# ENERGY DEPENDENCE OF ${{\boldsymbol \omega}}$ $\rightarrow$ ${{\boldsymbol \pi}^{+}}{{\boldsymbol \pi}^{-}}{{\boldsymbol \pi}^{0}}$ DALITZ PLOT INSPIRE search

The following experiments fit to one or more of the coefficients $\alpha$, $\beta$, $\gamma$ for $\vert$matrix element$\vert ^2$ ${}\propto$ $\mathit P$ (1 + 2$\alpha$ Z + 2$\beta$ Z${}^{3/2}$ sin$(3\phi )$ + 2$\gamma Z{}^{2}$ + $\mathit O(Z{}^{5/2}$)) where $\mathit P$ is the ${\mathit P}{\mathrm -wave}$ phase-space factor and Z, $\phi$ are kinematical variables as defined in ADLARSON 2017 .

VALUE EVTS DOCUMENT ID TECN  COMMENT
$\bf{ 0.133 \pm0.008}$ OUR AVERAGE
$0.1321$ $\pm0.0067$ $\pm0.0046$ 260k 1
BES3 ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \omega}}{{\mathit \eta}}$
$0.147$ $\pm0.036$ 44k
WASA $\alpha$ in ${{\mathit p}}$ ${{\mathit d}}$ $\rightarrow$ ${}^{3}\mathrm {He}{{\mathit \omega}}$, ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit p}}{{\mathit p}}{{\mathit \omega}}$
1  Keeping a term linear in Z only. A fit with the terms proportional to Z and Z${}^{3/2}$ gives $\alpha$ = $0.133$ $\pm0.041$ and $\beta$ = $0.037$ $\pm0.054$.
PR D98 112007 Dalitz Plot Analysis of the Decay $\omega \rightarrow \pi^{+}\pi^{-}\pi^{0}$
PL B770 418 Measurement of the ${{\mathit \omega}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ Dalitz Plot Distribution