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ABDALLAH 2010 use data on the final states ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit j}}{{\mathit j}}{{\mathit \ell}}{{\mathit \nu}}$, ${{\mathit j}}{{\mathit j}}{{\mathit j}}{{\mathit j}}$, ${{\mathit j}}{{\mathit j}}{{\mathit X}}$, ${{\mathit \ell}}{{\mathit X}}$, at center-of-mass energies between $189 - 209$ GeV at LEP2, where ${{\mathit j}}$ = jet, ${{\mathit \ell}}$ = lepton, and ${{\mathit X}}$ represents missing momentum. The fit is carried out keeping all other parameters fixed at their SM values.

SCHAEL 2005A study single$-$photon, single$-{{\mathit W}}$, and $WW-$pair production from 183 to 209 GeV. The result quoted here is derived from the $WW-$pair production sample. Each parameter is determined from a single$-$parameter fit in which the other parameters assume their Standard Model values.

ABBIENDI 2004D combine results from ${{\mathit W}^{+}}{{\mathit W}^{-}}$ in all decay channels. Only $\mathit CP$-conserving couplings are considered and each parameter is determined from a single-parameter fit in which the other parameters assume their Standard Model values. The 95$\%$ confidence interval is $0.923<\mathit g{}^{{{\mathit Z}}}_{1}<1.054$.

⁴

ACHARD 2004D study $WW-$pair production, single$-{{\mathit W}}$ production and single$-$photon production with missing energy from 189 to 209 GeV. The result quoted here is obtained from the $WW-$pair production sample including data from 161 to 183 GeV, ACCIARRI 1999Q. Each parameter is determined from a single$-$parameter fit in which the other parameters assume their Standard Model values.

⁵

SIRUNYAN 2020BA study electroweak production of a ${{\mathit W}}$ boson in association with two jets, using ${{\mathit W}}$ decays in the electron or muon channel. The isolated muons (electrons) are required to have a transverse momentum larger than 25 (30) GeV, while the transverse momentum of the two jets has to be larger than 50 and 30 GeV. A total of 2.382 (1.051) million events are selected in the muon (electron) channel, with a Standard Model expectation of $2.39$ $\pm0.17$ ($1.054$ $\pm0.058$) million events. Analyzing the transverse momentum distribution of the charged leptons from ${{\mathit W}}$ decay, the following 95$\%$ C.L. limit is obtained: 0.971 $<$ ${{\mathit g}_{{{1}}}^{Z}}$ $<$ 1.044. Combining this result with that from the closely-related electroweak ${{\mathit Z}}$-jet-jet production SIRUNYAN 2018BZ, the limit becomes: 0.979 $<$ ${{\mathit g}_{{{1}}}^{Z}}$ $<$ 1.034.

⁶

SIRUNYAN 2019CL study ${{\mathit W}}{{\mathit W}}$ and ${{\mathit W}}{{\mathit Z}}$ production in lepton + jet events, with one ${{\mathit W}}$ boson decaying leptonically (electron or muon), and another ${{\mathit W}}$ or ${{\mathit Z}}$ boson decaying hadronically, reconstructed as a single massive large-radius jet. In the electron channel 2,456 (2,235) events are selected in the ${{\mathit W}}{{\mathit W}}({{\mathit W}}{{\mathit Z}}$) category, while in the muon channel 3,996 (3572) events are selected in the ${{\mathit W}}{{\mathit W}}({{\mathit W}}{{\mathit Z}}$) category. Analysing the di-boson invariant mass distribution, the following 95$\%$ C.L. limit is obtained: 0.9939 $<$ ${{\mathit g}_{{{1}}}^{Z}}$ $<$ 1.0074.

