Vector boson scattering and anomalous quartic couplings in final states with $\ell\nu$qq or $\ell\ell$qq plus jets using proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 138 fb$^{-1}$ of proton-proton collision data at 13 TeV collected by the CMS detector, this study presents a measurement of electroweak ZV (V=W, Z) boson pair production with two jets, achieving an observed significance of 1.3 standard deviations and setting world-leading constraints on anomalous quartic gauge couplings through a combination with previous WV channel results.

The Gist

The Big Picture: A High-Speed Billiard Game

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful billiard table. Instead of billiard balls, they smash protons together at nearly the speed of light.

Usually, when these protons collide, they shatter into a chaotic mess of debris. But sometimes, something much more subtle happens. Instead of a direct crash, the protons "graze" each other. They emit invisible force-carrying particles (called Vector Bosons, like the W and Z bosons), which then bounce off one another before the protons themselves continue on their way.

This process is called Vector Boson Scattering (VBS). Think of it like two people on ice skates throwing heavy bowling balls at each other. The people (the protons) barely touch, but the balls (the bosons) collide violently in the middle. The "scars" of this collision are two jets of particles flying off in opposite directions (forward and backward), while the bowling balls themselves decay into other particles.

What Did They Look For?

The CMS team (one of the giant detectors at CERN) was hunting for a specific, rare event:

1. The Setup: Two protons collide.
2. The Action: They exchange a Z boson and another boson (W or Z).
3. The Result: These two bosons scatter off each other.
4. The Clues:
   • One boson decays into two charged particles (electrons or muons) that the detector can easily spot.
   • The other boson decays into quarks, which turn into jets of particles.
   • Two "forward jets" fly off in opposite directions, acting like the skaters' footprints.

This specific combination (Z boson + another boson + two forward jets) had never been seen before at the LHC. It's like finding a specific, rare handshake between two strangers in a crowded stadium.

The Challenge: Finding a Needle in a Haystack

The problem is that this rare event is incredibly hard to find because it looks very similar to common background noise.

• The Haystack: Most collisions are just messy "QCD" events (strong force interactions) or standard particle decays that happen billions of times more often.
• The Needle: The signal they want is the "Electroweak" scattering event.

To find the needle, the scientists used a Deep Neural Network (DNN). Think of this as a super-smart AI referee. They trained this AI on millions of simulated collisions, teaching it to spot the tiny, subtle differences between the "noise" (background) and the "signal" (the rare scattering event). The AI looked at the energy, angles, and spacing of the particles to make a judgment call.

The Results: A Whisper, Not a Shout

After analyzing data from 2016 to 2018 (138 "inverse femtobarns" of data—a massive amount of collisions), here is what they found:

1. Did they see it? Yes, but it's faint. The data showed a signal that was 1.3 times stronger than random chance would predict. In the world of particle physics, this is a "hint" or a "tantalizing whisper," but not yet a confirmed "discovery" (which usually requires a 5-sigma, or 5-sigma, certainty).
2. What does it mean? Even though they didn't "discover" it with high confidence, they successfully measured how often it happens. The result is consistent with the Standard Model (our current best theory of physics), but the uncertainty is still large.

The Real Goal: Testing the Rules of the Universe

Why bother if the signal is faint? Because this experiment is a stress test for the laws of physics.

The scientists are using this data to look for Anomalous Quartic Gauge Couplings. That's a mouthful, so let's use an analogy:

• The Standard Model is like the rulebook for how billiard balls interact. It says, "If you hit them this hard, they will bounce off at this specific angle."
• New Physics (Beyond the Standard Model) would be like a rulebook that says, "Actually, if you hit them really hard, they might turn into jelly or teleport."

The researchers are checking if the bosons scatter exactly as the rulebook predicts. If they scatter differently (especially at very high energies), it would mean the rulebook is wrong and there is new, unknown physics hiding in the cracks.

They used a mathematical framework called Effective Field Theory (EFT) to set limits. Think of this as drawing a "fence" around the possible values of new physics.

