CMS-SMP-22-018

CMS-SMP-22-018 ; CERN-EP-2025-020
Observation of $\mathrm{W}\mathrm{Z}\gamma$ production and constraints on new physics scenarios in proton-proton collisions at $\sqrt{s} =$ 13 TeV
CMS Collaboration
27 March 2025
Submitted to Phys. Rev. D
Abstract: A measurement of the $\mathrm{W}\mathrm{Z}\gamma$ triboson production cross section is presented. The analysis is based on a data sample of proton-proton collisions at a center-of-mass energy of $\sqrt{s}=$ 13 TeV recorded with the CMS detector at the LHC, corresponding to an integrated luminosity of 138 fb $^{-1}$ . The analysis focuses on the final state with three charged leptons, $\ell^{\pm}\nu\ell^{+}\ell^{-}$ , where $\ell = \mathrm{e}$ or $\mu$ , accompanied by an additional photon. The observed (expected) significance of the $\mathrm{W}\mathrm{Z}\gamma$ signal is 5.4 (3.8) standard deviations. The cross section is measured in a fiducial region to be 5.48 $\pm$ 1.11 fb, which is compatible with the prediction of 3.69 $\pm$ 0.24 fb at next-to-leading order in quantum chromodynamics. Exclusion limits are set on anomalous quartic gauge couplings and on the production cross sections of massive axion-like particles.
Links: e-print arXiv:2503.21977 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Feynman diagrams for $\mathrm{W}\mathrm{Z}\gamma$ production at LO, including production through a QGC vertex (left), a representative diagram for TGC production (second from left), and a multiperipheral interaction (third from left). The rightmost diagram shows the $\mathrm{W}\mathrm{Z}\gamma$ production including an ALP, denoted ${\mathrm{a}}$ , which decays to a Z boson and a photon.
png pdf	Figure 1-a: Feynman diagrams for $\mathrm{W}\mathrm{Z}\gamma$ production at LO, including production through a QGC vertex (left), a representative diagram for TGC production (second from left), and a multiperipheral interaction (third from left). The rightmost diagram shows the $\mathrm{W}\mathrm{Z}\gamma$ production including an ALP, denoted ${\mathrm{a}}$ , which decays to a Z boson and a photon.
png pdf	Figure 1-b: Feynman diagrams for $\mathrm{W}\mathrm{Z}\gamma$ production at LO, including production through a QGC vertex (left), a representative diagram for TGC production (second from left), and a multiperipheral interaction (third from left). The rightmost diagram shows the $\mathrm{W}\mathrm{Z}\gamma$ production including an ALP, denoted ${\mathrm{a}}$ , which decays to a Z boson and a photon.
png pdf	Figure 1-c: Feynman diagrams for $\mathrm{W}\mathrm{Z}\gamma$ production at LO, including production through a QGC vertex (left), a representative diagram for TGC production (second from left), and a multiperipheral interaction (third from left). The rightmost diagram shows the $\mathrm{W}\mathrm{Z}\gamma$ production including an ALP, denoted ${\mathrm{a}}$ , which decays to a Z boson and a photon.
png pdf	Figure 1-d: Feynman diagrams for $\mathrm{W}\mathrm{Z}\gamma$ production at LO, including production through a QGC vertex (left), a representative diagram for TGC production (second from left), and a multiperipheral interaction (third from left). The rightmost diagram shows the $\mathrm{W}\mathrm{Z}\gamma$ production including an ALP, denoted ${\mathrm{a}}$ , which decays to a Z boson and a photon.
png pdf	Figure 2: The distributions of the variables used in the simultaneous fit for the nonprompt $\ell$ CR (upper left), nonprompt $\gamma$ CR (upper right), ZZ CR (lower left), and SR (lower right) after the fit to the data. The black points with error bars represent the data and their statistical uncertainties, whereas the shaded band represents the total uncertainties. The bottom panel in each figure shows the ratio of the number of events observed in data to that of the total SM prediction. The last bin of each plot has been extended to include the overflow contribution.
png pdf	Figure 2-a: The distributions of the variables used in the simultaneous fit for the nonprompt $\ell$ CR (upper left), nonprompt $\gamma$ CR (upper right), ZZ CR (lower left), and SR (lower right) after the fit to the data. The black points with error bars represent the data and their statistical uncertainties, whereas the shaded band represents the total uncertainties. The bottom panel in each figure shows the ratio of the number of events observed in data to that of the total SM prediction. The last bin of each plot has been extended to include the overflow contribution.
