Anomalous ${{\mathit W}}$ quartic couplings are measured by the experiments at LEP, the Tevatron, and the LHC. Some of the recent results from the Tevatron and LHC experiments individually surpass the combined LEP-2 results in precision (see below). As discussed in the review on the “Anomalous ${{\mathit W}}/{{\mathit Z}}$ quartic couplings (QGCS),” the measurements are typically done using different operator expansions which then do not allow the results to be compared and averaged. At least one common framework should be agreed upon for the use in the future publications by the experiments.

Some publications from LHC experiments derive limits for various assumed values of the form-factor cutoff $\Lambda _{FF}$. The values quoted below are for $\Lambda _{FF}$ $\rightarrow$ $\infty{}$.

VALUE DOCUMENT ID TECN  COMMENT • • We do not use the following data for averages, fits, limits, etc. • • 1 SIRUNYAN 2021 CMS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 13 TeV 2 TUMASYAN 2021 A CMS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 13 TeV 3 TUMASYAN 2021 B CMS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 13 TeV 4 SIRUNAYN 2020 CMS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 13 TeV 5 SIRUNYAN 2020 AL CMS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 13 TeV 6 SIRUNYAN 2020 BD CMS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 13 TeV 7 SIRUNYAN 2019 BM CMS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 13 TeV 8 SIRUNYAN 2019 BP CMS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 13 TeV 9 SIRUNYAN 2019 CQ CMS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 13 TeV 10 SIRUNYAN 2018 CC CMS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 13 TeV 11 AABOUD 2017 AA ATLS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 8 TeV 12 AABOUD 2017 AG ATLS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 8 TeV 13 AABOUD 2017 D ATLS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 8 TeV 14 AABOUD 2017 J ATLS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 8 TeV 15 AABOUD 2017 M ATLS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 8 TeV 16 KHACHATRYAN 2017 AA CMS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 8 TeV 17 KHACHATRYAN 2017 M CMS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 8 TeV 18 SIRUNYAN 2017 AD CMS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 13 TeV 19 SIRUNYAN 2017 AR CMS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 8 TeV 20 AABOUD 2016 E ATLS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 8 TeV 21 AAD 2016 Q ATLS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 8 TeV 22 KHACHATRYAN 2016 AX CMS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 8 TeV 23 AAD 2015 N ATLS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 8 TeV 24 KHACHATRYAN 2015 D CMS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 8 TeV 25 AAD 2014 AM ATLS 26 CHATRCHYAN 2014 Q CMS 27 ABAZOV 2013 D D0 28 CHATRCHYAN 2013 AA CMS 29 ABBIENDI 2004 B OPAL 30 ABBIENDI 2004 L OPAL 31 HEISTER 2004 A ALEP 32 ABDALLAH 2003 I DLPH 33 ACHARD 2002 F L3 1  SIRUNYAN 2021 study electroweak ${{\mathit Z}}$-pair production in association with two jets, with the ${{\mathit Z}}$ bosons decaying to oppositely-charged electron or muon pairs. Leptons with high transverse momentum are selected, with the di-lepton invariant mass of the two ${{\mathit Z}}$ boson candidates between 60 GeV and 120 GeV, and the four-lepton invariant mass larger than 180 GeV. A total of 365 events are selected in the data, while the number of expected events is $370$ $\pm48$. Analyzing the four-lepton invariant mass distribution, the following 95$\%$ C.L. limits are derived: $-0.24$ $<$ f$_{T,0}/\Lambda {}^{4}$ $<$ 0.22, $-0.31$ $<$ f$_{T,1}/\Lambda {}^{4}$ $<$ 0.31, $-0.63$ $<$ f$_{T,2}/\Lambda {}^{4}$ $<$ 0.59, $-0.43$ $<$ f$_{T,8}/\Lambda {}^{4}$ $<$ $0.43$, $-0.92$ $<$ f$_{T,9}/\Lambda {}^{4}$ $<$ 0.92, in units of TeV${}^{-4}$. 2  TUMASYAN 2021A study electroweak ${{\mathit Z}}{{\mathit \gamma}}$ production in association with two jets, where the ${{\mathit Z}}$ boson decays to electron or muon pairs and the pair of two jets has high invariant mass, superseeding SIRUNYAN 2020AL. The number of observed (expected) electron events in the barrel and endcap regions are 375 ($349$ $\pm9$) and 174 ($166$ $\pm6$) events, respectively, while for muon events the respective numbers are 584 ($612$ $\pm13$) and 320 ($303$ $\pm8$). Analysing the ${{\mathit Z}}{{\mathit \gamma}}$ invariant mass distribution, the following 95$\%$ C.L. limits are derived: $-15.8$ $<$ f$_{M,0}/\Lambda {}^{4}$ $<$ 16.0, $-35.0$ $<$ f$_{M,1}/\Lambda {}^{4}$ $<$ 34.7, $-6.55$ $<$ f$_{M,2}/\Lambda {}^{4}$ $<$ 6.49, $-13.0$ $<$ f$_{M,3}/\Lambda {}^{4}$ $<$ 13.0, $-13.0$ $<$ f$_{M,4}/\Lambda {}^{4}$ $<$ 12.7, $-22.2$ $<$ f$_{M,5}/\Lambda {}^{4}$ $<$ 21.3, $-56.6$ $<$ f$_{M,7}/\Lambda {}^{4}$ $<$ 55.9, $-0.64$ $<$ f$_{T,0}/\Lambda {}^{4}$ $<$ 0.57, $-0.81$ $<$ f$_{T,1}/\Lambda {}^{4}$ $<$ 0.90, $-1.68$ $<$ f$_{T,2}/\Lambda {}^{4}$ $<$ 1.54, $-0.58$ $<$ f$_{T,5}/\Lambda {}^{4}$ $<$ 0.64, $-1.30$ $<$ f$_{T,6}/\Lambda {}^{4}$ $<$ 1.33, $-2.15$ $<$ f$_{T,7}/\Lambda {}^{4}$ $<$ 2.43, $-0.47$ $<$ f$_{T,8}/\Lambda {}^{4}$ $<$ 0.47, $-0.91$ $<$ f$_{T,9}/\Lambda {}^{4}$ $<$ 0.91, in units of TeV${}^{-4}$. 