Limits on the Anomalous $\mathit{ZZ}\gamma$ and $\mathit{Z}\gamma \gamma$ Couplings in $\mathit{p}\overline{p}$ Collisions at $\sqrt{\mathit{s}}=1.8\mathrm{}$ TeV

We performed a direct search for the anomalous $\mathrm{ZZ}\gamma$ and $Z\gamma \gamma$ couplings by studying $p\overline{p}\to \ell \ell \gamma +X$ $(\ell =e,\mu )$ events at $\sqrt{s}=1.8\mathrm{}$ TeV with the D0 detector at the Fermilab Tevatron Collider. A fit to the transverse energy spectrum of the photon in the signal events, based on the data set corresponding to an integrated luminosity of $14.3{\mathrm{pb}}^{-1\mathrm{}}$ ( $13.7{\mathrm{pb}}^{-1\mathrm{}}$) for the electron (muon) channel, yields the following $95\%$ confidence level limits on the anomalous $\mathrm{CP}$-conserving $\mathrm{ZZ}\gamma$ couplings: $|h_{30}^Z|<1.8\mathrm{}$ ( $h_{40}^Z=0\mathrm{}$) and $|h_{40}^Z|<0.5\mathrm{}$ ( $h_{30}^Z=0\mathrm{}$), for a form-factor scale $\Lambda =500\mathrm{}$ GeV. Limits for the $Z\gamma \gamma$ couplings and $\mathrm{CP}$-violating couplings are also discussed.