CMS-SMP-24-002

CMS-SMP-24-002 ; CERN-EP-2025-232
Measurement of Z$ \gamma $ production in proton-proton collisions at $ \sqrt{s}= $ 13.6 TeV and constraints on neutral triple gauge couplings
CMS Collaboration
9 December 2025
Submitted to Phys. Rev. Lett.
Abstract: A measurement of the Z$ \gamma $ production cross section in proton-proton collisions at a center-of-mass energy of 13.6 TeV is presented. Data corresponding to an integrated luminosity of 34.8 fb$^{-1}$, collected by the CMS experiment at the LHC in 2022 are used. Events with an oppositely charged pair of muons or electrons, with an invariant mass corresponding to a Z boson, together with an isolated photon are selected. The measured fiducial cross section for the combined electron and muon channels is 1.896 $ \pm $ 0.033 (stat) $ \pm $ 0.054 (syst) $ \pm $ 0.006 (theo) pb, in agreement with the standard model prediction of 1.922 $ \pm $ 0.094 pb. Constraints on neutral triple gauge couplings generated by dimension-8 operators in a recently proposed effective field theory framework are determined for the first time.
Links: e-print arXiv:2512.08582 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Leading order Feynman diagrams for Z$ \gamma $ production in proton-proton collisions and an example anomalous gauge coupling diagram. Left: initial-state radiation. Center: final-state radiation. Right: diagram involving anomalous gauge couplings that are forbidden in the SM at tree level. The red point indicates the anomalous Z$ \gamma$Z* or Z$ \gamma\gamma^{\ast} $ gauge coupling vertices.
png pdf	Figure 2: Post-fit distributions of $ m_{\ell\ell\gamma} $ in the electron (left) and muon channel (right). The experimental data are shown as points with associated statistical uncertainties, while the hatched bands represent the total uncertainties. Uneven bin sizes GeV are used to ensure sufficient statistical precision in each bin. The last bins include overflow events.
png pdf	Figure 2-a: Post-fit distributions of $ m_{\ell\ell\gamma} $ in the electron (left) and muon channel (right). The experimental data are shown as points with associated statistical uncertainties, while the hatched bands represent the total uncertainties. Uneven bin sizes GeV are used to ensure sufficient statistical precision in each bin. The last bins include overflow events.
png pdf	Figure 2-b: Post-fit distributions of $ m_{\ell\ell\gamma} $ in the electron (left) and muon channel (right). The experimental data are shown as points with associated statistical uncertainties, while the hatched bands represent the total uncertainties. Uneven bin sizes GeV are used to ensure sufficient statistical precision in each bin. The last bins include overflow events.
png pdf	Figure 3: Post-fit distributions of $ m_{\ell\ell\gamma} $ for the electron channel (left) and the muon channel (right) with the stricter photon $ p_{\mathrm{T}} $ requirement. The experimental data are shown as points with associated statistical uncertainties, while the hatched bands represent the total uncertainties. Uneven bin sizes are used to ensure sufficient statistical precision in each bin. A representative nTGC signal $ \tilde{c}_{G+} $ and its statistical uncertainty is shown as the red curve. The nTGC sensitivity mainly comes from the last bin which includes overflow events.
png pdf	Figure 3-a: Post-fit distributions of $ m_{\ell\ell\gamma} $ for the electron channel (left) and the muon channel (right) with the stricter photon $ p_{\mathrm{T}} $ requirement. The experimental data are shown as points with associated statistical uncertainties, while the hatched bands represent the total uncertainties. Uneven bin sizes are used to ensure sufficient statistical precision in each bin. A representative nTGC signal $ \tilde{c}_{G+} $ and its statistical uncertainty is shown as the red curve. The nTGC sensitivity mainly comes from the last bin which includes overflow events.
png pdf	Figure 3-b: Post-fit distributions of $ m_{\ell\ell\gamma} $ for the electron channel (left) and the muon channel (right) with the stricter photon $ p_{\mathrm{T}} $ requirement. The experimental data are shown as points with associated statistical uncertainties, while the hatched bands represent the total uncertainties. Uneven bin sizes are used to ensure sufficient statistical precision in each bin. A representative nTGC signal $ \tilde{c}_{G+} $ and its statistical uncertainty is shown as the red curve. The nTGC sensitivity mainly comes from the last bin which includes overflow events.

Tables
png pdf	Table 1: The observed fiducial $ \ell^{+}\ell^{-}\gamma $ cross section of the process in each channel. The quoted uncertainties include statistical, systematical and theoretical components. Branching ratio $ \mathcal{B} $ is for the $ \mathrm{Z} \to \ell^{+}\ell^{-}\gamma $ process.
png pdf	Table 2: Expected and observed 95% CL limits on nTGC parameters for the combination of the measurements in the electron and muon channels. The first three rows show the results using VPM that preserves only the $ \mathrm{U}(1)_{\mathrm{EM}} $ symmetry, while the last three rows show the results from GSPM that preserves the $ \mathrm{SU}(2)_\mathrm{L}\otimes\mathrm{U}(1)_{\mathrm{Y}} $ symmetry.
png pdf	Table 3: Expected and observed 95% CL limits for VPM parameter $ h_4^\mathrm{Z} $ and for GSPM parameter $ \tilde{c}_{G+} $ converted into $ h_4^\mathrm{Z} $ via Eq. (1).

Summary

In summary, a measurement of Z$ \gamma $ production using leptonic final states in proton-proton collisions at a center-of-mass energy of 13.6 TeV has been presented. The data set used corresponds to an integrated luminosity of 34.8 fb$ ^{-1} $, collected by the CMS experiment at the LHC during 2022. Events with a pair of oppositely charged muons or electrons together with an isolated photon are selected. The measured fiducial cross section for the combined electron and muon channels is 1.896 $ \pm $ 0.033 (stat) $ \pm $ 0.054 (syst) $ \pm $ 0.006 (theo) pb, in agreement with the standard model prediction of 1.922 $ \pm $ 0.094 pb. The $ m_{\ell\ell\gamma} $ distribution is used to set 95% confidence level limits on neutral triple gauge couplings. These limits are derived, for the first time, in the context of a recently proposed framework of the effective field theory based on dimension-8 operators, which maintains $ \mathrm{SU}(2)_\mathrm{L}\otimes\mathrm{U}(1)_{\mathrm{Y}} $ gauge symmetry [16].

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