# 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 ${{\boldsymbol \omega}}$ $\rightarrow$ ${{\boldsymbol \pi}^{0}}{{\boldsymbol \mu}^{+}}{{\boldsymbol \mu}^{-}}$ DECAY INSPIRE search

VALUE (GeV) EVTS DOCUMENT ID TECN  COMMENT
$\bf{ 0.670 \pm0.006}$ OUR AVERAGE
$0.6707$ $\pm0.0039$ $\pm0.0056$ 1
 2016
NA60 400 GeV (${{\mathit p}}-{{\mathit A}}$) collisions
$0.668$ $\pm0.009$ $\pm0.003$ 3k 2
 2009
NA60 158$\mathit A$ In$−$In collisions
• • • We do not use the following data for averages, fits, limits, etc. • • •
$0.65$ $\pm0.03$
 1981 B
CNTR 25$-$33 ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \omega}}{{\mathit n}}$
1  ARNALDI 2016 reports $\Lambda {}^{-2}({{\mathit \omega}}$) = $2.223$ $\pm0.026$ $\pm0.037$ GeV${}^{-2}$ which we converted to the quoted $\Lambda$ value.
2  ARNALDI 2009 reports $\Lambda {}^{-2}({{\mathit \omega}}$) = $2.24$ $\pm0.06$ $\pm0.02$ GeV${}^{-2}$ which we converted to the quoted $\Lambda$ value.
References:
 ARNALDI 2016
PL B757 437 Precision Study of the ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}{{\mathit \gamma}}$ and ${{\mathit \omega}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}{{\mathit \pi}^{0}}$ Electromagnetic Transition Form-Factors and of the ${{\mathit \rho}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ Line Shape in NA60
 ARNALDI 2009
PL B677 260 Study of the Electromagnetic Transition Form-Factors in ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}{{\mathit \gamma}}$ and ${{\mathit \omega}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}{{\mathit \pi}^{0}}$ Decays with NA60
PL 102B 296 Study of the Electromagnetic Transition Formfactor in ${{\mathit \omega}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ Decay