Combining the LEP-2 results taking into account the correlations, the following 95$\%$ CL limits are derived [SCHAEL 2013A]:

$-0.28<$ $\mathit f{}^{{{\mathit Z}}}_{4}<+0.32$, $-0.34<$ $\mathit f{}^{{{\mathit Z}}}_{5}<+0.35$, $-0.17<$ $\mathit f{}^{{{\mathit \gamma}}}_{4}<+0.19$, $-0.35<$ $\mathit f{}^{{{\mathit \gamma}}}_{5}$ $<+0.32$.

Some of the recent results from the Tevatron and LHC experiments individually surpass the combined LEP-2 results in precision (see below).

VALUE DOCUMENT ID TECN  COMMENT • • We do not use the following data for averages, fits, limits, etc. • • 1 SIRUNYAN 2021 Q CMS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 13 TeV 2 AABOUD 2019 AY ATLS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 13 TeV 3 AABOUD 2018 Q ATLS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 13 TeV 4 SIRUNYAN 2018 BT CMS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 13 TeV 5 KHACHATRYAN 2015 B CMS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 8 TeV 6 KHACHATRYAN 2015 BC CMS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 7, 8 TeV 7 AAD 2013 Z ATLS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 7 TeV 8 CHATRCHYAN 2013 B CMS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 7 TeV 9 SCHAEL 2009 ALEP ${\it{}E}^{\it{}ee}_{\rm{}cm}$ = $192 - 209$ GeV 10 ABAZOV 2008 K D0 ${\it{}E}^{\it{}p\overline{\it{}p}}_{\rm{}cm}$ = 1.96 TeV 11 ABDALLAH 2007 C DLPH ${\it{}E}^{\it{}ee}_{\rm{}cm}$ = $183 - 208$ GeV 12 ABBIENDI 2004 C OPAL 13 ACHARD 2003 D L3 1  SIRUNYAN 2021Q measure ${{\mathit Z}}{{\mathit Z}}$ production where both ${{\mathit Z}}$ bosons decay in the electron or muon channel. Analyzing the four-lepton invariant mass distribution, the following limits are derived at 95$\%$ C.L. in units of $10^{-4}$: $-6.6$ $<$ ${{\mathit f}_{{4}}^{Z}}$ $<$ 6.0, $-5.5$ $<$ ${{\mathit f}_{{5}}^{Z}}$ $<$ 7.5, $-7.8$ $<$ ${{\mathit f}}{}^{{{\mathit \gamma}}}_{4}$ $<$ 7.1, $-6.8$ $<$ ${{\mathit f}}{}^{{{\mathit \gamma}}}_{5}$ $<$ 7.5. This set of parameters is linearly related to a set of EFT parameters, resulting in the following limits at 95$\%$ C.L. in units of TeV${}^{-4}$: $-2.3$ $<$ c$_{ {{\widetilde{\mathit B}}} {{\mathit W}} }/\Lambda {}^{4}$ $<$ 2.5, $-1.4$ $<$ c$_{ {{\mathit W}} {{\mathit W}} }/\Lambda {}^{4}$ $<$ 1.2, $-1.4$ $<$ c$_{ {{\mathit B}} {{\mathit W}} }/\Lambda {}^{4}$ $<$ 1.3, $-1.2$ $<$ c$_{ {{\mathit B}} {{\mathit B}} }/\Lambda {}^{4}$ $<$ 1.2. 2  AABOUD 2019AY study ${{\mathit Z}}{{\mathit Z}}$ production in the ${{\mathit \ell}}{{\mathit \ell}}{{\mathit \nu}}{{\mathit \nu}}$ decay channel. Events with a pair of isolated high-transverse momentum charged leptons (electron pairs or muon pairs), and with large missing energy, are selected. In the data, 371 (416) di-electron (di-muon) events are found, with a total expected background of $128$ $\pm8$ ($143$ $\pm8$) events. Analysing the transverse momentum distribution of the charged dilepton system above 150 GeV, the following 95$\%$ C.L. limits are derived in units of $10^{-3}$: $-1.2$ $<$ ${{\mathit f}}{}^{{{\mathit \gamma}}}_{4}$ $<$ 1.2, $-1.0$ $<$ ${{\mathit f}_{{4}}^{Z}}$ $<$ 1.0, $-1.2$ $<$ ${{\mathit f}}{}^{{{\mathit \gamma}}}_{5}$ $<$ 1.2, $-1.0$ $<$ ${{\mathit f}_{{5}}^{Z}}$ $<$ 1.0. 