3  TUMASYAN 2021B measure ${{\mathit W}}$ or ${{\mathit Z}}$ boson production in association with two photons, using the leptonic decays modes of ${{\mathit W}}$ and ${{\mathit Z}}$ with electrons or muons. The number of selected ${{\mathit W}}$ $\rightarrow$ ${{\mathit e}}$( ${{\mathit \mu}}$) ${{\mathit \nu}}$ events is 1987 (2384) and the number of selected ${{\mathit Z}}$ $\rightarrow$ ${{\mathit e}}{{\mathit e}}$( ${{\mathit \mu}}{{\mathit \mu}}$) events is 110 (272) respectively. Analyzing the transverse momentum of the di-photon system, the following 95 $\%$ C.L. limits are derived in units of TeV${}^{-4}$: In the ${{\mathit W}}$ production channel, the observed limits are: $-39.9$ $<$ f$_{M,2}/\Lambda {}^{4}$ $<$ 39.5, $-63.8$ $<$ f$_{M,3}/\Lambda {}^{4}$ $<$ 65.0, $-1.30$ $<$ f$_{T,0}/\Lambda {}^{4}$ $<$ 1.30, $-1.70$ $<$ f$_{T,1}/\Lambda {}^{4}$ $<$ 1.66, $-3.64$ $<$ f$_{T,2}/\Lambda {}^{4}$ $<$ 3.64, $-0.52$ $<$ f$_{T,5}/\Lambda {}^{4}$ $<$ 0.60, $-0.60$ $<$ f$_{T,6}/\Lambda {}^{4}$ $<$ 0.68, $-1.16$ $<$ f$_{T,7}/\Lambda {}^{4}$ $<$ 1.16. In the ${{\mathit Z}}$ production channel, the observed limits are: $-5.70$ $<$ f$_{T,0}/\Lambda {}^{4}$ $<$ 5.46, $-5.70$ $<$ f$_{T,1}/\Lambda {}^{4}$ $<$ 5.46, $-11.4$ $<$ f$_{T,2}/\Lambda {}^{4}$ $<$ 10.9, $-2.92$ $<$ f$_{T,5}/\Lambda {}^{4}$ $<$ 2.92, $-3.80$ $<$ f$_{T,6}/\Lambda {}^{4}$ $<$ 3.88, $-7.88$ $<$ f$_{T,7}/\Lambda {}^{4}$ $<$ 7.72, $-1.06$ $<$ f$_{T,8}/\Lambda {}^{4}$ $<$ 1.10, $-1.82$ $<$ f$_{T,9}/\Lambda {}^{4}$ $<$ 1.82, in units of TeV${}^{-4}$. 4  SIRUNAYN 2020 study ${{\mathit W}}{{\mathit Z}}$ and same-sign ${{\mathit W}}{{\mathit W}}$ production in association with two jets, using the leptonic decays modes of the ${{\mathit W}}$ and ${{\mathit Z}}$ bosons with electrons or muons. Overall, 524 ${{\mathit W}}{{\mathit W}}$ events and 229 ${{\mathit W}}{{\mathit Z}}$ events are selected, with a Standard Model expectation of $535$ $\pm52$ and $216$ $\pm21$ events, respectively. Analyzing the transverse mass spectrum of the di-boson system and the di-jet invariant mass, the following 95$\%$ C.L. limits are derived, not using any unitarization procedure: $-0.25$ $<$ f$_{T,0}/\Lambda {}^{4}$ $<$ $0.28$, $-0.12$ $<$ f$_{T,1}/\Lambda {}^{4}$ $<$ $0.14$, $-0.35$ $<$ f$_{T,2}/\Lambda {}^{4}$ $<$ $0.48$, $-2.7$ $<$ f$_{M,0}/\Lambda {}^{4}$ $<$ $2.9$, $-4.1$ $<$ f$_{M,1}/\Lambda {}^{4}$ $<$ $4.2$, $-5.4$ $<$ f$_{M,6}/\Lambda {}^{4}$ $<$ $5.8$, $-5.7$ $<$ f$_{M,7}/\Lambda {}^{4}$ $<$ $6.0$, $-5.7$ $<$ f$_{S,0}/\Lambda {}^{4}$ $<$ $6.1$, $-16$ $<$ f$_{S,1}/\Lambda {}^{4}$ $<$ $17$, in units of TeV${}^{-4}$. The article also reports limits on these couplings by cutting the EFT expansion at the unitarity limit. 5  SIRUNYAN 2020AL study electroweak production of a ${{\mathit Z}}$ boson and a photon in association with two jets in the electron and muon decay modes of the ${{\mathit Z}}$. A signal with a significance of 3.9 standard deviations is observed, compared to a Standard Model expectation of 5.2 standard deviations. Combining with KHACHATRYAN 2017AA data at 8 TeV the final observed and expected signal significance is 4.7 and 5.5 standard deviations. Analyzing the ${{\mathit Z}}$-photon invariant mass distribution, the following 95$\%$ C.L. limits are derived: $-19.5$ $<$ f$_{M,0}/\Lambda {}^{4}$ $<$ $20.3$, $-40.5$ $<$ f$_{M,1}/\Lambda {}^{4}$ $<$ $39.5$, $-8.22$ $<$ f$_{M,2}/\Lambda {}^{4}$ $<$ $8.10$, $-17.7$ $<$ f$_{M,3}/\Lambda {}^{4}$ $<$ $17.9$, $-15.3$ $<$ f$_{M,4}/\Lambda {}^{4}$ $<$ $15.8$, $-25.1$ $<$ f$_{M,5}/\Lambda {}^{4}$ $<$ $24.5$, $-38.9$ $<$ f$_{M,6}/\Lambda {}^{4}$ $<$ $40.6$, $-60.3$ $<$ f$_{M,7}/\Lambda {}^{4}$ $<$ $62.5$, $-0.74$ $<$ f$_{T,0}/\Lambda {}^{4}$ $<$ $0.69$, $-0.98$ $<$ f$_{T,1}/\Lambda {}^{4}$ $<$ $0.96$, $-1.97$ $<$ f$_{T,2}/\Lambda {}^{4}$ $<$ $1.86$, $-0.70$ $<$ f$_{T,5}/\Lambda {}^{4}$ $<$ $0.75$, $-1.64$ $<$ f$_{T,6}/\Lambda {}^{4}$ $<$ $1.68$, $-2.59$ $<$ f$_{T,7}/\Lambda {}^{4}$ $<$ $2.82$, $-0.47$ $<$ f$_{T,8}/\Lambda {}^{4}$ $<$ $0.47$, $-1.27$ $<$ f$_{T,9}/\Lambda {}^{4}$ $<$ $1.27$, in units of TeV${}^{-4}$. 