png pdf	Figure 2-b: The distributions of the variables used in the simultaneous fit for the nonprompt $\ell$ CR (upper left), nonprompt $\gamma$ CR (upper right), ZZ CR (lower left), and SR (lower right) after the fit to the data. The black points with error bars represent the data and their statistical uncertainties, whereas the shaded band represents the total uncertainties. The bottom panel in each figure shows the ratio of the number of events observed in data to that of the total SM prediction. The last bin of each plot has been extended to include the overflow contribution.
png pdf	Figure 2-c: The distributions of the variables used in the simultaneous fit for the nonprompt $\ell$ CR (upper left), nonprompt $\gamma$ CR (upper right), ZZ CR (lower left), and SR (lower right) after the fit to the data. The black points with error bars represent the data and their statistical uncertainties, whereas the shaded band represents the total uncertainties. The bottom panel in each figure shows the ratio of the number of events observed in data to that of the total SM prediction. The last bin of each plot has been extended to include the overflow contribution.
png pdf	Figure 2-d: The distributions of the variables used in the simultaneous fit for the nonprompt $\ell$ CR (upper left), nonprompt $\gamma$ CR (upper right), ZZ CR (lower left), and SR (lower right) after the fit to the data. The black points with error bars represent the data and their statistical uncertainties, whereas the shaded band represents the total uncertainties. The bottom panel in each figure shows the ratio of the number of events observed in data to that of the total SM prediction. The last bin of each plot has been extended to include the overflow contribution.
png pdf	Figure 3: Expected and observed 95% upper limits on the product of the cross section and branching fraction $\sigma(\mathrm{p}\mathrm{p}\to \mathrm{W}{{\mathrm{a}} })\mathcal{B}(\mathrm{W}\to \ell^{+}\nu_{\ell})\mathcal{B}({\mathrm{a}} \to \mathrm{Z}\gamma)\mathcal{B}(\mathrm{Z}\to \ell^{+} \ell^{-})$ as a function of the ALP mass from 110 to 400 GeV (left). The red line corresponds to the theoretical prediction for 1 $/f_{\mathrm{a}} =$ 2 TeV $^{-1}$ . Expected and observed 95% upper limits on the photophobic ALP model parameter 1 $/f_{\mathrm{a}}$ as a function of ALP mass reinterpreted from 1 $/f_{\mathrm{a}} =$ 2 TeV $^{-1}$ (right). The blue line indicates the point at which the energy scale of $f_{\mathrm{a}}$ matches that of the ALP mass. The model may not be valid in the region where $m_{\mathrm{a}} > f_{\mathrm{a}}$ , as discussed in Ref. [22].
png pdf	Figure 3-a: Expected and observed 95% upper limits on the product of the cross section and branching fraction $\sigma(\mathrm{p}\mathrm{p}\to \mathrm{W}{{\mathrm{a}} })\mathcal{B}(\mathrm{W}\to \ell^{+}\nu_{\ell})\mathcal{B}({\mathrm{a}} \to \mathrm{Z}\gamma)\mathcal{B}(\mathrm{Z}\to \ell^{+} \ell^{-})$ as a function of the ALP mass from 110 to 400 GeV (left). The red line corresponds to the theoretical prediction for 1 $/f_{\mathrm{a}} =$ 2 TeV $^{-1}$ . Expected and observed 95% upper limits on the photophobic ALP model parameter 1 $/f_{\mathrm{a}}$ as a function of ALP mass reinterpreted from 1 $/f_{\mathrm{a}} =$ 2 TeV $^{-1}$ (right). The blue line indicates the point at which the energy scale of $f_{\mathrm{a}}$ matches that of the ALP mass. The model may not be valid in the region where $m_{\mathrm{a}} > f_{\mathrm{a}}$ , as discussed in Ref. [22].
png pdf	Figure 3-b: Expected and observed 95% upper limits on the product of the cross section and branching fraction $\sigma(\mathrm{p}\mathrm{p}\to \mathrm{W}{{\mathrm{a}} })\mathcal{B}(\mathrm{W}\to \ell^{+}\nu_{\ell})\mathcal{B}({\mathrm{a}} \to \mathrm{Z}\gamma)\mathcal{B}(\mathrm{Z}\to \ell^{+} \ell^{-})$ as a function of the ALP mass from 110 to 400 GeV (left). The red line corresponds to the theoretical prediction for 1 $/f_{\mathrm{a}} =$ 2 TeV $^{-1}$ . Expected and observed 95% upper limits on the photophobic ALP model parameter 1 $/f_{\mathrm{a}}$ as a function of ALP mass reinterpreted from 1 $/f_{\mathrm{a}} =$ 2 TeV $^{-1}$ (right). The blue line indicates the point at which the energy scale of $f_{\mathrm{a}}$ matches that of the ALP mass. The model may not be valid in the region where $m_{\mathrm{a}} > f_{\mathrm{a}}$ , as discussed in Ref. [22].

