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Measurement of the Z $\gamma$ production cross section and search for anomalous neutral triple gauge couplings in pp collisions at $\sqrt{s}$ = 13 TeV

Using 138 fb $^{-1}$ of proton-proton collision data at $\sqrt{s}$ = 13 TeV collected by the CMS experiment, this study measures the fiducial cross section for Z $\gamma$ production with a high- $p_\mathrm{T}$ photon and the Z boson decaying to neutrinos, finding results consistent with the Standard Model while establishing the most stringent limits to date on anomalous neutral triple gauge couplings.

Original authors: CMS Collaboration

Published 2026-10-27

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CC BY 4.0

Original authors: CMS Collaboration

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The universe is held together by a set of invisible rules that dictate how particles interact. Physicists call these rules the Standard Model, a theory that has successfully predicted the behavior of matter for decades. Within this framework, certain forces are carried by particles known as bosons. Sometimes, these bosons can interact with one another, but the Standard Model places strict limits on how they can do so. Specifically, it predicts that three neutral particles—particles with no electric charge—should never meet at a single point to interact directly. If such an interaction were observed, it would signal that the current rules are incomplete and that new, unknown physics is at play. This possibility is what drives researchers to look for "anomalous" interactions, or unexpected deviations from the predicted behavior, in the high-energy collisions of particle accelerators.

A team of scientists working with the CMS experiment at CERN's Large Hadron Collider has recently conducted a precise search for these forbidden interactions. They focused on a specific event where a Z boson, a heavy carrier of the weak force, is produced alongside a high-energy photon, a particle of light. In the Standard Model, this pair is created through a well-understood process, but if new physics exists, the particles might interact in a way that boosts their energy or changes how often they appear. The researchers analyzed data from proton-proton collisions that occurred between 2016 and 2018, a period that provided a massive dataset equivalent to 138 inverse femtobarns of integrated luminosity. To spot these rare events, they looked for a signature that is difficult to miss: a single, very energetic photon accompanied by a large amount of missing energy. This missing energy is a telltale sign that a Z boson has decayed into two neutrinos, particles that pass through the detector without leaving a trace, carrying away momentum that the machine cannot directly measure.

The team identified thousands of these events, filtering out background noise from other particle collisions that could mimic the signal. They measured the rate at which these Z boson and photon pairs were produced and compared it against the most advanced theoretical predictions available. The result was a measurement of the production cross section, which essentially describes the probability of this event happening, of 23.3 femtobarns. This value aligns closely with the Standard Model's prediction, falling well within the range of expected statistical fluctuations. The researchers also examined the energy distribution of the photons, looking for any sudden spikes or shifts that would indicate the presence of new forces. The data followed the smooth curve predicted by established theory, showing no evidence of the anomalous interactions that would suggest new physics.

Because the data matched the standard predictions so closely, the scientists were able to set very strict limits on the existence of the forbidden interactions they were searching for. They calculated the maximum strength any such new interaction could have without contradicting their observations. For the specific types of interactions that preserve a fundamental symmetry known as CP symmetry, the study determined that any deviation from the Standard Model must be smaller than a few parts in ten thousand. These limits are the most stringent constraints to date on these particular parameters, effectively ruling out a wide range of theoretical models that predicted stronger effects. While the search did not find the new physics it sought, the precision of the measurement confirms that the Standard Model remains robust even at the highest energy scales currently accessible to humanity. The work stands as a testament to the power of large-scale experimentation to test the boundaries of our understanding of the universe.

Technical Summary: Measurement of the Zγ Production Cross Section and Search for Anomalous Neutral Triple Gauge Couplings

Problem and Motivation
This paper addresses the need to test the electroweak sector of the Standard Model (SM) by measuring the production cross section of a Z boson associated with a high-transverse momentum ( $p_T$ ) photon ( $Z\gamma$ ). In the SM, vertices involving three neutral electroweak bosons ( $ZZZ$ , $Z\gamma\gamma$ , and $ZZ\gamma$ ) are forbidden at the tree level due to $SU(2)_L \times U(1)_Y$ symmetry. However, the presence of new physics could manifest as anomalous neutral triple gauge couplings (aNTGCs). These couplings introduce additional interaction channels that alter the kinematic distributions of $Z\gamma$ production, particularly at high energies. The study focuses on the $Z(\nu\nu)\gamma$ channel, where the Z boson decays into a neutrino pair, providing a clean signature of a high- $p_T$ photon and large missing transverse momentum ( $p^{\text{miss}}_T$ ). This channel is selected for its superior signal-to-background ratio compared to charged-lepton decay modes, despite the irreducible background from $W(\ell\nu)\gamma$ processes.

