# ${{\boldsymbol \pi}^{+}}{{\boldsymbol \pi}^{-}}{{\boldsymbol \pi}^{0}}$ $/$ ${{\boldsymbol \rho}}{{\boldsymbol \pi}}$ AMPLITUDE RATIO ${{\boldsymbol a}_{{1}}}$ IN DECAY OF $~$ ${{\boldsymbol \phi}}$ $\rightarrow$ ${{\boldsymbol \pi}^{+}}{{\boldsymbol \pi}^{-}}{{\boldsymbol \pi}^{0}}$ INSPIRE search

NIECKNIG 2012 describes final-state interactions between the three pions in a dispersive framework using data on the ${{\mathit \pi}}{{\mathit \pi}}$ ${\mathit P}{\mathrm -wave}$ scattering phase shift.
VALUE ($10^{-2}$) CL% EVTS DOCUMENT ID TECN  COMMENT
$\bf{ 9.1 \pm1.2}$ OUR AVERAGE
$10.1$ $\pm4.4$ $\pm1.7$ 80k 1
 2006
CMD2 $1.017 - 1.021$ ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$
$9.0$ $\pm1.1$ $\pm0.6$ 1.98M 2, 3
 2003
KLOE 1.02 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$
• • • We do not use the following data for averages, fits, limits, etc. • • •
$-6<\mathit a_{1}<6$ 500k 3
 2002
SND ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$
$-16<{{\mathit a}_{{1}}}<11$ 90 9.8k 1, 4
 1998
CMD2 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}}{{\mathit \gamma}}$
1  Dalitz plot analysis taking into account interference between the contact and ${{\mathit \rho}}{{\mathit \pi}}$ amplitudes.
2  From a fit without limitations on charged and neutral ${{\mathit \rho}}~$masses and widths.
3  Recalculated by us to match the notations of AKHMETSHIN 1998 .
4  Assuming zero phase for the contact term.
References:
 AKHMETSHIN 2006
PL B642 203 Study of ${{\mathit \phi}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ with CMD-2 Detector
 ALOISIO 2003
PL B561 55 Study of the Decay ${{\mathit \phi}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ with the Detector
 ACHASOV 2002
PR D65 032002 Study of the ${{\mathit \pi}}{{\mathit \pi}}$ Mass Spectra in the Process ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ at $\sqrt {s }$ = 1020 MeV
 AKHMETSHIN 1998
PL B434 426 Study of Dynamics of ${{\mathit \phi}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ Decay with CMD-2 Detector