# PARAMETER $\Lambda$ IN ${{\boldsymbol \eta}}$ $\rightarrow$ ${{\boldsymbol \ell}^{+}}{{\boldsymbol \ell}^{-}}{{\boldsymbol \gamma}}$ DECAY INSPIRE search

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 $−$ ${{\mathit M}}{}^{2}_{ {{\mathit \ell}} {{\mathit \ell}} }/{{\mathit \Lambda}^{2}}){}^{-2}$, where for the parameter $\Lambda$ vector dominance predicts $\Lambda$ $\approx{}$ 0.770 GeV.
VALUE (${\mathrm {GeV/}}\mathit c{}^{2}$) EVTS DOCUMENT ID TECN  COMMENT
$\bf{ 0.716 \pm0.011}$ OUR AVERAGE
$0.712$ $\pm0.020$ 1
 2017 B
A2MM ${{\mathit \gamma}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit p}}$
$0.7191$ $\pm0.0125$ $\pm0.0093$ 2
 2016
NA60 400 GeV ${{\mathit p}}-{{\mathit A}}$ collisions
$0.716$ $\pm0.031$ $\pm0.009$ 3
 2009
NA60 158$\mathit A$ In$−$In collisions
$0.72$ $\pm0.09$ 600
 1980
SPEC ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit n}}$ , ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$
1  ADLARSON 2017B reports $\Lambda {}^{-2}$( ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ ) = $1.97$ $\pm0.11$ (GeV/c${}^{2}){}^{-2}$ which we converted to the quoted $\Lambda$ value and uncertainty (total=statistical plus systematic).
2  ARNALDI 2016 reports $\Lambda {}^{-2}$( ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ ) = $1.934$ $\pm0.067$ $\pm0.050$ (GeV/c${}^{2}){}^{-2}$ which we converted to the quoted $\Lambda$ value.
3  ARNALDI 2009 reports $\Lambda {}^{-2}$( ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ ) = $1.95$ $\pm0.17$ $\pm0.05$ (GeV/c${}^{2}){}^{-2}$ which 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
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
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 94B 548 Study of Electromagnetic Structure of ${{\mathit \eta}}$ Meson in ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}{{\mathit \gamma}}$ Decay