3  AABOUD 2018Q study ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit Z}}$ events at $\sqrt {s }$ = 13 TeV with ${{\mathit Z}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ or ${{\mathit Z}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ . The number of events observed in the 4${{\mathit e}}$, 2${{\mathit e}}$ 2${{\mathit \mu}}$, and 4${{\mathit \mu}}$ channels is 249, 465, and 303 respectively. Analysing the $p_T$ spectrum of the leading ${{\mathit Z}}$ boson, the following the following 95$\%$ C.L. limits are derived in units of $10^{-4}$: $-1.8$ $<$ ${{\mathit f}}{}^{{{\mathit \gamma}}}_{4}$ $<$ $1.8$, $-1.5$ $<$ ${{\mathit f}}{}^{Z}_{4}$ $<$ $1.5$, $-1.8$ $<$ ${{\mathit f}}{}^{{{\mathit \gamma}}}_{5}$ $<$ $1.8$, $-1.5$ $<$ ${{\mathit f}}{}^{Z}_{5}$ $<$ $1.5$. 4  SIRUNYAN 2018BT study ${{\mathit p}}{{\mathit p}}{{\mathit Z}}{{\mathit Z}}$ events at $\sqrt {s }$ = 13 TeV with ${{\mathit Z}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ or ${{\mathit Z}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ . The number of events observed in the 4${{\mathit e}}$, 2 ${{\mathit e}}$2 ${{\mathit \mu}}$ , and 4${{\mathit \mu}}$ channels is 220, 543 and 335 respectively. Analysing the 4-lepton invariant mass spectrum, the following 95$\%$ C.L. limits are derived in units of $10^{-3}$: $-1.2$ $<$ ${{\mathit f}}{}^{{{\mathit \gamma}}}_{4}$ $<$ $1.3$, $-1.2$ $<$ ${{\mathit f}}{}^{Z}_{4}$ $<$ $1.0$, $-1.2$ $<$ ${{\mathit f}}{}^{{{\mathit \gamma}}}_{5}$ $<$ $1.3$, $-1.0$ $<$ ${{\mathit f}}{}^{Z}_{5}$ $<$ $1.3$. 5  KHACHATRYAN 2015B study ${{\mathit Z}}{{\mathit Z}}$ production in 8 TeV ${{\mathit p}}{{\mathit p}}$ collisions. In the decay modes ${{\mathit Z}}$ ${{\mathit Z}}$ $\rightarrow$ 4 ${{\mathit e}}$ , 4${{\mathit \mu}}$, 2 ${{\mathit e}}$2 ${{\mathit \mu}}$ , 54, 75, 148 events are observed, with an expected background of $2.2$ $\pm0.9$, $1.2$ $\pm0.6$, and $2.4$ $\pm1.0$ events, respectively. Analysing the 4-lepton invariant mass spectrum in the range from 110 GeV to 1200 GeV, the following 95$\%$ C.L. limits are obtained: $\vert {{\mathit f}}{}^{Z}_{4}\vert $ $<$ 0.004, $\vert {{\mathit f}}{}^{Z}_{5}\vert $ $<$ 0.004, $\vert {{\mathit f}}{}^{{{\mathit \gamma}}}_{4}\vert $ $<$ 0.005, $\vert {{\mathit f}}{}^{{{\mathit \gamma}}}_{5}\vert $ $<$ 0.005. 6  KHACHATRYAN 2015BC use the cross section measurement of the final state ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit Z}}$ $\rightarrow$ 2 ${{\mathit \ell}}$2 ${{\mathit \nu}}$ , (${{\mathit \ell}}$ being an electron or a muon) at 7 and 8 TeV to put limits on these triple gauge couplings. Effective mass of the charged lepton pair is required to be in the range $83.5 - 98.5$ GeV and the dilepton $p_T$ $>$ 45 GeV. The reduced missing $\mathit E_{T}$ is required to be $>$ 65 GeV, which takes into account the fake missing $\mathit E_{T}$ due to detector effects. The numbers of ${{\mathit e}^{+}}{{\mathit e}^{-}}$ and ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ events selected are 35 and 40 at 7 TeV and 176 and 271 at 8 TeV respectively. The production cross sections so obtained are in