# ${{\boldsymbol a}_{{0}}}/\Lambda {}^{2}$, ${{\boldsymbol a}_{{c}}}/\Lambda {}^{2}$, ${{\boldsymbol a}_{{n}}}/\Lambda {}^{2}$, ${{\boldsymbol \kappa}_{{0}}^{W}}/\Lambda {}^{2}$, ${{\boldsymbol \kappa}_{{c}}^{W}}/\Lambda {}^{2}$, ${{\boldsymbol f}}_{T,0}/\Lambda {}^{4}$, ${{\boldsymbol f}}_{M,i}/\Lambda {}^{4}$, ${{\boldsymbol \alpha}_{{4}}}$, ${{\boldsymbol \alpha}_{{5}}}$, F$_{S,i}/\Lambda {}^{4}$, F$_{M,i}/\Lambda {}^{4}$, F$_{T,i}/\Lambda {}^{4}$ INSPIRE search

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
 2017 AA
ATLS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 8 TeV
2
 2017 AG
${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 8 TeV
3
 2017 D
ATLS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 8 TeV
4
 2017 J
ATLS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 8 TeV
5
 2017 M
ATLS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 8 TeV
6
 2017 AA
CMS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 8 TeV
7
 2017 M
CMS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 8 TeV
8
${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 13 TeV
9
 2017 AR
${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 8 TeV
10
 2016 E
ATLS
11
 2016 Q
ATLS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 8 TeV
12
 2016 AX
CMS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 8 TeV
13
 2015 N
ATLS
14
 2015 D
CMS
15
 2014 AM
ATLS
16
 2014 Q
CMS
17
 2013 D
D0
18
 2013 AA
CMS
19
 2004 B
OPAL
20
 2004 L
OPAL
21
 2004 A
ALEP
22
 2003 I
DLPH
23
 2002 F
L3
1  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.
2  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.
3  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.
4  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.
5  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 $-0.48$ $<$ ${{\mathit \alpha}_{{5}}}$ $<$ $0.62$.
6  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.
7  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.
8  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.
9  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.
10  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: $-1.7$ $<$ ${{\mathit a}^{W}_{{0}}}/\Lambda {}^{2}$ $<$ 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${}^{-4}$.
11  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 $\Lambda _{{\mathrm {FF}}}$.
12  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: $\vert {{\mathit a}^{W}_{{0}}}/\Lambda {}^{2}\vert$ $<$ $1.1 \times 10^{-6}$ GeV${}^{-2}$ (${{\mathit a}^{W}_{{C}}}$ = 0), and $\vert {{\mathit a}^{W}_{{C}}}/\Lambda {}^{2}\vert$ $<$ $4.1 \times 10^{-6}$ GeV${}^{-2}$ (${{\mathit a}^{W}_{{0}}}$ = 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${}^{-4}$.
13  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 $-0.9 - 0.9$, $-0.8 - 0.8$, and $-1.5 - 1.4$ respectively, without application of a form factor $\Lambda _{{\mathrm {FF}}}$.
14  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.
15  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.
16  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${}^{-4}$.
17  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).
18  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).
19  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${}^{-2}$.
20  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${}^{-2}$.
21  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${}^{-2}$.
22  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${}^{-2}$.