6  SIRUNYAN 2020BD study electroweak ${{\mathit W}}{{\mathit \gamma}}$ production in association with two jets, where the ${{\mathit W}}$ boson decays to electron or muon and the two jets have high invariant mass. The number of observed (expected) electron events with the photon in the barrel and endcap regions are 393 ($397.1$ $\pm18.5$) and 159 ($145.2$ $\pm10.0$) respectively, while for muon events the respective numbers are 565 ($537.9$ $\pm21.4$) and 201 ($188.2$ $\pm10.5$). Analyzing the ${{\mathit W}}{{\mathit \gamma}}$ invariant mass distribution, the following 95$\%$ C.L. limits are derived: $-8.1$ $<$ f$_{M,0}/\Lambda {}^{4}$ $<$ 8.0, $-12$ $<$ f$_{M,1}/\Lambda {}^{4}$ $<$ 12, $-2.8$ $<$ f$_{M,2}/\Lambda {}^{4}$ $<$ 2.8, $-4.4$ $<$ f$_{M,3}/\Lambda {}^{4}$ $<$ 4.4, $-5.0$ $<$ f$_{M,4}/\Lambda {}^{4}$ $<$ 5.0, $-8.3$ $<$ f$_{M,5}/\Lambda {}^{4}$ $<$ 8.3, $-16$ $<$ f$_{M,6}/\Lambda {}^{4}$ $<$ 16, $-21$ $<$ f$_{M,7}/\Lambda {}^{4}$ $<$ 20, $-0.6$ $<$ f$_{T,0}/\Lambda {}^{4}$ $<$ 0.6, $-0.4$ $<$ f$_{T,1}/\Lambda {}^{4}$ $<$ 0.4, $-1.0$ $<$ f$_{T,2}/\Lambda {}^{4}$ $<$ 1.2, $-0.5$ $<$ f$_{T,5}/\Lambda {}^{4}$ $<$ 0.5, $-0.4$ $<$ f$_{T,6}/\Lambda {}^{4}$ $<$ 0.4, $-0.9$ $<$ f$_{T,7}/\Lambda {}^{4}$ $<$ 0.9, in units of TeV${}^{-4}$. 7  SIRUNYAN 2019BM search for the final state ${{\mathit W}^{+}}{{\mathit W}^{-}}{{\mathit W}^{\pm}}$ using ${{\mathit W}}$ decays to electrons or muons. Two event samples are considered, events with three leptons, or events with two oppositely charged leptons accompanied by two jets. In a kinematic region selected to enhance the effect of anomalous couplings, no events are selected in the data, and 95$\%$ C.L. upper limits are obtained as follows: $-1.2$ $<$ f$_{T,0}/\Lambda {}^{4}$ $<$ $1.2$, $-3.3$ $<$ f$_{T,1}/\Lambda {}^{4}$ $<$ $3.3$, $-2.7$ $<$ f$_{T,2}/\Lambda {}^{4}$ $<$ $2.6$, in units of TeV$^{-4}$ and without application of a form factor. 8  SIRUNYAN 2019BP study ${{\mathit W}}{{\mathit Z}}$ plus 2 jets production, using ${{\mathit W}}$ and ${{\mathit Z}}$ decay channels with electrons or muons. In the data, 75 events are selected, with a fitted SM signal of $15.1$ $\pm1.6$ events and a fitted background of $62.4$ $\pm2.8$ events. The transverse mass distribution of the ${{\mathit W}}{{\mathit Z}}$ system is analyzed to set the following limits at 95$\%$ C.L., in units of TeV${}^{-4}$: $-9.15$ $<$ f$_{M,0}/\Lambda {}^{4}$ $<$ 9.15, $-9.15$ $<$ f$_{M,1}/\Lambda {}^{4}$ $<$ 9.45, $-26.5$ $<$ f$_{S,0}/\Lambda {}^{4}$ $<$ 27.5, $-41.2$ $<$ f$_{S,1}/\Lambda {}^{4}$ $<$ 42.8, $-0.75$ $<$ f$_{T,0}/\Lambda {}^{4}$ $<$ 0.81, $-0.49$ $<$ f$_{T,1}/\Lambda {}^{4}$ $<$ 0.55, $-1.49$ $<$ f$_{T,2}/\Lambda {}^{4}$ $<$ 1.85. 9  SIRUNYAN 2019CQ search for anomalous electroweak production of vector boson pairs in association with two jets. Events are selected by requiring two jets with a large invariant mass and rapidity separation, one or two leptons (electrons or muons), and a ${{\mathit W}}$ or ${{\mathit Z}}$ boson decaying hadronically. In the ${{\mathit W}}{{\mathit V}}$ ( ${{\mathit Z}}{{\mathit V}}$ ) channel, 347 (47) events are selected in the data, with a total expected background of $352$ $\pm19$ ($50.3$ $\pm5.8$) events. Analysing the mass distribution of the ${{\mathit W}}{{\mathit V}}$ or ${{\mathit Z}}{{\mathit V}}$ system, the following 95$\%$ C.L. limits are obtained: $-2.7<$ f$_{S,0}/\Lambda {}^{4}$ $<$ 2.7, $-3.4$ $<$ f$_{S,1}/\Lambda {}^{4}$ $<$ 3.4, $-0.69$ $<$ f$_{M,0}/\Lambda {}^{4}$ $<$ 0.70, $-2.0$ $<$ f$_{M,1}/\Lambda {}^{4}$ $<$ 2.1, $-1.3$ $<$ f$_{M,6}/\Lambda {}^{4}$ $<$ 1.3, $-3.4$ $<$ f$_{M,7}/\Lambda {}^{4}$ $<$ 3.4, $-0.12$ $<$ f$_{T,0}/\Lambda {}^{4}$ $<$ 0.11, $-0.12$ $<$ f$_{T,1}/\Lambda {}^{4}$ $<$ 0.13, $-0.28$ $<$ f$_{T,2}/\Lambda {}^{4}$ $<$ 0.28, in units of TeV${}^{-4}$. 10  SIRUNYAN 2018CC study ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV leading to a pair of same-sign ${{\mathit W}}$ pairs decaying leptonically (${{\mathit e}}$ or ${{\mathit \mu}}$) associated with a pair of jets. Isolated leptons with $p_T$ $>$ 25 (20) GeV for the leading (trailing) lepton, with $\vert {{\mathit \eta}}\vert $ $<$ 2.5 (2.4) for ${{\mathit e}}$ (${{\mathit \mu}}$) and jets with $p_T$ $>$ 30 GeV, $\vert {{\mathit \eta}}\vert $ $<$ 5.0, $\vert \Delta {{\mathit \eta}_{{jj}}}\vert $ $>$ 2.5 and ${{\mathit m}_{{jj}}}$ $>$ 500 GeV is required. Further cuts are applied to minimize ${{\mathit Z}}$ $\rightarrow$ ${{\mathit e}}{{\mathit e}}$ events, non-prompt leptons and hadronically decaying taus. The number of selected events is 201, with an expected SM signal of $66.9$ $\pm2.4$ and background of $138$ $\pm13$ events. Analysing the dilepton invariant mass spectrum the following 95$\%$ C.L. limits are derived: $-7.7<$ f$_{S,0}/\Lambda {}^{4}$ $<$ $7.7$, $-21.6$ $<$ f$_{S,1}/\Lambda {}^{4}$ $<21.8$, $-6.0$ $<$ f$_{M,0}/\Lambda {}^{4}$ $<$ $5.9$, $-8.7$ $<$ f$_{M,1}/\Lambda {}^{4}$ $<$ $9.1$, $-11.9$ $<$ f$_{M,6}/\Lambda {}^{4}$ $<$ $11.8$, $-13.3$ $<$ f$_{M,7}/\Lambda {}^{4}$ $<$ $12.9$, $-0.62$ $<$ f$_{T,0}/\Lambda {}^{4}$ $<$ $0.65$, $-0.28$ $<$ f$_{T,1}/\Lambda {}^{4}$ $<0.31$, $-0.89$ $<$ f$_{T,2}/\Lambda {}^{4}$ $<1.02$. 