# PARAMETER $\Lambda$ IN ${{\boldsymbol \omega}}$ $\rightarrow$ ${{\boldsymbol \pi}^{0}}{{\boldsymbol \ell}^{+}}{{\boldsymbol \ell}^{-}}$ DECAY

In the pole approximation the electromagnetic transition form factor for a resonance of mass $\mathit M$ is given by the expression: $\vert \mathit F\vert ^2$ = (1 $−$ ${{\mathit M}^{2}}/{{\mathit \Lambda}^{2}}){}^{-2}$, where for the parameter $\Lambda$ vector dominance predicts $\Lambda$ = $\mathit M_{p}$ $\approx{}$ 0.770 GeV. The ARNALDI 2009 measurement is in obvious conflict with this expectation. Note that for ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ decay ARNALDI 2009 and DZHELYADIN 1980 obtain the value of $\Lambda$ consistent with vector dominance.

# PARAMETER $\Lambda$ IN $\omega\to\pi^0 e^+ e^-$ DECAY INSPIRE search

VALUE (GeV) EVTS DOCUMENT ID TECN  COMMENT
$0.709$ $\pm0.037$ 1.1k 1
 2017 B
A2MM ${{\mathit \gamma}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \omega}}{{\mathit p}}$
1  ADLARSON 2017B reports $\Lambda {}^{-2}$( ${{\mathit \omega}}{{\mathit \pi}^{0}}$ ) = $1.99$ $\pm0.21$ GeV${}^{-2}$ that we converted to the quoted $\Lambda$ value.
References:
PR C95 035208 Measurement of the ${{\mathit \omega}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ and ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \gamma}}$ Dalitz Decays with the A2 Setup at MAMI