⁷

SIRUNYAN 2018BZ study ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit Z}}~\mathit jet~jet$ events at 13 TeV where ${{\mathit Z}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $/$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$. Isolated electrons and muons are selected with $p_T$ of the leading/sub-leading lepton $>$ 30/20 GeV and $\vert {{\mathit \eta}}\vert $ $<$ 2.4, with the di-lepton invariant mass within 15 GeV of the ${{\mathit Z}}$ mass. The two highest $p_T$ jets are selected with $p_T$ of the leading/sub-leading jet $>$ 50/30 GeV respectively and dijet invariant mass $>$ 200 GeV. Templates in the transverse momentum of the ${{\mathit Z}}$ are utilized to set limits on the triple gauge couplings in the EFT and the LEP parametrizations. The following 95$\%$ C.L. limit is obtained: $0.965$ $<$ $\mathit g{}^{{{\mathit Z}}}_{1}$ $<$ $1.042$.

⁸

AABOUD 2017S analyze electroweak production of a ${{\mathit W}}$ boson in association with two jets at high dijet invariant mass, with the ${{\mathit W}}$ boson decaying to electron or muon plus neutrino. In the signal region of dijet mass larger than 1 TeV and leading-jet transverse momentum larger than 600 GeV, 30 events are observed in the data with $39$ $\pm4$ events expected in the Standard Model, yielding the following limit at 95$\%$ CL for the form factor cut-off scale ${{\mathit \Lambda}_{{{FF}}}}\rightarrow\infty{}$: $0.87<\mathit g{}^{{{\mathit Z}}}_{1}<1.12$.

⁹

AABOUD 2017U analyze production of ${{\mathit W}}{{\mathit W}}$ or ${{\mathit W}}{{\mathit Z}}$ boson pairs with one ${{\mathit W}}$ boson decaying to electron or muon plus neutrino, and the other ${{\mathit W}}$ or ${{\mathit Z}}$ boson decaying hadronically. The hadronic decay system is reconstructed as either a resolved two-jet system or as a single large jet. Analysing the transverse momentum distribution of the hadronic system above 100 GeV yields the following limit at 95$\%$ CL for the form factor cut-off scale ${{\mathit \Lambda}_{{{FF}}}}\rightarrow\infty{}$: $0.979$ $<$ $\mathit g{}^{{{\mathit Z}}}_{1}$ $<$ $1.024$.

¹⁰

KHACHATRYAN 2017O analyse ${{\mathit W}}{{\mathit Z}}$ production where each boson decays into electrons or muons. Events are required to have a tri-lepton invariant mass larger than 100 GeV, with one of the lepton pairs having an invariant mass within 20 GeV of the ${{\mathit Z}}$ boson mass. The ${{\mathit Z}}$ transverse momentum spectrum is analyzed to set a 95$\%$ C.L. limit of: $0.982$ $<$ $\mathit g{}^{{{\mathit Z}}}_{1}$ $<$ $1.035$.

¹¹

SIRUNYAN 2017X study ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit W}}{{\mathit W}}/{{\mathit W}}$ ${{\mathit Z}}$ $\rightarrow$ ${{\mathit \ell}}{{\mathit \nu}}{{\mathit q}}{{\overline{\mathit q}}}$ production at 8 TeV where ${{\mathit \ell}}$ is an electron or muon with $p_T$ $>$ 30 or 25 GeV respectively. Suitable cuts are put on the $p_T$ of the dijet system and the missing $\mathit E_{T}$ of the event yielding a total of 285 and 204 ${{\mathit W}}{{\mathit V}}$ events observed in the electron and muon channels. The following 95$\%$ C.L. limit is obtained: 0.9913 $<$ ${{\mathit g}_{{{1}}}^{Z}}$ $<$ 1.024.

¹²

AAD 2016AR study ${{\mathit W}}{{\mathit W}}$ production in ${{\mathit p}}{{\mathit p}}$ collisions and select 6636 ${{\mathit W}}{{\mathit W}}$ candidates in decay modes with electrons or muons with an expected background of $1546$ $\pm157$ events. Assuming the LEP formulation and setting the form-factor $\Lambda $ to infinity, a fit to the transverse momentum distribution of the leading charged lepton, leads to a 95$\%$ C.L. range of 0.984 $<$ ${{\mathit g}^{Z}_{\mathrm 1}}<$ 1.027.