11  AABOUD 2017AA analyze ${{\mathit W}^{\pm}}{{\mathit W}^{\pm}}$ production in association with two jets and ${{\mathit W}}$ decay modes with electrons or muons. In the kinematic region of VBS the effect of anomalous QGCs is enhanced by requiring the transverse mass of the ${{\mathit W}}{{\mathit W}}$ system to be larger than 400 GeV. In the data, 8 events are selected with a total background expected from SM processes of $3.8$ $\pm0.6$ events. Assuming the other QGC coupling to have the SM value of zero, the observed event yield is used to determine 95$\%$ CL limits on the QGCs: $-0.14<{{\mathit \alpha}_{{4}}}<$ 0.15 and $-0.22<{{\mathit \alpha}_{{5}}}<$ 0.22. Supersedes AAD 2014AM. 12  AABOUD 2017AG determine the ${{\mathit W}}{{\mathit W}}{{\mathit \gamma}}$ and ${{\mathit W}}{{\mathit Z}}{{\mathit \gamma}}$ cross sections in 8 TeV ${{\mathit p}}{{\mathit p}}$ interactions by studying the final states ${{\mathit e}}{{\mathit \nu}}{{\mathit \mu}}{{\mathit \nu}}{{\mathit \gamma}}$ and ${{\mathit e}}{{\mathit \nu}}{{\mathit j}}{{\mathit j}}{{\mathit \gamma}}$ or ${{\mathit \mu}}{{\mathit \nu}}{{\mathit j}}{{\mathit j}}{{\mathit \gamma}}$ . Upper limits on the production cross sections are derived in a fiducial region optimized for BSM physics. These are used to derive the following 95$\%$ C.L. upper limits for quartic couplings assuming the form scale factor, $\Lambda _{FF}$ = $\infty{}$ (all in units of $10^{3}$ TeV${}^{-4}$): $-0.3$ $<$ f$_{M,0}/\Lambda {}^{4}$ $<$ 0.3, $-0.5$ $<$ f$_{M,1}/\Lambda {}^{4}$ $<$ 0.5, $-1.8$ $<$ f$_{M,2}/\Lambda {}^{4}$ $<$ 1.8, $-1.1$ $<$ f$_{M,4}/\Lambda {}^{4}$ $<$ 1.1, $-1.7$ $<$ f$_{M,5}/\Lambda {}^{4}$ $<$ 1.7, $-0.6$ $<$ f$_{M,6}/\Lambda {}^{4}$ $<$ 0.6, $-1.1$ $<$ f$_{M,7}/\Lambda {}^{4}$ $<$ 1.1, $-0.1$ $<$ f$_{T,0}/\Lambda {}^{4}$ $<$ 0.1, $-0.2$ $<$ f$_{T,1}/\Lambda {}^{4}$ $<$ 0.2, $-0.4$ $<$ f$_{T,4}/\Lambda {}^{4}$ $<$ 0.4, $-1.5$ $<$ f$_{T,5}/\Lambda {}^{4}$ $<$ 1.6, $-1.9$ $<$ f$_{T,6}/\Lambda {}^{4}$ $<$ 1.9, $-4.3$ $<$ f$_{T,7}/\Lambda {}^{4}$ $<$ 4.3. 13  AABOUD 2017D analyze electroweak diboson ( ${{\mathit W}}{{\mathit V}}$ , ${{\mathit V}}$ = ${{\mathit W}}$, ${{\mathit Z}}$) production in association with a high-mass dijet system. In the data, 32 events are selected with an expected total background of $32$ $\pm12$ events. Analysing the transverse mass distribution of the ${{\mathit W}}{{\mathit V}}$ system, the following limits are set at 95$\%$ C.L.: $-0.024$ $<$ ${{\mathit \alpha}_{{4}}}$ $<$ 0.030 and $-0.028$ $<$ ${{\mathit \alpha}_{{5}}}$ $<$ 0.033. 14  AABOUD 2017J analyze the ${{\mathit Z}}{{\mathit \gamma}}$ production in association with a high-mass dijet system, with the ${{\mathit Z}}$ boson decaying into a pair of electrons, muons, or neutrinos. In the charged lepton (neutrino) channel, events are selected with a dijet mass larger than 500 (600) GeV and a transverse photon energy larger than 250 (150) GeV, with 2 (4) events selected in the data and $0.30$ $\pm0.08$ ($1.6$ $\pm0.5$) expected background events. The observed event yield is used to determine 95$\%$ CL limits as follows: $-4.1 \times 10^{3}$ $<$ f$_{T,9}/\Lambda {}^{4}$ $<$ $4.2 \times 10^{3}$, $-1.9 \times 10^{3}$ $<$ f$_{T,8}/\Lambda {}^{4}$ $<$ $2.1 \times 10^{3}$, $-19$ $<$ f$_{T,0}/\Lambda {}^{4}$ $<$ $16$, $-160$ $<$ f$_{M,0}/\Lambda {}^{4}$ $<$ $180$, $-350$ $<$ f$_{M,1}/\Lambda {}^{4}$ $<$ $340$, $-890$ $<$ f$_{M,2}/\Lambda {}^{4}$ $<$ $890$, $-1.7 \times 10^{3}$ $<$ f$_{M,3}/\Lambda {}^{4}$ $<$ $1.7 \times 10^{3}$, in units of TeV${}^{-4}$ and without application of a form factor. 15  AABOUD 2017M analyze tri-boson ${{\mathit W}^{\pm}}{{\mathit W}^{\pm}}{{\mathit W}^{\mp}}$ production in decay channels with three charged leptons or two like-sign charged leptons with two jets, where the lepton can be an electron or muon. In the data, 24 tri-lepton events and 21 di-lepton plus jets events are selected, compared to a total event yield expected in the SM of $30.8$ $\pm3.0$ and $21.9$ $\pm2.0$, respectively. Analysing the tri-lepton transverse mass or the transverse momentum sum of the two leptons, two jets and the missing transverse energy, the following limits at 95$\%$ CL are derived for the form factor cut-off scale $\Lambda _{FF}\rightarrow\infty{}$: $-0.13$ $<$ f$_{S,0}/\Lambda {}^{4}$ $<$ $0.18$, $-0.21$ $<$ f$_{S,1}/\Lambda {}^{4}$ $<$ $0.27$, in units of $10^{4}$ TeV${}^{-4}$, which are converted into the following limits: $-0.49$ $<$ ${{\mathit \alpha}_{{4}}}$ $<$ $0.75$ and $-0.48$ $<$ ${{\mathit \alpha}_{{5}}}$ $<$ $0.62$. 