Tables
png pdf	Table 1: Summary of the event selections in the SR, nonprompt CRs, and the ZZ CR. The nonprompt CRs are used to validate and constrain the nonprompt lepton and photon contributions, and the ZZ CR is used to constrain the ZZ contribution. A `` $\text{--}$ '' indicates that no requirement is placed on the corresponding observable. The aQGC SR is the same as the SR with the exception that $p_{\mathrm{T}}^{\gamma} >$ 60 GeV.
png pdf	Table 2: Summary of the relative contributions of related groups of uncertainties to the value of the signal strength in the measurement of the SM $\mathrm{W}\mathrm{Z}\gamma$ signal.
png pdf	Table 3: The number of events in data and predictions after the combined fit for the relevant processes in the SR and CRs. All analysis uncertainties are included.
png pdf	Table 4: Exclusion limits at the 95% CL for each aQGC coefficient, assuming all other coefficients are set to zero. Unitarity bounds corresponding to each operator are also listed.

Summary

A measurement of the production of

$\mathrm{W}\mathrm{Z}\gamma$ with both W and Z bosons decaying leptonically has been presented. Results are based on the data collected in proton-proton (pp) collisions at

$\sqrt{s}=$ 13 TeV by the CMS detector during 2016-2018, corresponding to an integrated luminosity of 138 fb

$^{-1}$ . Events are selected by requiring an identified photon, missing transverse momentum, as well as three identified leptons, of which two correspond to an on-shell Z boson. The observed significance for the standard model (SM) signal is 5.4 standard deviations, while a significance of 3.8 standard deviations is expected based on the SM prediction. The measured fiducial cross section of leptonic

$\mathrm{W}\mathrm{Z}\gamma$ production is

$\sigma_{\mathrm{p}\mathrm{p}\to\ell^{\pm}\nu\ell^{+}\ell^{-}\gamma}=$ 5.48

$\pm$ 1.11 fb, with prompt

$\ell = \mathrm{e}$ or

$\mu$ , which is compatible with the prediction of 3.69

$\pm$ 0.24 fb at next-to-leading order in quantum chromodynamics. Constraints are placed on anomalous quartic gauge couplings in terms of dimension-eight operators in effective field theory. Upper limits on the photophobic axion-like particles (ALPs), denoted a, are set as a function of the ALP mass. Equivalent limits for the ALP mass and coupling parameters are reported, including some of the most stringent constraints for mass values between

$m_{{\mathrm{a}} }=$ 200-400 GeV, as well as the first interpretation for masses between

$m_{{\mathrm{a}} }=$ 110-200 GeV.

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