# ${{\boldsymbol \eta}^{\,'}{(958)}}$ $\rightarrow$ ${{\boldsymbol \eta}}{{\boldsymbol \pi}}{{\boldsymbol \pi}}$ DECAY PARAMETERS $\vert$MATRIX ELEMENT$\vert ^2$ ${}\propto$ 1 + $\boldsymbol a~Y$ + $\boldsymbol b~Y{}^{2}$ + $\boldsymbol c~X$ + $\boldsymbol d~X{}^{2}$

$\mathit X$ and $\mathit Y$ are Dalitz variables and $\mathit a,~b,~c$, and $\mathit d$ are real-valued parameters. 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. We do not average measurements in the section below because parameter values from each experiment are strongly correlated.

# $\boldsymbol d$ decay parameter INSPIRE search

VALUE EVTS DOCUMENT ID TECN  COMMENT
• • • We do not use the following data for averages, fits, limits, etc. • • •
$-0.063$ $\pm0.004$ $\pm0.003$ 351k
 2018
BES3 ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$
$-0.074$ $\pm0.009$ $\pm0.004$ 56k
 2018
BES3 ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$
$-0.050$ $\pm0.009$ $\pm0.005$ 124k
 2018 A
A2MM ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$
$-0.051$ $\pm0.008$ $\pm0.006$ 1
 2018 A
RVUE ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$
$-0.073$ $\pm0.012$ $\pm0.003$ 44k 2
 2011
BES3 ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \eta}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$
$0.018$ $\pm0.078$ $\pm0.006$ 15k 3
 2009
GAM4 32.5 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \eta}^{\,'}}{{\mathit n}}$
$-0.082$ $\pm0.017$ $\pm0.008$ 20k 4
 2007
VES 27 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \eta}^{\,'}}{{\mathit n}}$ , ${{\mathit \pi}^{-}}$ ${{\mathit A}}$ $\rightarrow$ ${{\mathit \eta}^{\,'}}{{\mathit \pi}^{-}}{{\mathit A}^{*}}$
1  Theoretical analysis of ADLARSON 2018A using resonance chiral perturbation theory to one loop.
2  See ABLIKIM 2011 for the full correlation matrix.
3  From ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ decay. If $\mathit c$ ${}\equiv$ 0 from Bose-Einstein symmetry, $\mathit d$ = $-0.067$ $\pm0.020$ $\pm0.003$.
4  From ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ decay.
References:
 ABLIKIM 2018
PR D97 012003 Measurement of the Matrix Elements for the Decays ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ and ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$
 ADLARSON 2018A
PR D98 012001 Measurement of the decay $\eta^{\prime}\to\pi^{0}\pi^{0}\eta$ at MAMI
 GONZALEZ-SOLIS 2018A
EPJ C78 758 $\eta ^{\prime }\rightarrow \eta \pi \pi$ decays in unitarized resonance chiral theory
 ABLIKIM 2011
PR D83 012003 Measurement of the Matrix Element for the Decay ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$
 BLIK 2009
PAN 72 231 Measurement of the Matrix Element for the Decay ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ with the GAMS-4$\pi$ Spectrometer
 DOROFEEV 2007
PL B651 22 Study of ${{\mathit \eta}^{\,'}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ Dalitz Plot