16  KHACHATRYAN 2017AA analyse electroweak production of ${{\mathit Z}}{{\mathit \gamma}}$ in association with two hadronic jets, with the ${{\mathit Z}}$ boson decaying to electron or muon pairs. Events with photon transverse momentum larger than 60 GeV and di-jet invariant mass larger than 400 GeV are selected. The ${{\mathit Z}}{{\mathit \gamma}}$ inavariant mass spectrum is analysed to set 95$\%$ C.L. limits as follows: $-71$ $<$ f$_{M,0}/\Lambda {}^{4}$ $<$ $75$, $-190$ $<$ f$_{M,1}/\Lambda {}^{4}$ $<$ $182$, $-32$ $<$ f$_{M,2}/\Lambda {}^{4}$ $<$ $31$, $-58$ $<$ f$_{M,3}/\Lambda {}^{4}$ $<$ $59$, $-3.8$ $<$ f$_{T,0}/\Lambda {}^{4}$ $<$ $3.4$, $-4.4$ $<$ f$_{T,1}/\Lambda {}^{4}$ $<$ $4.4$, $-9.9$ $<$ f$_{T,2}/\Lambda {}^{4}$ $<$ $9.0$, $-1.8$ $<$ f$_{T,8}/\Lambda {}^{4}$ $<$ $1.8$, $-4.0$ $<$ f$_{T,9}/\Lambda {}^{4}$ $<$ $4.0$, in units of TeV${}^{-4}$ and without application of a form factor. 17  KHACHATRYAN 2017M analyse electroweak production of ${{\mathit W}}{{\mathit \gamma}}$ in association with two hadronic jets, with the ${{\mathit W}}$ boson decaying to electrons or muons. Events with photon transverse momentum larger than 200 GeV and di-jet invariant mass larger than 200 GeV are selected. The ${{\mathit W}}$ transverse momentum spectrum is analysed to set 95$\%$ C.L. limits as follows: $-77$ $<$ f$_{M,0}/\Lambda {}^{4}$ $<$ $74$, $-125$ $<$ f$_{M,1}/\Lambda {}^{4}$ $<$ $129$, $-26$ $<$ f$_{M,2}/\Lambda {}^{4}$ $<$ $26$, $-43$ $<$ f$_{M,3}/\Lambda {}^{4}$ $<$ $44$, $-40$ $<$ f$_{M,4}/\Lambda {}^{4}$ $<$ $40$, $-65$ $<$ f$_{M,5}/\Lambda {}^{4}$ $<$ $65$, $-129$ $<$ f$_{M,6}/\Lambda {}^{4}$ $<$ $129$, $-164$ $<$ f$_{M,7}/\Lambda {}^{4}$ $<$ $162$, $-5.4$ $<$ f$_{T,0}/\Lambda {}^{4}$ $<$ $5.6$, $-3.7$ $<$ f$_{T,1}/\Lambda {}^{4}$ $<$ $4.0$, $-11$ $<$ f$_{T,2}/\Lambda {}^{4}$ $<$ $12$, $-3.8$ $<$ f$_{T,5}/\Lambda {}^{4}$ $<$ $3.8$, $-2.8$ $<$ f$_{T,6}/\Lambda {}^{4}$ $<$ $3.0$, $-7.3$ $<$ f$_{T,7}/\Lambda {}^{4}$ $<$ $7.7$, in units of TeV${}^{-4}$ and without application of a form factor. 18  SIRUNYAN 2017AD study ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV to determine the cross section of ${{\mathit Z}}{{\mathit Z}}{{\mathit j}}{{\mathit j}}$ with the ${{\mathit Z}}$ decaying to ${{\mathit e}}{{\mathit e}}$ or ${{\mathit \mu}}{{\mathit \mu}}$ . The ${{\mathit Z}}{{\mathit Z}}$ mass distribution is used to set upper limits on the anomalous quartic couplings. The 95$\%$ upper limits for the relevant quartic couplings in units of TeV${}^{-4}$ are: $-0.46$ $<$ f$_{T,0}/\Lambda {}^{4}$ $<$ 0.44, $-0.61$ $<$ f$_{T,1}/\Lambda {}^{4}$ $<$ 0.61, $-1.2$ $<$ f$_{T,2}/\Lambda {}^{4}$ $<$ 1.2, $-0.84$ $<$ f$_{T,8}/\Lambda {}^{4}$ $<$ 0.84, $-1.8$ $<$ f$_{T,9}/\Lambda {}^{4}$ $<$ 1.8. 19  SIRUNYAN 2017AR study ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 8 TeV to determine the cross section of ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit W}}{{\mathit \gamma}}{{\mathit \gamma}}$ and ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit \gamma}}{{\mathit \gamma}}$ where ${{\mathit W}}$ $\rightarrow$ ${{\mathit \ell}}{{\mathit \nu}}$ and ${{\mathit Z}}$ $\rightarrow$ ${{\mathit \ell}^{+}}{{\mathit \ell}^{-}}$ , ${{\mathit \ell}}$ being an electron or a muon. The number of ${{\mathit W}}$ events in the ${{\mathit e}}$ and ${{\mathit \mu}}$ channels is 63 and 108 respectively, and the number of ${{\mathit Z}}$ events in the ${{\mathit e}}$ and ${{\mathit \mu}}$ channels is 117 and 141. To increase sensitivity, the transverse momentum of the leading photon is required to be larger than 70 GeV. The 95$\%$ C.L. upper limits in units of TeV${}^{-4}$ are $-701$ $<$ f$_{M,2}/\Lambda {}^{4}$ $<$ 683, $-1170$ $<$ f$_{M,3}/\Lambda {}^{4}$ $<$ 1220, $-33.5$ $<$ f$_{T,0}/\Lambda {}^{4}$ $<$ 34.0, $-44.3$ $<$ f$_{T,1}/\Lambda {}^{4}$ $<$ 44.8, $-93.8$ $<$ f$_{T,2}/\Lambda {}^{4}$ $<$ 93.2. 