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

$\mathit X$ 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.

$\mathit D$ decay parameter

INSPIRE   PDGID:
M002D0
VALUE EVTS DOCUMENT ID TECN  COMMENT
• • We do not use the following data for averages, fits, limits, etc. • •
$-0.053$ $\pm0.004$ $\pm0.004$ 351k
ABLIKIM
2018
BES3 ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$
$-0.061$ $\pm0.009$ $\pm0.005$ 56k
ABLIKIM
2018
BES3 ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$
$-0.059$ $\pm0.012$ $\pm0.004$ 44k 1
ABLIKIM
2011
BES3 ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \eta}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$
$-0.066$ $\pm0.030$ $\pm0.015$ 7k 2
AMELIN
2005A
 VES 28 ${{\mathit \pi}^{-}}$ ${{\mathit A}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{-}}{{\mathit A}^{*}}$
$0.00$ $\pm0.03$ $\pm0.00$ 5.4k 3
ALDE
1986
GAM2 38 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit n}}{{\mathit \eta}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$
$0$ 3, 4
KALBFLEISCH
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2  Superseded by DOROFEEV 2007 , which found this parameterization unacceptable.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 $\mathit C$ = 0.
4  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 ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{-}}{{\mathit \pi}^{+}}$
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