agreement with SM predictions. The following 95$\%$ C.L. limits are set: $-0.0028$ $<$ ${{\mathit f}_{{4}}^{Z}}$ $<$ 0.0032, $-0.0037$ $<$ ${{\mathit f}}{}^{{{\mathit \gamma}}}_{4}$ $<$ 0.0033, $-0.0029$ $<$ ${{\mathit f}_{{5}}^{Z}}$ $<$ 0.0031, $-0.0033$ $<$ ${{\mathit f}}{}^{{{\mathit \gamma}}}_{5}$ $<$ 0.0037. Combining with previous results (KHACHATRYAN 2015B and CHATRCHYAN 2013B) which include 7 TeV and 8 TeV data on the final states ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit Z}}$ $\rightarrow$ 2 ${{\mathit \ell}}$2 ${{\mathit \ell}^{\,'}}$ where ${{\mathit \ell}}$ and ${{\mathit \ell}^{\,'}}$ are an electron or a muon, the best limits are $-0.0022$ $<$ ${{\mathit f}_{{4}}^{Z}}$ $<$ 0.0026, $-0.0029$ $<$ ${{\mathit f}}{}^{{{\mathit \gamma}}}_{4}$ $<$ 0.0026, $-0.0023$ $<$ ${{\mathit f}_{{5}}^{Z}}$ $<$ 0.0023, $-0.0026$ $<$ ${{\mathit f}}{}^{{{\mathit \gamma}}}_{5}$ $<$ 0.0027. 7  AAD 2013Z study ${{\mathit Z}}{{\mathit Z}}$ production in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 7 TeV. In the ${{\mathit Z}}$ ${{\mathit Z}}$ $\rightarrow$ ${{\mathit \ell}^{+}}{{\mathit \ell}^{-}}{{\mathit \ell}^{'+}}{{\mathit \ell}^{'-}}$ final state they observe a total of 66 events with an expected background of $0.9$ $\pm1.3$. In the ${{\mathit Z}}$ ${{\mathit Z}}$ $\rightarrow$ ${{\mathit \ell}^{+}}{{\mathit \ell}^{-}}{{\mathit \nu}}{{\mathit \nu}}$ final state they observe a total of 87 events with an expected background of $46.9$ $\pm5.2$. The limits on anomalous TGCs are determined using the observed and expected numbers of these ${{\mathit Z}}{{\mathit Z}}$ events binned in ${{\mathit p}_{{T}}^{Z}}$. The 95$\%$ C.L. are as follows: for form factor scale ${{\mathit \Lambda}}$ = $\infty{}$, $-0.015$ $<$ ${{\mathit f}}{}^{{{\mathit \gamma}}}_{4}$ $<$ 0.015, $-0.013$ $<$ ${{\mathit f}}{}^{Z}_{4}$ $<$ 0.013, $-0.016$ $<$ ${{\mathit f}}{}^{{{\mathit \gamma}}}_{5}$ $<$ 0.015, $-0.013$ $<$ ${{\mathit f}}{}^{Z}_{5}$ $<$ 0.013; for form factor scale ${{\mathit \Lambda}}$ = 3 TeV, $-0.022$ $<$ ${{\mathit f}}{}^{{{\mathit \gamma}}}_{4}$ $<$ 0.023, $-0.019$ $<$ ${{\mathit f}}{}^{Z}_{4}$ $<$ 0.019, $-0.023$ $<$ ${{\mathit f}}{}^{{{\mathit \gamma}}}_{5}$ $<$ 0.023, $-0.020$ $<$ ${{\mathit f}}{}^{Z}_{5}$ $<$ 0.019. 8  CHATRCHYAN 2013B study ${{\mathit Z}}{{\mathit Z}}$ production in ${{\mathit p}}{{\mathit p}}$ collisions and select 54 ${{\mathit Z}}{{\mathit Z}}$ candidates in the ${{\mathit Z}}$ decay channel with electrons or muons with an expected background of $1.4$ $\pm0.5$ events. The resulting 95$\%$ C.L. ranges are: $-0.013$ $<$ ${{\mathit f}}{}^{{{\mathit \gamma}}}_{4}$ $<$ 0.015, $-0.011$ $<$ ${{\mathit f}}{}^{Z}_{4}$ $<$ 0.012, $-0.014$ $<$ ${{\mathit f}}{}^{{{\mathit \gamma}}}_{5}$ $<$ 0.014, $-0.012$ $<$ ${{\mathit f}}{}^{Z}_{5}$ $<$ 0.012. 9  Using data collected in the center of mass energy range $192 - 209$ GeV, SCHAEL 2009 select 318 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit Z}}$ events with 319.4 expected from the standard model. Using this data they derive the following 95$\%$ CL limits: $-0.321<{{\mathit f}}{}^{{{\mathit \gamma}}}_{4}<$ 0.318, $-0.534<{{\mathit f}_{{4}}^{Z}}<$ 0.534, $-0.724<{{\mathit f}}{}^{{{\mathit \gamma}}}_{5}<$ 0.733, $-1.194<{{\mathit f}_{{5}}^{Z}}<$ 1.190. 