• The Result: They built the tightest fence in the world for these specific rules. They proved that if new physics exists, it must be very weak or very heavy. They didn't find a breach in the fence, but they made the fence much stronger than anyone else has before.

Summary

• The Mission: Catch a rare, ghostly collision where force particles bounce off each other.
• The Method: Use a super-smart AI to filter through trillions of collisions to find the few that match the pattern.
• The Outcome: They found a hint of the event (consistent with current theories) and used it to set the world's strictest limits on "weird" new physics.
• The Takeaway: The universe is behaving exactly as the Standard Model predicts so far, but the scientists have now built a much sharper microscope to keep looking for cracks in the theory.

In short: They didn't find a new particle, but they proved that the universe is playing by the rules we think it is, and they drew the sharpest boundary lines yet on where those rules might eventually break.

Technical Summary

1. Problem and Motivation

Vector Boson Scattering (VBS) is a crucial process for probing the mechanism of electroweak symmetry breaking and the non-Abelian gauge structure of the Standard Model (SM). Specifically, VBS involves the scattering of two weak bosons ($W$ or $Z$) emitted from incoming quarks, resulting in a diboson final state accompanied by two forward jets.

While fully leptonic VBS channels have been well-studied, channels where one boson decays hadronically ($V \to q\bar{q}$) offer higher branching fractions but suffer from large backgrounds (primarily QCD multijet and Drell-Yan processes).

• The Gap: Previous CMS analyses had established evidence for $W^\pm V$ VBS in the $\ell\nu qq$ channel. However, the complementary $ZV$ VBS process (where $Z \to \ell^+\ell^-$ and $V \to q\bar{q}$) had not yet been observed at the LHC.
• The Goal: This paper aims to:
  1. Perform the first measurement of the electroweak production of $ZV$($V=W, Z$) in association with two jets using the full Run 2 dataset.
  2. Combine these results with previous $WV$ measurements to constrain Anomalous Quartic Gauge Couplings (aQGCs) using an Effective Field Theory (EFT) framework, specifically focusing on dimension-8 operators.

2. Methodology

Data and Simulation

• Dataset: Proton-proton collisions at $\sqrt{s} = 13$ TeV collected by the CMS detector during 2016–2018, corresponding to an integrated luminosity of 138 fb$^{-1}$.
• Signal Modeling: Purely electroweak (EW) VBS contributions are simulated at Leading Order (LO) using MADGRAPH5_aMC@NLO. The simulation includes interference with top-quark associated production ($tZq$) to preserve gauge invariance.
• Background Modeling:
  • Drell-Yan (DY): Simulated at LO with up to 4 additional partons.
  • Top Quark ($t\bar{t}$, single top): Simulated at Next-to-Leading Order (NLO) using POWHEG.
  • QCD VBS: Neglected in the signal region as it contributes $<3\%$ to the cross-section in the phase space of interest.
  • Non-prompt Leptons: Estimated using a data-driven "fake rate" method.

Event Reconstruction and Selection

The analysis targets final states with:

1. Leptons: Two isolated, same-flavor, opposite-charge leptons ($e$ or $\mu$) with invariant mass $76 < m_{\ell\ell} < 106$ GeV (consistent with a $Z$ boson).
2. Jets: Two forward "VBS jets" characterized by large invariant mass ($m_{jj} > 500$ GeV) and large pseudorapidity separation ($|\Delta\eta_{jj}| > 2.5$).
3. Hadronic Boson ($V$): Reconstructed via two topologies:
   • Resolved: Two distinct small-radius jets ($R=0.4$, AK4) reconstructing the $W/Z$ mass.
   • Merged: A single large-radius jet ($R=0.8$, AK8) for highly boosted bosons, using Soft Drop mass declustering and N-subjettiness ($\tau_2/\tau_1$) to distinguish boson decays from QCD jets.