20  AABOUD 2016E study ${{\mathit W}}{{\mathit W}}$ production in two-photon mediated ${{\mathit p}}{{\mathit p}}$ collisions at 8 TeV where the ${{\mathit W}}$ boson decays into an electron or muon, probing the ${{\mathit \gamma}}{{\mathit \gamma}}{{\mathit W}}{{\mathit W}}$ vertex for anomalous quartic gauge couplings. The lepton $p_T$ is required to be larger than 30 GeV. Limits on anomalous couplings are determined from events with $p_T$ larger than 120 GeV where the aQGC effect is enhanced and the SM background reduced; in the data corresponding to an integrated luminosity of 20.2${\mathrm {fb}}{}^{-1}$, 1 event is selected with an expected SM background of $0.37$ $\pm0.13$ events. The 95$\%$ C.L. limits without a form-factor cutoff ($\Lambda _{{\mathrm {cutoff}}}\rightarrow\infty{}$) are as follows: $-1.7$ $<$ ${{\mathit a}^{W}_{\mathrm 0}}/\Lambda {}^{2}$ $<$ 1.7 and $-6.4$ $<$ ${{\mathit a}^{W}_{C}}/\Lambda {}^{2}$ $<$ 6.3 in units of $10^{-6}$ GeV${}^{-2}$. In terms of another set of variables: $-6.6$ $<$ f$_{M,0}/\Lambda {}^{4}$ $<$ 6.6 and $-24$ $<$ f$_{M,1}/\Lambda {}^{4}$ $<$ 25 in units of $10^{-11}$ GeV${}^{-4}$. 21  AAD 2016Q study ${{\mathit Z}}{{\mathit \gamma}}{{\mathit \gamma}}$ production in ${{\mathit p}}{{\mathit p}}$ collisions. In events with no additional jets, 29 (22) ${{\mathit Z}}$ decays to electron (muon) pairs are selected, with an expected background of $3.3$ $\pm1.1$ ($6.5$ $\pm2.0$) events, as well as 19 ${{\mathit Z}}$ decays to netrino pairs with an expected background of $8.3$ $\pm4.4$ events. Analysing the photon transverse momentum distribution for ${\mathit m}_{\mathrm { {{\mathit \gamma}} {{\mathit \gamma}} }}$ above 200 GeV (300 GeV) for lepton (neutrino) events, yields the 95$\%$ C.L. limits: $-1.6 \times 10^{4}$ $<$ f$_{M,2}/\Lambda {}^{4}$ $<$ $1.6 \times 10^{4}$, $-2.9 \times 10^{4}$ $<$ f$_{M,3}/\Lambda {}^{4}$ $<$ $2.7 \times 10^{4}$, $-86$ $<$ f$_{T,0}/\Lambda {}^{4}$ $<$ $103$, $-0.69 \times 10^{3}$ $<$ f$_{T,5}/\Lambda {}^{4}$ $<$ $0.68 \times 10^{3}$, $-0.74 \times 10^{4}$ $<$ f$_{T,9}/\Lambda {}^{4}$ $<$ $0.74 \times 10^{4}$ in units of TeV${}^{-4}$ and without application of a form factor $\Lambda _{{\mathrm {FF}}}$. 22  KHACHATRYAN 2016AX searches for anomalous ${{\mathit W}}{{\mathit W}}{{\mathit \gamma}}{{\mathit \gamma}}$ quartic gauge couplings in the two-photon-mediated process ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit p}}{{\mathit p}}{{\mathit W}}{{\mathit W}}$ , assuming the ${{\mathit W}}{{\mathit W}}{{\mathit \gamma}}$ triple gauge boson couplings to be at their Standard Model values. 13 events containing an ${{\mathit e}^{\pm}}$ ${{\mathit \mu}^{\mp}}$ pair with $p_T({{\mathit e}}$, ${{\mathit \mu}}$) $>$ 30 GeV are selected in a total luminosity of 19.7 ${\mathrm {fb}}{}^{-1}$, with an expected ${{\mathit \gamma}}$ ${{\mathit \gamma}}$ $\rightarrow$ ${{\mathit W}}{{\mathit W}}$ signal of $5.3$ $\pm0.1$ events and an expected background of $3.9$ $\pm0.5$ events. When combining with the data collected at 7 TeV (CHATRCHYAN 2013AA), and not assuming a form factor, the following 1-parameter limits at 95$\%$ C.L. are obtained from the $p_T({{\mathit e}}$, ${{\mathit \mu}}$) spectrum: $\vert {{\mathit a}^{W}_{\mathrm 0}}/\Lambda {}^{2}\vert $ $<$ $1.1 \times 10^{-6}$ GeV${}^{-2}$ (${{\mathit a}^{W}_{C}}$ = 0), and $\vert {{\mathit a}^{W}_{C}}/\Lambda {}^{2}\vert $ $<$ $4.1 \times 10^{-6}$ GeV${}^{-2}$ (${{\mathit a}^{W}_{\mathrm 0}}$ = 0). In terms of another set of variables: $\vert $f$_{M,0}/\Lambda {}^{4}\vert $ $<$ $4.2 \times 10^{-12}$ GeV${}^{-4}$, $\vert $f$_{M,1}/\Lambda {}^{4}\vert $ $<$ $16 \times 10^{-12}$ GeV${}^{-4}$, $\vert $f$_{M,2}/\Lambda {}^{4}\vert $ $<$ $2.1 \times 10^{-12}$ GeV${}^{-4}$, $\vert $f$_{M,3}/\Lambda {}^{4}\vert $ $<$ $7.8 \times 10^{-12}$ GeV${}^{-4}$. 23  AAD 2015N study ${{\mathit W}}{{\mathit \gamma}}{{\mathit \gamma}}$ events in 8 TeV ${{\mathit p}}{{\mathit p}}$ interactions, where the ${{\mathit W}}$ decays into an electron or a muon. The events are characterized by an isolated lepton, a missing transverse energy due to the decay neutrino, and two isolated photons, with the $p_T$ of the lepton and the photons being $>$ 20 GeV. The number of candidate events observed in the electron channel for N(jet) ${}\geq{}$ 0 and N(jet) = 0 is 47 and 15, the corresponding numbers for the muon channel being 110 and 53. The backgrounds expected are $30.2$ $\pm7.4$, $8.7$ $\pm3.0$, $52.1$ $\pm12.2$, and $24.4$ $\pm8.3$ respectively. The 95$\%$ C.L. limits on the values of the parameters ${{\mathit f}}_{T,0}/{{\mathit \Lambda}^{4}}$, ${{\mathit f}}_{M,2}/{{\mathit \Lambda}^{4}}$ and ${{\mathit f}}_{M,3}/{{\mathit \Lambda}^{4}}$ are $-0.9 - 90$, $-0.8 - 0.8 \times 10^{4}$, and $-1.5 - 1.4 \times 10^{4}$ respectively, without application of a form factor $\Lambda _{{\mathrm {FF}}}$. 