Measurement of the $W^{+}W^{-}\gamma$ Cross Section and Direct Limits on Anomalous Quartic Gauge Couplings at LEP

The process e$^+$e$^-\rightarrow {\rm W}^+{\rm W}^-\gamma$ is analysed using the data collected with the L3 detector at LEP at a centre-of-mass energy of $188.6$ GeV, corresponding to an integrated luminosity of 176.8 pb$^{-1}$. Based on a sample of 42 selected ${\rm W}^+{\rm W}^-$ candidates containing an isolated hard photon, the ${\rm W}^+{\rm W}^-\gamma$ cross section, defined within phase-space cuts, is measured to be: $\sigma_{{\rm WW}\gamma} = 290 \pm 80 \pm 16$ fb, consistent with the Standard Model expectation. Including the process e$^+$e$^-\rightarrow \nu\bar\nu \g\g$, limits are derived on anomalous contributions to the Standard Model quartic vertices ${\rm W}^+{\rm W}^-\gamma\gamma$ and ${\rm W}^+{\rm W}^-{\rm Z}\gamma$ at 95\%~CL: \begin{eqnarray*} -0.043 \GeV^{-2} & < & a_0/\Lambda^2 ~ < ~ 0.043 \GeV^{-2} \\ \phantom{0}-0.08 \GeV^{-2} & < & a_c/\Lambda^2 ~ < ~ 0.13\phantom{0} \GeV^{-2} \\ \phantom{0}-0.41 \GeV^{-2} & < & a_n/\Lambda^2 ~ < ~ 0.37\phantom{0} \GeV^{-2}. \end{eqnarray*}