Combining published and unpublished preliminary LEP results the following 95$\%$ CL intervals for the QGCs associated with the ${{\mathit Z}}{{\mathit Z}}{{\mathit \gamma}}{{\mathit \gamma}}$ vertex are derived (CERN-PH-EP/2005-051 or hep-ex/0511027):

$-0.008<\mathit a{}^{{{\mathit Z}}}_{0}/\Lambda {}^{2}<+0.021$ $-0.029<\mathit a{}^{{{\mathit Z}}}_{{{\mathit c}}}/\Lambda {}^{2}<+0.039$

Anomalous ${{\mathit Z}}$ quartic couplings have also been measured by the Tevatron and LHC experiments. As discussed in the review on "Anomalous ${{\mathit W}}/{{\mathit Z}}$ quartic couplings," the coupling parameters in the Anomalous QGC Lagrangian may relate to processes involving only the ${{\mathit W}}$ or only to the ${{\mathit Z}}$ or to both. Thus, results on all other AQGCs are reported together in the ${{\mathit W}}$ listings.

VALUE DOCUMENT ID TECN • • We do not use the following data for averages, fits, limits, etc. • • 1 ABBIENDI 2004 L OPAL 2 HEISTER 2004 A ALEP 3 ACHARD 2002 G L3 1  ABBIENDI 2004L select 20 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \nu}}{{\overline{\mathit \nu}}}{{\mathit \gamma}}{{\mathit \gamma}}$ acoplanar events in the energy range $180 - 209$ GeV and 176 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit q}}{{\overline{\mathit q}}}{{\mathit \gamma}}{{\mathit \gamma}}$ events in the energy range $130 - 209$ GeV. These samples are used to constrain possible anomalous ${{\mathit W}^{+}}{{\mathit W}^{-}}{{\mathit \gamma}}{{\mathit \gamma}}$ and ${{\mathit Z}}{{\mathit Z}}$ ${{\mathit \gamma}}$ ${{\mathit \gamma}}$ quartic couplings. Further combining with the ${{\mathit W}^{+}}{{\mathit W}^{-}}{{\mathit \gamma}}$ sample of ABBIENDI 2004B the following one--parameter 95$\%$ CL limits are obtained: $-0.007$ $<$ ${{\mathit a}_{{0}}^{Z}}/\Lambda {}^{2}$ $<$ 0.023 GeV${}^{-2}$, $-0.029$ $<$ ${{\mathit a}_{{c}}^{Z}}/\Lambda {}^{2}$ $<$ 0.029 GeV${}^{-2}$, $-0.020$ $<$ ${{\mathit a}_{{0}}^{W}}/\Lambda {}^{2}$ $<$ 0.020 GeV${}^{-2}$, $-0.052$ $<$ ${{\mathit a}_{{c}}^{W}}/\Lambda {}^{2}$ $<$ 0.037 GeV${}^{-2}$. 2  In the CM energy range 183 to 209 GeV HEISTER 2004A select 30 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \nu}}{{\overline{\mathit \nu}}}{{\mathit \gamma}}{{\mathit \gamma}}$ events with two acoplanar, high energy and high transverse momentum photons. The photon--photon acoplanarity is required to be $>$ 5$^\circ{}$, $\mathit E_{{{\mathit \gamma}}}/\sqrt {s }$ $>$ 0.025 (the more energetic photon having energy $>$ 0.2 $\sqrt {s }$), p$_{T_{\gamma }}/E_{{\mathrm {beam}}}$ $>$ 0.05 and $\vert $cos $ \theta _{\gamma } \vert $ $<$ 0.94. A likelihood fit to the photon energy and recoil missing mass yields the following one--parameter 95$\%$ CL limits: $-0.012$ $<$ ${{\mathit a}_{{0}}^{Z}}/\Lambda {}^{2}$ $<$ 0.019 GeV${}^{-2}$, $-0.041$ $<$ ${{\mathit a}_{{c}}^{Z}}/\Lambda {}^{2}$ $<$ 0.044 GeV${}^{-2}$, $-0.060$ $<$ ${{\mathit a}_{{0}}^{W}}/\Lambda {}^{2}$ $<$ 0.055 GeV${}^{-2}$, $-0.099$ $<$ ${{\mathit a}_{{c}}^{W}}/\Lambda {}^{2}$ $<$ 0.093 GeV${}^{-2}$. 3  ACHARD 2002G study ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit \gamma}}{{\mathit \gamma}}$ $\rightarrow$ ${{\mathit q}}{{\overline{\mathit q}}}{{\mathit \gamma}}{{\mathit \gamma}}$ events using data at center-of-mass energies from 200 to 209 GeV. The photons are required to be isolated, each with energy $>5~$GeV and $\vert $cos $\theta \vert <0.97$, and the di-jet invariant mass to be compatible with that of the ${{\mathit Z}}~$boson ($74 - 111$ GeV). Cuts on ${{\mathit Z}}~$velocity ($\beta <0.73$) and on the energy of the most energetic photon reduce the backgrounds due to non-resonant production of the ${{\mathit q}}{{\overline{\mathit q}}}{{\mathit \gamma}}{{\mathit \gamma}}$ state and due to ISR respectively, yielding a total of 40 candidate events of which $8.6$ are expected to be due to background. The energy spectra of the least energetic photon are fitted for all ten center-of-mass energy values from 130 GeV to 209 GeV (as obtained adding to the present analysis $130 - 202$ GeV data of ACCIARRI 2001E, for a total of 137 events with an expected background of $34.1$ events) to obtain the fitted values $\mathit a_{0}/\Lambda {}^{2}$= $0.00$ ${}^{+0.02}_{-0.01}$ GeV${}^{-2}$ and $\mathit a_{\mathit c}/\Lambda {}^{2}$= $0.03$ ${}^{+0.01}_{-0.02}$ GeV${}^{-2}$, where the other parameter is kept fixed to its Standard Model value (0). A simultaneous fit to both parameters yields the 95$\%$ CL limits $-0.02$ GeV${}^{-2}<\mathit a_{0}/\Lambda {}^{2}<0.03$ GeV${}^{-2}$ and $-0.07$ GeV${}^{-2}<\mathit a_{\mathit c}/\Lambda {}^{2}<0.05$ GeV${}^{-2}$.

References:

ABBIENDI 2004L PR D70 032005 Constraints on Anomalous Quartic Gauge Boson Couplings from ${{\mathit \nu}}{{\overline{\mathit \nu}}}{{\mathit \gamma}}{{\mathit \gamma}}$ and ${\mathit {\mathit q}}$ ${\mathit {\overline{\mathit q}}}$ ${{\mathit \gamma}}{{\mathit \gamma}}$ Events at LEP-2 HEISTER 2004A PL B602 31 Constraints on Anomalous QGC's in ${{\mathit e}^{+}}{{\mathit e}^{-}}$ Interactions from $183 - 209$ GeV ACHARD 2002G PL B540 43 The ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit \gamma}}{{\mathit \gamma}}$ $\rightarrow$ ${\mathit {\mathit q}}$ ${\mathit {\overline{\mathit q}}}$ ${{\mathit \gamma}}{{\mathit \gamma}}$ Reaction at LEP and Constraints on anomalous Quartic Gauge Boson Couplings