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

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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 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 3 ACHASOV 2002 SND ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ $-16<{{\mathit a}_{{1}}}<11$ 90 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