Constraints on anomalous quartic gauge boson couplings from $\nu \overline{\nu }\gamma \gamma$ and $q\overline{q}\gamma \gamma$ events at CERN LEP2

Anomalous quartic couplings between the electroweak gauge bosons may contribute to the $\nu \overline{\nu }\gamma \gamma$ and $q\overline{q}\gamma \gamma$ final states produced in $e^{+}{e}^{-}$ collisions. This analysis uses the LEP2 OPAL data sample at center-of-mass energies up to 209 GeV. Event selections identify $\nu \overline{\nu }\gamma \gamma$ and $q\overline{q}\gamma \gamma$ events in which the two photons are reconstructed within the detector acceptance. The cross section for the process $e^{+}{e}^{-}\to q\overline{q}\gamma \gamma$ is measured. Averaging over all energies, the ratio of the observed $e^{+}{e}^{-}\to q\overline{q}\gamma \gamma$ cross section to the standard model expectation is $\mathrm{R}(\mathrm{data}/\mathrm{SM})=0.92\mathrm{}\pm 0.07\pm 0.04,$ where the errors represent the statistical and systematic uncertainties respectively. The $\nu \overline{\nu }\gamma \gamma$ and $q\overline{q}\gamma \gamma$ data are used to constrain possible anomalous $W^{+}{W}^{-}\gamma \gamma$ and $\mathrm{ZZ}\gamma \gamma$ couplings. Combining with previous OPAL results from the $W^{+}{W}^{-}\gamma$ final state, the 95% confidence level limits on the anomalous coupling parameters $a_0^{\mathrm{Z}},$ $a_{\mathrm{c}}^{\mathrm{Z}},$ $a_0^{\mathrm{W}}$ and $a_{\mathrm{c}}^{\mathrm{W}}$ are found to be $-0.007\hspace{0.5em}{\mathrm{GeV}}^{-2}<a_0^{\mathrm{Z}}/{\Lambda }^2<0.023\mathrm{}\hspace{0.5em}{\mathrm{GeV}}^{-2},$ $-0.029\hspace{0.5em}{\mathrm{GeV}}^{-2}<a_{\mathrm{c}}^{\mathrm{Z}}/{\Lambda }^2<0.029\mathrm{}\hspace{0.5em}{\mathrm{GeV}}^{-2},$ $-0.020\hspace{0.5em}{\mathrm{GeV}}^{-2}<a_0^{\mathrm{W}}/{\Lambda }^2<0.020\mathrm{}\hspace{0.5em}{\mathrm{GeV}}^{-2},$ $-0.052\hspace{0.5em}{\mathrm{GeV}}^{-2}<a_{\mathrm{c}}^{\mathrm{W}}/{\Lambda }^2<0.037\mathrm{}\hspace{0.5em}{\mathrm{GeV}}^{-2},$ where $\Lambda$ is the energy scale of the new physics. Limits found when allowing two or more parameters to vary are also presented.