10  ABAZOV 2008K search for ${{\mathit Z}}{{\mathit Z}}$ and ${{\mathit Z}}{{\mathit \gamma}^{*}}$ events with 1$~$fb${}^{-1}$ ${{\mathit p}}{{\overline{\mathit p}}}$ data at $\sqrt {s }$ = 1.96 TeV in ( ${{\mathit e}}{{\mathit e}}$)( ${{\mathit e}}{{\mathit e}}$), ( ${{\mathit \mu}}{{\mathit \mu}}$)( ${{\mathit \mu}}{{\mathit \mu}}$), ( ${{\mathit e}}{{\mathit e}}$)( ${{\mathit \mu}}{{\mathit \mu}}$) final states requiring the lepton pair masses to be $>$ 30 GeV. They observe 1 event, which is consistent with an expected signal of $1.71$ $\pm0.15$ events and a background of $0.13$ $\pm0.03$ events. From this they derive the following limits, for a form factor ($\Lambda $) value of 1.2 TeV: $-0.28<{{\mathit f}_{{40}}^{Z}}<$ 0.28, $-0.31<{{\mathit f}_{{50}}^{Z}}<$ 0.29, $-0.26<{{\mathit f}_{{40}^#p{gamma}}}<$ 0.26, $-0.30<{{\mathit f}_{{50}^#p{gamma}}}<$ 0.28. 11  Using data collected at $\sqrt {s }$ = $183 - 208$ GeV, ABDALLAH 2007C select 171 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit Z}}$ events with ${{\mathit Z}}$ $\rightarrow$ ${{\mathit q}}{{\overline{\mathit q}}}$ or lepton pair (except an explicit ${{\mathit \tau}}$ pair), and 74 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit \gamma}^{*}}$ events with a ${{\mathit q}}{{\overline{\mathit q}}}{{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ or ${{\mathit q}}{{\overline{\mathit q}}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ signature, to derive 95$\%$ CL limits on ${{\mathit f}_{{i}}^{V}}$. Each limit is derived with other parameters set to zero. They report: $-0.40<{{\mathit f}_{{4}}^{Z}}<$ 0.42, $-0.38<{{\mathit f}_{{5}}^{Z}}<$ 0.62, $-0.23<{{\mathit f}}{}^{{{\mathit \gamma}}}_{4}<$ 0.25, $-0.52<{{\mathit f}}{}^{{{\mathit \gamma}}}_{5}<$ 0.48. 12  ABBIENDI 2004C study ${{\mathit Z}}{{\mathit Z}}$ production in ${{\mathit e}^{+}}{{\mathit e}^{-}}$ collisions in the C.M. energy range $190 - 209$ GeV. They select 340 events with an expected background of 180 events. Including the ABBIENDI 2000N data at 183 and 189 GeV (118 events with an expected background of 65 events) they report the following 95$\%$ CL limits: $-0.45<\mathit f{}^{{{\mathit Z}}}_{4}<0.58$, $-0.94<\mathit f{}^{{{\mathit Z}}}_{5}<0.25$, $-0.32<\mathit f{}^{{{\mathit \gamma}}}_{4}<0.33$, and $-0.71<\mathit f{}^{{{\mathit \gamma}}}_{5}<0.59$. 13  ACHARD 2003D study ${{\mathit Z}}$-boson pair production in ${{\mathit e}^{+}}{{\mathit e}^{-}}$ collisions in the C.M. energy range $200 - 209$ GeV. They select 549 events with an expected background of 432 events. Including the ACCIARRI 1999G and ACCIARRI 1999O data (183 and 189 GeV respectively, 286 events with an expected background of 241 events) and the $192 - 202$ GeV ACCIARRI 2001I results (656 events, expected background of 512 events), they report the following 95$\%$ CL limits: $-0.48{}\leq{}\mathit f{}^{{{\mathit Z}}}_{4}{}\leq{}0.46$, $-0.36{}\leq{}\mathit f{}^{{{\mathit Z}}}_{5}{}\leq{}1.03$, $-0.28{}\leq{}\mathit f{}^{{{\mathit \gamma}}}_{4}{}\leq{}0.28$, and $-0.40{}\leq{}\mathit f{}^{{{\mathit \gamma}}}_{5}{}\leq{}0.47$.