24  KHACHATRYAN 2015D study vector-boson-scattering tagged by two jets, requiring two same-sign charged leptons arising from ${{\mathit W}^{\pm}}{{\mathit W}^{\pm}}$ production and decay. The two jets must have a transverse momentum larger than 30 GeV, while the leptons, electrons or muons, must have a transverse momentum $>$ 20 GeV. The dijet mass is required to be $>$ 500 GeV, the dilepton mass $>$ 50 GeV, with additional requirement of differing from the ${{\mathit Z}}$ mass by $>$ 15 GeV. In the two categories ${{\mathit W}^{+}}{{\mathit W}^{+}}$ and ${{\mathit W}^{-}}{{\mathit W}^{-}}$ , 10 and 2 data events are observed in a data sample corresponding to an integrated luminosity of 19.4 fb${}^{-1}$, with an expected background of $3.1$ $\pm0.6$ and $2.6$ $\pm0.5$ events. Analysing the distribution of the dilepton invariant mass, the following limits at 95$\%$ C.L. are obtained, in units of TeV${}^{-4}$: $-38$ $<$ F$_{S,0}/\Lambda {}^{4}$ $<$ 40, $-118$ $<$ F$_{S,1}/\Lambda {}^{4}$ $<$ 120, $-33$ $<$ F$_{M,0}/\Lambda {}^{4}$ $<$ 32, $-44$ $<$ F$_{M,1}/\Lambda {}^{4}$ $<$ 47, $-65$ $<$ F$_{M,6}/\Lambda {}^{4}$ $<$ 63, $-70$ $<$ F$_{M,7}/\Lambda {}^{4}$ $<$ 66, $-4.2$ $<$ F$_{T,0}/\Lambda {}^{4}$ $<$ 4.6, $-1.9$ $<$ F$_{T,1}/\Lambda {}^{4}$ $<$ 2.2, $-5.2$ $<$ F$_{T,2}/\Lambda {}^{4}$ $<$ 6.4. 25  AAD 2014AM analyze electroweak production of ${{\mathit W}}{{\mathit W}}$ jet jet same-charge diboson plus two jets production, with the ${{\mathit W}}$ bosons decaying to electron or muon, to study the quartic ${{\mathit W}}{{\mathit W}}{{\mathit W}}{{\mathit W}}$ coupling. In a kinematic region enhancing the electroweak production over the strong production, 34 events are observed in the data while $29.8$ $\pm2.4$ events are expected with a backgound of $15.9$ $\pm1.9$ events. Assuming the other QGC coupling to have the SM value of zero, the observed event yield is used to determine 95$\%$ CL limits on the quartic gauge couplings: $-0.14<{{\mathit \alpha}_{{4}}}<$ 0.16 and $-0.23<{{\mathit \alpha}_{{5}}}<$ 0.24. 26  CHATRCHYAN 2014Q study ${{\mathit W}}{{\mathit V}}{{\mathit \gamma}}$ production in 8 TeV ${{\mathit p}}{{\mathit p}}$ collisions, in the single lepton final state, with ${{\mathit W}}$ $\rightarrow$ ${{\mathit \ell}}{{\mathit \nu}}$ , ${{\mathit Z}}$ $\rightarrow$ dijet or ${{\mathit W}}$ $\rightarrow$ ${{\mathit \ell}}{{\mathit \nu}}$ , ${{\mathit W}}$ $\rightarrow$ dijet, the dijet mass resolution precluding differentiation between the ${{\mathit W}}$ and ${{\mathit Z}}$. $p_T$ and pseudo-rapidity cuts are put on the lepton, the photon and the two jets to minimize backgrounds. The dijet mass is required to be between $70 - 100$ GeV and $\vert {{\mathit \Delta}}{{\mathit \eta}_{{jj}}}\vert $ $<$ 1.4. The selected number of muon (electron) events are 183 (139), with SM expectation being $194.2$ $\pm11.5$ ($147.9$ $\pm10.7$) including signal and background. The photon $\mathit E_{T}$ distribution is used to set limits on the anomalous quartic couplings. The following 95$\%$ CL limits are deduced (all in units of TeV${}^{-2}$ or TeV${}^{-4}$): $-21$ $<{{\mathit a}_{{0}}^{W}}/{{\mathit \Lambda}^{2}}<$ 20, $-34$ $<{{\mathit a}_{{c}}^{W}}/{{\mathit \Lambda}^{2}}<$ 32, $-12$ $<{{\mathit \kappa}_{{0}}^{W}}/{{\mathit \Lambda}^{2}}<$ 10 and $-18$ $<{{\mathit \kappa}_{{c}}^{W}}/{{\mathit \Lambda}^{2}}<$ 17; and $-25$ $<{{\mathit f}}_{T,0}/{{\mathit \Lambda}^{4}}<$ 24 TeV${}^{-4}$. 27  ABAZOV 2013D searches for anomalous ${{\mathit W}}{{\mathit W}}{{\mathit \gamma}}{{\mathit \gamma}}$ quartic gauge couplings in the two-photon-mediated process ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit p}}{{\mathit p}}{{\mathit W}}{{\mathit W}}$ , assuming the ${{\mathit W}}{{\mathit W}}{{\mathit \gamma}}$ triple gauge boson couplings to be at their Standard Model values. 946 events containing an ${{\mathit e}^{+}}{{\mathit e}^{-}}$ pair with missing energy are selected in a total luminosity of 9.7 fb${}^{-1}$, with an expectation of $983$ $\pm108$ events from Standard-Model processes. The following 1-parameter limits at 95$\%$ CL are otained: $\vert {{\mathit a}_{{0}}^{W}}/\Lambda {}^{2}\vert $ $<$ $4.3 \times 10^{-4}$ GeV${}^{-2}$ (${{\mathit a}_{{c}}^{W}}$ = 0), $\vert {{\mathit a}_{{c}}^{W}}/\Lambda {}^{2}\vert $ $<$ $1.5 \times 10^{-3}$ GeV${}^{-2}$ (${{\mathit a}_{{0}}^{W}}$ = 0). 28  CHATRCHYAN 2013AA searches for anomalous ${{\mathit W}}{{\mathit W}}{{\mathit \gamma}}{{\mathit \gamma}}$ quartic gauge couplings in the two-photon-mediated process ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit p}}{{\mathit p}}{{\mathit W}}{{\mathit W}}$ , assuming the ${{\mathit W}}{{\mathit W}}{{\mathit \gamma}}$ triple gauge boson couplings to be at their Standard Model values. 