¹³

AAD 2016P study ${{\mathit W}}{{\mathit Z}}$ production in ${{\mathit p}}{{\mathit p}}$ collisions and select 2091 ${{\mathit W}}{{\mathit Z}}$ candidates in 4 decay modes with electrons and muons, with an expected background of $1825$ $\pm7$ events. Analyzing the ${{\mathit W}}{{\mathit Z}}$ transverse momentum distribution, the resulting 95$\%$ C.L. limit is: 0.981$<{{\mathit g}^{Z}_{\mathrm 1}}<$ 1.029.

¹⁴

AAD 2014Y determine the electroweak ${{\mathit Z}}$-dijet cross section in 8 TeV ${{\mathit p}}{{\mathit p}}$ collisions. ${{\mathit Z}}$ $\rightarrow$ ${{\mathit e}}{{\mathit e}}$ and ${{\mathit Z}}$ $\rightarrow$ ${{\mathit \mu}}{{\mathit \mu}}$ decays are selected with the di-lepton $p_T>$ 20 GeV and mass in the $81 - 101$ GeV range. Minimum two jets are required with $p_T>$ 55 and 45 GeV and no additional jets with $p_T>$ 25 GeV in the rapidity interval between them. The normalized $p_T$ balance between the ${{\mathit Z}}$ and the two jets is required to be $<$ 0.15. This leads to a selection of 900 events with dijet mass $>$ 1 TeV. The number of signal and background events expected is 261 and 592 respectively. A Poisson likelihood method is used on an event by event basis to obtain the 95$\%$ CL limit 0.5 $<{{\mathit g}_{{{1}}}^{Z}}<$ 1.26 for a form factor value $\Lambda $ = $\infty{}$.

¹⁵

AAD 2013AL study ${{\mathit W}}{{\mathit W}}$ production in ${{\mathit p}}{{\mathit p}}$ collisions and select 1325 ${{\mathit W}}{{\mathit W}}$ candidates in decay modes with electrons or muons with an expected background of $369$ $\pm61$ events. Assuming the LEP formulation and setting the form-factor ${{\mathit \Lambda}}$ = infinity, a fit to the transverse momentum distribution of the leading charged lepton, leads to a 95$\%$ C.L. range of 0.961 $<$ $\mathit g{}^{{{\mathit Z}}}_{1}$ $<$ 1.052. Supersedes AAD 2012AC.

¹⁶

CHATRCHYAN 2013BF determine the ${{\mathit W}^{+}}{{\mathit W}^{-}}$ production cross section using unlike sign di-lepton (${{\mathit e}}$ or ${{\mathit \mu}}$) events with high $\not\!\!p_T$. The leptons have $p_T>$ 20 GeV/c and are isolated. 1134 candidate events are observed with an expected SM background of $247$ $\pm34$. The $p_T$ distribution of the leading lepton is fitted to obtain 95$\%$ C.L. limits of 0.905 ${}\leq{}{{\mathit g}_{{{1}}}^{Z}}{}\leq{}$ 1.095.

¹⁷

AAD 2012CD study ${{\mathit W}}{{\mathit Z}}$ production in ${{\mathit p}}{{\mathit p}}$ collisions and select 317 ${{\mathit W}}{{\mathit Z}}$ candidates in three ${{\mathit \ell}}{{\mathit \nu}}$ decay modes with an expected background of $68.0$ $\pm10.0$ events. The resulting 95$\%$ C.L. range is: 0.943 $<$ ${{\mathit g}^{Z}_{\mathrm 1}}<$ 1.093. Supersedes AAD 2012V.

