pdgLive

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.

²	SCHAEL 2005A study single$-$photon, single$-{{\mathit W}}$, and $WW-$pair production from 183 to 209 GeV. 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 $0.73<\kappa _{{{\mathit \gamma}}}<1.07$.

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 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

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 ${{\mathit \Lambda}_{{{FF}}}}\rightarrow\infty{}$: $0.939$ $<$ ${{\mathit \kappa}}_{{{\mathit \gamma}}}$ $<$ $1.064$.

⁶

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: 0.956 $<$ ${{\mathit \kappa}_{{{\gamma}}}}$ $<$ 1.063.

⁷

CHATRCHYAN 2014AB measure ${{\mathit W}}{{\mathit \gamma}}$ production cross section for ${{\mathit p}}{}^{\gamma }_{T}>$ 15 GeV and R(${{\mathit \ell}}{{\mathit \gamma}}$) $>$ 0.7, which is the separation between the ${{\mathit \gamma}}$ and the final state charged lepton (${{\mathit e}}$ or ${{\mathit \mu}}$) in the azimuthal angle-pseudorapidity (${{\mathit \phi}}−{{\mathit \eta}}$) plane. After background subtraction the number of ${{\mathit e}}{{\mathit \nu}}{{\mathit \gamma}}$ and ${{\mathit \mu}}{{\mathit \nu}}{{\mathit \gamma}}$ events is determined to be $3200$ $\pm325$ and $4970$ $\pm543$ respectively, compatible with expectations from the SM. This leads to a 95$\%$ CL limit of 0.62 $<{{\mathit \kappa}}_{{{\mathit \gamma}}}<$ 1.29, assuming other parameters have SM values.

⁸

AAD 2013AN study ${{\mathit W}}{{\mathit \gamma}}$ production in ${{\mathit p}}{{\mathit p}}$ collisions. In events with no additional jet, 4449 (6578) W decays to electron (muon) are selected, with an expected background of $1662$ $\pm262$ ($2538$ $\pm362$) events. Analysing the photon $p_T$ spectrum above 100 GeV yields a 95$\%$ C.L. limit of 0.59 $<$ $\kappa _{\gamma }$ $<$ 1.46. Supersedes AAD 2012BX.

⁹

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 0.79 ${}\leq{}{{\mathit k}}_{{{\mathit \gamma}}}{}\leq{}$ 1.22.

¹⁰

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 $\kappa _{{{\mathit \gamma}}}$ = $1.048$ ${}^{+0.106}_{-0.105}$.

¹¹

ABAZOV 2011AC study ${{\mathit W}}{{\mathit \gamma}}$ production in ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at 1.96 TeV, with the ${{\mathit W}}$ decay products containing an electron or a muon. They select 196 (363) events in the electron (muon) mode, with a SM expectation of 190 (372) events. A likelihood fit to the photon $\mathit E_{T}$ spectrum above 15 GeV yields at 95$\%$ C.L. the result: 0.6 $<{{\mathit \kappa}_{{{\gamma}}}}<$ 1.4 for a formfactor ${{\mathit \Lambda}}$ = 2 TeV.

¹²

CHATRCHYAN 2011M study ${{\mathit W}}{{\mathit \gamma}}$ production in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 7 TeV using 36$~$pb${}^{-1}{{\mathit p}}{{\mathit p}}$ data with the ${{\mathit W}}$ decaying to electron and muon. The total cross section is measured for photon transverse energy ${{\mathit E}}{}^{{{\mathit \gamma}}}_{T}>$ 10 GeV and spatial separation from charged leptons in the plane of pseudo rapidity and azimuthal angle $\Delta {{\mathit R}}({{\mathit \ell}},{{\mathit \gamma}})>$ 0.7. The number of candidate (background) events is 452 ($228$ $\pm21$) for the electron channel and 520 ($277$ $\pm25$) for the muon channel. Setting other couplings to their standard model value, they derive a 95$\%$ CL limit of $-0.11$ $<$ ${{\mathit \kappa}_{{{\gamma}}}}<$ 2.04.

¹³

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 0.37 $<$ ${{\mathit \kappa}}_{{{\mathit \gamma}}}<$ 1.72 for $\Lambda $ = 1.5 TeV and 0.43 $<$ ${{\mathit \kappa}}_{{{\mathit \gamma}}}<$ 1.65 for $\Lambda $ = 2 TeV.

¹⁴

AARON 2009B study single-${{\mathit W}}$ production in ${{\mathit e}}{{\mathit p}}$ collisions at 0.3 TeV C.M. energy. They select 53 ${{\mathit W}}$ $\rightarrow$ ${{\mathit e}}$ $/$ ${{\mathit \mu}}$ events with a standard model expectation of $54.1$ $\pm7.4$ events. Fitting the transverse momentum spectrum of the hadronic recoil system they obtain a 95$\%$ C.L. limit of $-3.7<{{\mathit \kappa}_{{{\gamma}}}}<-1.5$ or 0.3$<{{\mathit \kappa}_{{{\gamma}}}}<$1.5, where the ambiguity is due to the quadratic dependence of the cross section to the coupling parameter.