2 events containing an ${{\mathit e}^{\pm}}{{\mathit \mu}^{\mp}}$ pair with $p_T({{\mathit e}}$, ${{\mathit \mu}}$) $>$ 30 GeV are selected in a total luminosity of 5.05 fb${}^{-1}$, with an expected ${{\mathit p}}{{\mathit p}}{{\mathit W}}{{\mathit W}}$ signal of $2.2$ $\pm0.4$ events and an expected background of $0.84$ $\pm0.15$ events. The following 1-parameter limits at 95$\%$ CL are otained from the $p_T({{\mathit e}}$, ${{\mathit \mu}}$) spectrum: $\vert {{\mathit a}_{{0}}^{W}}/\Lambda {}^{2}\vert $ $<$ $4.0 \times 10^{-6}$ GeV${}^{-2}$ (${{\mathit a}_{{c}}^{W}}$ = 0), $\vert {{\mathit a}_{{c}}^{W}}/\Lambda {}^{2}\vert $ $<$ $1.5 \times 10^{-5}$ GeV${}^{-2}$ (${{\mathit a}_{{0}}^{W}}$ = 0). 29  ABBIENDI 2004B select 187 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit W}^{+}}{{\mathit W}^{-}}{{\mathit \gamma}}$ events in the C.M. energy range $180 - 209$ GeV, where $\mathit E_{{{\mathit \gamma}}}>$2.5 GeV, the photon has a polar angle $\vert $cos $\theta _{\gamma }$ $\vert <$ 0.975 and is well isolated from the nearest jet and charged lepton, and the effective masses of both fermion-antifermion systems agree with the ${{\mathit W}}$ mass within 3 $\Gamma _{{{\mathit W}}}$. The measured differential cross section as a function of the photon energy and photon polar angle is used to extract the 95$\%$ CL limits: $-0.020$ GeV${}^{-2}<\mathit a_{0}/\Lambda {}^{2}<0.020$ GeV${}^{-2}$, $-0.053$~GeV${}^{-2}<\mathit a_{c}/\Lambda {}^{2}<0.037$ GeV${}^{-2}$ and $-0.16$ GeV${}^{-2}<\mathit a_{n}/\Lambda {}^{2}<0.15$ GeV${}^{-2}$. 30  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${}^{-2}$. 31  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${}^{-2}$. 32  ABDALLAH 2003I select 122 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit W}^{+}}{{\mathit W}^{-}}{{\mathit \gamma}}$ events in the C.M. energy range $189 - 209$ GeV, where $\mathit E_{{{\mathit \gamma}}}>$5 GeV, the photon has a polar angle $\vert $cos $\theta _{{{\mathit \gamma}}}\vert <0.95$ and is well isolated from the nearest charged fermion. A fit to the photon energy spectra yields $\mathit a_{\mathit c}/\Lambda {}^{2}$= $0.000$ ${}^{+0.019}_{-0.040}$ GeV${}^{-2}$, $\mathit a_{0}/\Lambda {}^{2}$= $-0.004$ ${}^{+0.018}_{-0.010}$ GeV${}^{-2}$, ${{\widetilde{\mathit a}}}_{0}/\Lambda {}^{2}$= $-0.007$ ${}^{+0.019}_{-0.008}$ GeV${}^{-2}$, $\mathit a_{\mathit n}/\Lambda {}^{2}$= $-0.09$ ${}^{+0.16}_{-0.05}$ GeV${}^{-2}$, and ${{\widetilde{\mathit a}}}_{\mathit n}/\Lambda {}^{2}$= $+0.05$ ${}^{+0.07}_{-0.15}$ GeV${}^{-2}$, keeping the other parameters fixed to their Standard Model values$~$(0). The 95$\%$ CL limits are: $-0.063$ GeV${}^{-2}<\mathit a_{\mathit c}/\Lambda {}^{2}<+0.032$ GeV${}^{-2}$, $-0.020$ GeV${}^{-2}<\mathit a_{0}/\Lambda {}^{2}<+0.020$ GeV${}^{-2}$, $-0.020$ GeV${}^{-2}<{{\widetilde{\mathit a}}}_{0}/\Lambda {}^{2}<+0.020$ GeV${}^{-2}$, $-0.18$ GeV${}^{-2}<\mathit a_{\mathit n}/\Lambda {}^{2}<+0.14$ GeV${}^{-2}$, $-0.16$ GeV${}^{-2}<{{\widetilde{\mathit a}}}_{\mathit n}/\Lambda {}^{2}<+0.17$ GeV${}^{-2}$. 33  ACHARD 2002F select 86 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit W}^{+}}{{\mathit W}^{-}}{{\mathit \gamma}}$ events at $192 - 207$ GeV, where $\mathit E_{{{\mathit \gamma}}}>$5 GeV and the photon is well isolated. They also select 43 acoplanar ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \nu}}{{\overline{\mathit \nu}}}{{\mathit \gamma}}{{\mathit \gamma}}$ events in this energy range, where the photon energies are $>5~$GeV and $>1~$GeV and the photon polar angles are between 14$^\circ{}$ and 166$^\circ{}$. All these 43 events are in the recoil mass region corresponding to the ${{\mathit Z}}$ ($75 - 110$ GeV). Using the shape and normalization of the photon spectra in the ${{\mathit W}^{+}}{{\mathit W}^{-}}{{\mathit \gamma}}$ events, and combining with the 42 event sample from 189 GeV data (ACCIARRI 2000T), they obtain: $\mathit a_{0}/\Lambda {}^{2}$= $0.000$ $\pm0.010$ GeV${}^{-2}$, $\mathit a_{\mathit c}/\Lambda {}^{2}$= $-0.013$ $\pm0.023$ GeV${}^{-2}$, and $\mathit a_{\mathit n}/\Lambda {}^{2}$= $-0.002$ $\pm0.076$ GeV${}^{-2}$. Further combining the analyses of ${{\mathit W}^{+}}{{\mathit W}^{-}}{{\mathit \gamma}}$ events with the low recoil mass region of ${{\mathit \nu}}{{\overline{\mathit \nu}}}{{\mathit \gamma}}{{\mathit \gamma}}$ events (including samples collected at $183+189$ GeV), they obtain the following one-parameter 95$\%$ CL limits: $-0.015$ GeV${}^{-2}<\mathit a_{0}/\Lambda {}^{2}<0.015$ GeV${}^{-2}$, $-0.048$ GeV${}^{-2}<\mathit a_{\mathit c}/\Lambda {}^{2}<0.026$ GeV${}^{-2}$, and $-0.14$ GeV${}^{-2}<\mathit a_{\mathit n}/\Lambda {}^{2}<0.13$ GeV${}^{-2}$.

References:

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