ $\pm0.005$ $\pm0.003$ 44k 1
 2011
BES3 ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \eta}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$
$-0.072$ $\pm0.012$ $\pm0.006$ 7k 2
 2005 A
VES 28 ${{\mathit \pi}^{-}}$ ${{\mathit A}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{-}}{{\mathit A}^{*}}$
$-0.021$ $\pm0.018$ $\pm0.017$ 6.7k 3
 2000
CLEO 10.6 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit X}}$
$-0.058$ $\pm0.013$ $\pm0.003$ 5.4k 4
 1986
GAM2 38 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit n}}{{\mathit \eta}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$
$-0.08$ $\pm0.03$ 4, 5
 1974
RVUE ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$
1  See ABLIKIM 2011 for the full correlation matrix.
2  Superseded by DOROFEEV 2007 , which found this parameterization unacceptable. See below.
3  Assuming Im($\alpha$) = 0, $\mathit C$ = 0, and $\mathit D$ = 0.
4  Assuming $\mathit C$ = 0.
5  From the data of DAUBER 1964 , RITTENBERG 1969 , AGUILAR-BENITEZ 1972B, JACOBS 1973 , and DANBURG 1973 .
References:
 ABLIKIM 2018
PR D97 012003 Measurement of the Matrix Elements for the Decays ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ and ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$
 ABLIKIM 2011
PR D83 012003 Measurement of the Matrix Element for the Decay ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$
 AMELIN 2005A
PAN 68 372 Measurement of Form Factors for the Decay ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{-}}{{\mathit \pi}^{+}}$
 BRIERE 2000
PRL 84 26 Rare Decays of the ${{\mathit \eta}^{\,'}}$
 ALDE 1986
PL B177 115 Matrix Element of the ${{\mathit \eta}^{\,'}{(958)}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ Decay
 KALBFLEISCH 1974
PR D10 916 ${{\mathit \eta}^{\,'}{(958)}}$ Branching Ratio, Linear Matrix Element and Dipion Phase Shift