¹⁸

AALTONEN 2012AC study ${{\mathit W}}{{\mathit Z}}$ production in ${{\mathit p}}{{\overline{\mathit p}}}$ collisions and select 63 ${{\mathit W}}{{\mathit Z}}$ candidates in three ${{\mathit \ell}}{{\mathit \nu}}$ decay modes with an expected background of $7.9$ $\pm1.0$ events. Based on the cross section and shape of the ${{\mathit Z}}$ transverse momentum spectrum, the following 95$\%$ C.L. range is reported: 0.92 $<$ ${{\mathit g}_{{{1}}}^{Z}}$ $<$ 1.20 for a form factor of $\Lambda $ = 2 TeV.

¹⁹

ABAZOV 2012AG combine new results with already published results on ${{\mathit W}}{{\mathit \gamma}}$, ${{\mathit W}}{{\mathit W}}$ and ${{\mathit W}}{{\mathit Z}}$ production in order to determine the couplings with increased precision, superseding ABAZOV 2008R, ABAZOV 2011AC, ABAZOV 2009AJ, ABAZOV 2009AD. The 68$\%$ C.L. result for a formfactor cutoff of $\Lambda $ = 2 TeV is ${{\mathit g}_{{{1}}}^{Z}}$ = $1.022$ ${}^{+0.032}_{-0.030}$.

²⁰

ABAZOV 2011 study the ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ 3 ${{\mathit \ell}}{{\mathit \nu}}$ process arising in ${{\mathit W}}{{\mathit Z}}$ production. They observe 34 ${{\mathit W}}{{\mathit Z}}$ candidates with an estimated background of 6 events. An analysis of the $p_T$ spectrum of the ${{\mathit Z}}$ boson leads to a 95$\%$ C.L. limit of 0.944 $<$ ${{\mathit g}_{{{1}}}^{Z}}$ $<$ 1.154, for a form factor $\Lambda $ = 2 TeV.

²¹

AALTONEN 10K study ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit W}^{+}}{{\mathit W}^{-}}$ with ${{\mathit W}}$ $\rightarrow$ ${{\mathit e}}/{{\mathit \mu}}{{\mathit \nu}}$. The $p_T$ of the leading (second) lepton is required to be $>$ 20 (10) GeV. The final number of events selected is 654 of which $320$ $\pm47$ are estimated to be background. The 95$\%$ C.L. interval is 0.76 $<$ ${{\mathit g}^{Z}_{\mathrm 1}}<$ 1.34 for $\Lambda $ = 1.5 TeV and 0.78 $<$ ${{\mathit g}^{Z}_{\mathrm 1}}<$ 1.30 for $\Lambda $ = 2 TeV.

²²

ABAZOV 2009AD study the ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit \ell}}{{\mathit \nu}}~$2jet process arising in ${{\mathit W}}{{\mathit W}}$ and ${{\mathit W}}{{\mathit Z}}$ production. They select 12,473 (14,392) events in the electron (muon) channel with an expected di-boson signal of 436 (527) events. The results on the anomalous couplings are derived from an analysis of the $p_T$ spectrum of the 2-jet system and quoted at 68$\%$ C.L. and for a form factor of 2 TeV. This measurement is not used for obtaining the mean as it is for a specific form factor. The 95$\%$ confidence interval is 0.88 $<$ ${{\mathit g}_{{{1}}}^{Z}}<$ 1.20.

²³

ABAZOV 2009AJ study the ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ 2 ${{\mathit \ell}}$2 ${{\mathit \nu}}$ process arising in ${{\mathit W}}{{\mathit W}}$ production. They select 100 events with an expected ${{\mathit W}}{{\mathit W}}$ signal of 65 events. An analysis of the $p_T$ spectrum of the two charged leptons leads to 95$\%$ C.L. limits of 0.86 $<$ ${{\mathit g}_{{{1}}}^{Z}}<$ 1.3, for a form factor $\Lambda $ = 2 TeV.