Analysis Strategy

• Deep Neural Network (DNN): A fully connected DNN (implemented in Keras/TensorFlow) is trained to discriminate the EW VBS signal from backgrounds (DY, Top, QCD).
  • Inputs: Kinematic variables including dijet mass, $\Delta\eta_{jj}$, lepton Zeppenfeld variables, jet multiplicity, and quark-gluon likelihood (QGL).
  • Training: Separate models for Resolved/Merged topologies and $b$-tagged/$b$-vetoed regions.
• Statistical Fit: A simultaneous maximum likelihood (ML) fit is performed on the DNN output distributions in Signal Regions (SR) and Control Regions (CR) for Drell-Yan and Top quark backgrounds.
• EFT Interpretation: For the combination with $WV$ data, the analysis uses the invariant mass of the diboson system ($M_{ZV}$ or $M_{WV}$) rather than the DNN score. The fit scans Wilson coefficients ($f_i/\Lambda^4$) for 20 dimension-8 operators (including previously unanalyzed $T_3$ and $T_4$ operators).

3. Key Contributions

1. First Observation of $ZV$ VBS: This is the first measurement of the electroweak production of $ZV$ pairs with two jets in the $\ell\ell qq$ channel at the LHC.
2. Unified EFT Framework: The paper combines the new $ZV$ results with the previously published $WV$($\ell\nu qq$) results to provide the most stringent constraints to date on dimension-8 operators describing anomalous quartic gauge couplings.
3. Advanced Topology Handling: It successfully integrates both "resolved" (two jets) and "merged" (one large jet) topologies, enhancing sensitivity to high-momentum bosons.
4. Systematic Uncertainty Handling: The analysis rigorously treats systematic uncertainties (luminosity, jet energy scale, pileup, theoretical scales) and includes them as nuisance parameters in the likelihood fit, ensuring robust limits.

4. Results

Standard Model Measurement

• Signal Strength ($\mu$): The observed signal strength for the EW $ZV$ VBS process is measured to be:
  $$\mu = 0.63^{+0.53}_{-0.51}$$
  (Expected: $1.00^{+0.61}_{-0.58}$).
• Significance: The observed (expected) significance of the signal over the background-only hypothesis is 1.3 (1.8) standard deviations.
  • Note: While not a formal "observation" (which requires $5\sigma$), the result is consistent with the SM prediction and represents the first evidence-level measurement in this specific channel. The uncertainty is dominated by statistical limitations.

EFT Constraints (Anomalous Couplings)

• Combined Limits: By combining $ZV$ and $WV$ channels, the analysis sets 95% Confidence Level (CL) limits on 20 dimension-8 Wilson coefficients ($f_i/\Lambda^4$).
• World Best Limits: Several of these limits are the world's best to date. For example:
  • $f_{T0}/\Lambda^4$: Observed $[-0.092, 0.079]$ TeV$^{-4}$.
  • $f_{M0}/\Lambda^4$: Observed $[-0.539, 0.534]$ TeV$^{-4}$.
• Comparison: The combined limits are generally tighter than those reported by ATLAS for similar operators, with the exception of a few specific operators ($T_5, T_8, T_9$) where ATLAS has slightly better sensitivity.
• Unitarity: The limits were checked against unitarity bounds; applying a unitarization scheme had a negligible impact, indicating the limits are robust.

5. Significance

• Validation of SM: The measurement confirms the existence of the $ZV$ VBS process, consistent with Standard Model predictions, despite the challenging background environment.
• BSM Sensitivity: The results significantly tighten the constraints on physics Beyond the Standard Model (BSM) that would manifest as anomalous quartic gauge couplings. These operators are sensitive to new physics at energy scales higher than the direct LHC reach.
• Methodological Benchmark: The successful application of DNN discriminators and the combination of resolved/merged topologies sets a benchmark for future VBS analyses, including those in Run 3 and the High-Luminosity LHC era.
• EFT Completeness: By including the $T_3$ and $T_4$ operators and combining with $WV$ data, this analysis provides a more complete picture of the electroweak sector's quartic interactions than previous standalone measurements.

In summary, this paper represents a milestone in the study of vector boson scattering, moving from fully leptonic channels to mixed leptonic-hadronic channels and providing the most stringent constraints to date on dimension-8 effective field theory operators governing quartic gauge couplings.