References:

SIRUNYAN 2021Q EPJ C81 200 Measurements of ${\mathrm{p}} {\mathrm{p}} \rightarrow {\mathrm{Z}} {\mathrm{Z}} $ production cross sections and constraints on anomalous triple gauge couplings at $\sqrt{s} = 13\,\text {TeV} $ AABOUD 2019AY JHEP 1910 127 Measurement of $ZZ$ production in the $\ell\ell\nu\nu$ final state with the ATLAS detector in $pp$ collisions at $\sqrt{s} = 13$ TeV AABOUD 2018Q PR D97 032005 $ZZ \to \ell^{+}\ell^{-}\ell^{\prime +}\ell^{\prime -}$ cross-section measurements and search for anomalous triple gauge couplings in 13 TeV $pp$ collisions with the ATLAS detector SIRUNYAN 2018BT EPJ C78 165 Measurements of the $\mathrm {p}\mathrm {p}\rightarrow \mathrm{Z}\mathrm{Z}$ production cross section and the $\mathrm{Z}\rightarrow 4\ell $ branching fraction, and constraints on anomalous triple gauge couplings at $\sqrt{s} = 13\,\text {TeV} $ KHACHATRYAN 2015B PL B740 250 Measurement of the ${{\mathit p}}{{\mathit p}}\rightarrow{{\mathit Z}}{{\mathit Z}}$ Production Cross Section and Constraints on Anomalous Triple Gauge Couplings in Four-Lepton Final States at $\sqrt {s }$ = 8 TeV KHACHATRYAN 2015BC EPJ C75 511 Measurements of the ${{\mathit Z}}{{\mathit Z}}$ Production Cross Sections in the 2${{\mathit \ell}}2{{\mathit \nu}}$ Channel in Proton$−$Proton Collisions at $\sqrt {s }$ = 7 and 8 TeV and Combined Constraints on triple Gauge Couplings AAD 2013Z JHEP 1303 128 Measurement of ${{\mathit Z}}{{\mathit Z}}$ Production in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV and Limits on Anomalous ${{\mathit Z}}{{\mathit Z}}{{\mathit Z}}$ and ${{\mathit Z}}{{\mathit Z}}{{\mathit \gamma}}$ Couplings with the ATLAS Detector CHATRCHYAN 2013B JHEP 1301 063 Measurement of the ${{\mathit Z}}{{\mathit Z}}$ Production Cross Section and Search for Anomalous Couplings in 2${{\mathit \ell}}2{{\mathit \ell}^{\,'}}$ Final States in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV SCHAEL 2009 JHEP 0904 124 Measurement of ${{\mathit Z}}$-Pair Production in ${{\mathit e}^{+}}{{\mathit e}^{-}}$ Collisions and Constraints on Anomalous Neutral Gauge Couplings ABAZOV 2008K PRL 100 131801 Search for ${{\mathit Z}}{{\mathit Z}}$ and ${{\mathit Z}}{{\mathit \gamma}^{*}}$ Production in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.96 TeV and Limits on Anomalous ${{\mathit Z}}{{\mathit Z}}{{\mathit Z}}$ and ${{\mathit Z}}{{\mathit Z}}{{\mathit \gamma}^{*}}$ Couplings ABDALLAH 2007C EPJ C51 525 Study of Triple-Gauge-Boson Couplings ${{\mathit Z}}{{\mathit Z}}{{\mathit Z}}$ , ${{\mathit Z}}{{\mathit Z}}{{\mathit \gamma}}$ and ${{\mathit Z}}{{\mathit \gamma}}{{\mathit \gamma}}$ at LEP ABBIENDI 2004C EPJ C32 303 Study of ${{\mathit Z}}$ Pair Production and Anomalous Couplings in ${{\mathit e}^{+}}{{\mathit e}^{-}}$ Collisions at $\sqrt {s }$ between 190 GeV and 209 GeV ACHARD 2003D PL B572 133 ${{\mathit Z}}$ Boson Pair Production at LEP