Methodology
The analysis utilizes proton-proton collision data collected by the CMS experiment at the LHC at a center-of-mass energy of $\sqrt{s} = 13$ TeV, corresponding to an integrated luminosity of 138 fb $^{-1}$ from the 2016–2018 data-taking periods.

Event Selection: Signal events are characterized by exactly one photon with $p_T^\gamma > 225$ GeV and $p^{\text{miss}}_T > 200$ GeV. To suppress backgrounds, strict criteria are applied: the photon must be isolated from jets ( $\Delta\phi > 2$ ), the ratio $p_T^\gamma / p^{\text{miss}}_T < 1.4$ , and no additional leptons or high- $p_T$ jets aligned with the missing momentum are allowed. Specific veto regions are applied to avoid detector inefficiencies, such as the transition region between the barrel and endcap electromagnetic calorimeters and inoperable Hadronic Calorimeter (HCAL) modules in 2018.
Background Estimation:
- Jets misidentified as photons: Estimated using a "fake rate" method derived from data control regions with low $p^{\text{miss}}_T$ , inverting isolation criteria to determine the probability of a jet passing photon identification.
- Electrons misidentified as photons: Evaluated using the tag-and-probe technique on $Z \to e^+e^-$ events, measuring the efficiency of the pixel detector to reject electrons.
- $W(\ell\nu)\gamma$ background: Estimated via a simultaneous likelihood fit to the signal region and two control regions ( $CR_e$ and $CR_\mu$ ) enriched in $W(\ell\nu)\gamma$ events by requiring a reconstructed electron or muon. This data-driven approach constrains the normalization directly.
- Other backgrounds: Includes contributions from $Z/\gamma^*(\ell^+\ell^-)\gamma$ , $t\bar{t}\gamma$ , diboson processes, and instrumental backgrounds like APD spikes and beam-halo muons, estimated using simulation and dedicated control samples.
Statistical Analysis: A binned profile likelihood function is constructed using the COMBINE tool. The analysis simultaneously fits the observed photon $p_T$ spectrum in the signal and control regions. Systematic uncertainties, including luminosity, trigger efficiency, photon and jet energy scales, and theoretical modeling (PDFs, renormalization/factorization scales), are incorporated as nuisance parameters.
Unfolding: A likelihood-based unfolding technique is employed to correct the measured distributions for detector acceptance, efficiency, and resolution, reporting results at the generator level within a defined fiducial region.

Key Contributions and Results

Fiducial Cross Section: The inclusive fiducial cross section for $Z(\nu\nu)\gamma$ production with $p_T^\gamma > 225$ GeV is measured to be 23.3 $^{+1.4}_{-1.3}$ fb. This result is in agreement with Standard Model predictions, which are calculated as 26.07 $^{+0.96}_{-0.97}$ fb (NLO QCD) and 25.45 $^{+0.41}_{-0.33}$ fb (NNLO QCD) using MADGRAPH5 aMC@NLO and MATRIX, respectively.
Differential Cross Section: The differential cross section as a function of photon $p_T$ is measured in bins ranging from 225 to 1500 GeV. The measured values are consistent with SM predictions within uncertainties, although the NNLO predictions show slightly better agreement in the 275–450 GeV range compared to NLO predictions.
Constraints on Anomalous Couplings: The study places constraints on the CP-conserving anomalous coupling parameters $h_3^V$ $h_{3}^{V}$ and $h_4^V$ $h_{4}^{V}$ (where $V = \gamma, Z$ $V = γ, Z$ ) affecting the $ZZ\gamma$ $Z Z γ$ and $Z\gamma\gamma$ $Z γ γ$ vertices. The observed 95% confidence level intervals are:
- $h_3^\gamma$ : $(-3.4, 3.5) \times 10^{-4}$
- $h_4^\gamma$ : $(-6.8, 6.8) \times 10^{-7}$
- $h_3^Z$ : $(-2.2, 2.2) \times 10^{-4}$
- $h_4^Z$ : $(-4.1, 4.2) \times 10^{-7}$

Significance
The paper claims that these results represent the strictest limits to date on the parameters $h_3^\gamma$ , $h_3^Z$ , and $h_4^Z$ . By utilizing the high- $p_T$ tail of the photon spectrum, the analysis effectively probes energy scales where the interference between SM and anomalous amplitudes becomes negligible, allowing for quadratic sensitivity to the couplings. The measurement confirms the Standard Model prediction for $Z\gamma$ production in the neutral decay channel and finds no evidence for anomalous neutral triple gauge couplings, thereby constraining potential extensions to the SM electroweak sector.

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