²⁴

ABDALLAH 2008C determine this triple gauge coupling from the measurement of the spin density matrix elements in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit W}^{+}}{{\mathit W}^{-}}$ $\rightarrow$ ( ${{\mathit q}}{{\mathit q}}$) ( ${{\mathit \ell}}{{\mathit \nu}}$), where ${{\mathit \ell}}$ = ${{\mathit e}}$ or ${{\mathit \mu}}$. Values of all other couplings are fixed to their standard model values.

²⁵

ABAZOV 2007Z set limits on anomalous TGCs using the measured cross section and $p_T({{\mathit Z}}$) distribution in ${{\mathit W}}{{\mathit Z}}$ production with both the ${{\mathit W}}$ and the ${{\mathit Z}}$ decaying leptonically into electrons and muons. Setting the other couplings to their standard model values, the 95$\%$ C.L. limit for a form factor scale $\Lambda $ = 2 TeV is 0.86 $<{{\mathit g}_{{{1}}}^{Z}}<$ 1.35.

²⁶

ABAZOV 2005S study ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit W}}{{\mathit Z}}$ production with a subsequent trilepton decay to ${{\mathit \ell}}{{\mathit \nu}}{{\mathit \ell}^{\,'}}{{\overline{\mathit \ell}}^{\,'}}$ (${{\mathit \ell}}$ and ${{\mathit \ell}^{\,'}}$ = ${{\mathit e}}$ or ${{\mathit \mu}}$). Three events (estimated background $0.71$ $\pm0.08$ events) with $WZ$ decay characteristics are observed from which they derive limits on the anomalous couplings. The 95$\%$ CL limit for a form factor scale $\Lambda $ = 1.5 TeV is $0.51$ $<$ $\mathit g{}^{{{\mathit Z}}}_{1}$ $<$ 1.66, fixing ${{\mathit \lambda}_{{{Z}}}}$ and ${{\mathit \kappa}_{{{Z}}}}$ to their Standard Model values.

²⁷

ABREU 2001I combine results from ${{\mathit e}^{+}}{{\mathit e}^{-}}$ interactions at 189 GeV leading to ${{\mathit W}^{+}}{{\mathit W}^{-}}$ and ${{\mathit W}}{{\mathit e}}{{\mathit \nu}_{{{e}}}}$ final states with results from ABREU 1999L at 183 GeV. The 95$\%$ confidence interval is $0.84<\mathit g{}^{{{\mathit Z}}}_{1}<1.13$.

²⁸

ABBOTT 1999I perform a simultaneous fit to the ${{\mathit W}}{{\mathit \gamma}}$, ${{\mathit W}}$ ${{\mathit W}}$ $\rightarrow$ dilepton, ${{\mathit W}}{{\mathit W}}/{{\mathit W}}$ ${{\mathit Z}}$ $\rightarrow$ ${{\mathit e}}{{\mathit \nu}}{{\mathit j}}{{\mathit j}}$, ${{\mathit W}}{{\mathit W}}/{{\mathit W}}$ ${{\mathit Z}}$ $\rightarrow$ ${{\mathit \mu}}{{\mathit \nu}}{{\mathit j}}{{\mathit j}}$, and ${{\mathit W}}$ ${{\mathit Z}}$ $\rightarrow$ trilepton data samples. For $\Lambda $ = $2.0$ TeV, the 95$\%$CL limits are $0.63<\mathit g{}^{{{\mathit Z}}}_{1}<1.57$, fixing ${{\mathit \lambda}_{{{Z}}}}$ and ${{\mathit \kappa}_{{{Z}}}}$ to their Standard Model values, and assuming Standard Model values for the ${{\mathit W}}{{\mathit W}}{{\mathit \gamma}}$ couplings.

References

Except where otherwise noted, content of the 2025 Review of Particle Physics is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) license. The publication of the Review of Particle Physics is supported by US DOE, MEXT (Japan), INFN (Italy) and CERN. Individual collaborators receive support for their PDG activities from their respective institutes or funding agencies. © 2025. See LBNL disclaimers.

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