${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ $/$ ${{\mathit \rho}}{{\mathit \pi}}$ AMPLITUDE RATIO ${{\mathit a}_{{{1}}}}$ IN DECAY OF $~$ ${{\mathit \phi}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ 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.

M004D1

VALUE ($ 10^{-2} $)

CL%

EVTS

DOCUMENT ID

TECN

COMMENT

$\bf{ 9.1 \pm1.2}$

OUR AVERAGE

$10.1$ $\pm4.4$ $\pm1.7$

80k

AKHMETSHIN

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}

ALOISIO

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

ACHASOV

2002

SND

${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$

$-16<{{\mathit a}_{{{1}}}}<11$

9.8k

¹ ^{, 4}

AKHMETSHIN

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