23  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:
 AABOUD 2017J
JHEP 1707 107 Studies of ${{\mathit Z}}{{\mathit \gamma}}$ Production in Association with a High-Mass Dijet System in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV with the ATLAS Detector
 AABOUD 2017AA
PR D96 012007 Measurement of ${{\mathit W}^{\pm}}{{\mathit W}^{\pm}}$ Vector-Boson Scattering and Limits on Anomalous Quartic Gauge Couplings with the ATLAS Detector
 AABOUD 2017AG
EPJ C77 646 Study of ${{\mathit W}}{{\mathit W}}{{\mathit \gamma}}$ and ${{\mathit W}}{{\mathit Z}}{{\mathit \gamma}}$ Production in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV and Search for Anomalous Quartic Gauge Couplings with the ATLAS Experiment
 AABOUD 2017D
PR D95 032001 Search for Anomalous Electroweak Production of ${{\mathit W}}{{\mathit W}}/{{\mathit W}}{{\mathit Z}}$ in Association with a High-Mass Dijet System in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV with the ATLAS Detector
 AABOUD 2017M
EPJ C77 141 Search for Triboson ${{\mathit W}^{\pm}}{{\mathit W}^{\pm}}{{\mathit W}^{\mp}}$ Production in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV with the ATLAS Detector
 KHACHATRYAN 2017M
JHEP 1706 106 Measurement of Electroweak-Induced Production of ${{\mathit W}}{{\mathit \gamma}}$ with Two Jets in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV and Constraints on Anomalous Quartic Gauge Couplings
 KHACHATRYAN 2017AA
PL B770 380 Measurement of the Cross Section for Electroweak Production of ${{\mathit Z}}{{\mathit \gamma}}$ in Association with Two Jets and Constraints on Anomalous Quartic Gauge Couplings in Proton-Proton Collisions at $\sqrt {s }$ =8 TeV
PL B774 682 Measurement of Vector Boson Scattering and Constraints on Anomalous Quartic Couplings from Events with Four Leptons and Two Jets in Proton-Proton Collisions at $\sqrt {s }$ = 13 TeV
 SIRUNYAN 2017AR
JHEP 1710 072 Measurements of the ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit W}}{{\mathit \gamma}}{{\mathit \gamma}}$ and ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit \gamma}}{{\mathit \gamma}}$ Cross Sections and Limits on Anomalous Quartic Gauge Couplings at $\sqrt {s }$ = 8 TeV
 AABOUD 2016E
PR D94 032011 Measurement of Exclusive ${{\mathit \gamma}}$ ${{\mathit \gamma}}$ $\rightarrow$ ${{\mathit W}^{+}}{{\mathit W}^{-}}$ Production and Search for Exclusive Higgs Boson Production in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV using the ATLAS Detector
PR D93 112002 Measurements of ${{\mathit Z}}{{\mathit \gamma}}$ and ${{\mathit Z}}{{\mathit \gamma}}{{\mathit \gamma}}$ Production in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV with the ATLAS Detector
 KHACHATRYAN 2016AX
JHEP 1608 119 Evidence for Exclusive ${{\mathit \gamma}}$ ${{\mathit \gamma}}$ $\rightarrow$ ${{\mathit W}^{+}}{{\mathit W}^{-}}$ Production and Constraints on Anomalous Quartic Gauge Couplings in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 and 8 TeV
PRL 115 031802 Evidence of ${{\mathit W}}{{\mathit \gamma}}{{\mathit \gamma}}$ Production in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV and Limits on Anomalous Quartic Gauge Couplings with the ATLAS Detector
 KHACHATRYAN 2015D
PRL 114 051801 Study of Vector Boson Scattering and Search for New Physics in Events with Two Same-Sign Leptons and Two Jets
PRL 113 141803 Evidence for Electroweak Production of ${{\mathit W}^{\pm}}{{\mathit W}^{\pm}}{{\mathit j}}{{\mathit j}}$ in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV with the ATLAS Detector
 CHATRCHYAN 2014Q
PR D90 032008 Search for ${{\mathit W}}{{\mathit W}}{{\mathit \gamma}}$ and ${{\mathit W}}{{\mathit Z}}{{\mathit \gamma}}$ Production and Constraints on Anomalous Quartic Gauge Couplings in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV
 ABAZOV 2013D
PR D88 012005 Search for Anomalous Quartic ${{\mathit W}}{{\mathit W}}{{\mathit \gamma}}{{\mathit \gamma}}$ Couplings in Dielectron and Missing Energy Final States in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.96 TeV
 CHATRCHYAN 2013AA
JHEP 1307 116 Study of Exclusive Two-Photon Production of ${{\mathit W}^{+}}{{\mathit W}^{-}}$ in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV and Constraints on Anomalous Quartic Gauge Couplings
 ABBIENDI 2004B
PL B580 17 A Study of ${{\mathit W}^{+}}{{\mathit W}^{-}}{{\mathit \gamma}}$ Events at LEP
 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
 ABDALLAH 2003I
EPJ C31 139 Measurement of the ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit W}^{+}}{{\mathit W}^{-}}{{\mathit \gamma}}$ Cross-Section and Limits on Anomalous Quartic Gauge Couplings with DELPHI
 ACHARD 2002F
PL B527 29 Study of the ${{\mathit W}^{+}}{{\mathit W}^{-}}{{\mathit \gamma}}$ Process and Limits on Anomalous Quartic Gauge Boson Couplings at LEP