¹⁵

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 0.56 $<$ ${{\mathit \kappa}_{{{\gamma}}}}<$ 1.55.

¹⁶

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 0.46 $<$ ${{\mathit \kappa}_{{{\gamma}}}}<$ 1.83, for a form factor $\Lambda $ = 2 TeV.

¹⁷

ABAZOV 2008R use 0.7 fb${}^{-1}{{\mathit p}}{{\overline{\mathit p}}}$ data at $\sqrt {s }$ = 1.96 TeV to select 263 ${{\mathit W}}{{\mathit \gamma}}{+}$ ${{\mathit X}}$ events, of which 187 constitute signal, with the ${{\mathit W}}$ decaying into an electron or a muon, which is required to be well separated from a photon with $\mathit E_{T}>$ 9 GeV. A likelihood fit to the photon $\mathit E_{T}$ spectrum yields a 95$\%$ CL limit 0.49 $<\kappa _{\gamma }<$ 1.51 with other couplings fixed to their Standard Model values.

¹⁸

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.

¹⁹

AALTONEN 2007L set limits on anomalous TGCs using the $p_T({{\mathit W}}$) distribution in ${{\mathit W}}{{\mathit W}}$ and ${{\mathit W}}{{\mathit Z}}$ production with the ${{\mathit W}}$ decaying to an electron or muon and the ${{\mathit Z}}$ to 2 jets. Setting other couplings to their standard model value, the 95$\%$ C.L. limits are 0.54 $<{{\mathit \kappa}_{{{\gamma}}}}<$ 1.39 for a form factor scale $\Lambda $ = 1.5 TeV.

²⁰

ABAZOV 2006H study ${{\overline{\mathit p}}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit W}}{{\mathit W}}$ production with a subsequent decay ${{\mathit W}}$ ${{\mathit W}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit \nu}_{{{e}}}}{{\mathit e}^{-}}{{\overline{\mathit \nu}}_{{{e}}}}$, ${{\mathit W}}$ ${{\mathit W}}$ $\rightarrow$ ${{\mathit e}^{\pm}}{{\mathit \nu}_{{{e}}}}{{\mathit \mu}^{\mp}}{{\mathit \nu}_{{{\mu}}}}$ or ${{\mathit W}}$ ${{\mathit W}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{{\mu}}}}{{\mathit \mu}^{-}}{{\overline{\mathit \nu}}_{{{\mu}}}}$. The 95$\%$ C.L. limit for a form factor scale $\Lambda $ = 1 TeV is $\text{- 0.05}<\kappa _{\gamma }<$2.29, fixing $\lambda _{\gamma }$=0. With the assumption that the ${{\mathit W}}{{\mathit W}}{{\mathit \gamma}}$ and ${{\mathit W}}{{\mathit W}}{{\mathit Z}}$ couplings are equal the 95$\%$ C.L. one-dimensional limit ($\Lambda $ = 2 TeV) is 0.68 $<\kappa <$ 1.45.

²¹

ABAZOV 2005J perform a likelihood fit to the photon $\mathit E_{T}$ spectrum of ${{\mathit W}}{{\mathit \gamma}}$ $+$ X events, where the ${{\mathit W}}$ decays to an electron or muon which is required to be well separated from the photon. For $\Lambda $ = 2.0 TeV the 95$\%$ CL limits are $0.12$ $<$ ${{\mathit \kappa}_{{{\gamma}}}}$ $<$ 1.96. In the fit $\lambda _{{{\mathit \gamma}}}$ is kept fixed to its Standard Model value.

²²

ABREU 2001I combine results from ${{\mathit e}^{+}}{{\mathit e}^{-}}$ interactions at 189 GeV leading to ${{\mathit W}^{+}}{{\mathit W}^{-}}$, ${{\mathit W}}{{\mathit e}}{{\mathit \nu}_{{{e}}}}$, and ${{\mathit \nu}}{{\overline{\mathit \nu}}}{{\mathit \gamma}}$ final states with results from ABREU 1999L at 183 GeV. The 95$\%$ confidence interval is $0.87<{{\mathit \kappa}_{{{\gamma}}}}<1.68$.

²³	BREITWEG 2000 search for ${{\mathit W}}$ production in events with large hadronic $p_T$. For $p_T>$20 GeV, the upper limit on the cross section gives the 95$\%$CL limit $-3.7<{{\mathit \kappa}_{{{\gamma}}}}<2.5$ (for $\lambda _{\gamma }$=0).

²⁴

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 $0.75<{{\mathit \kappa}_{{{\gamma}}}}<1.39$.

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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