Multiboson and VBS measurements in ATLAS and CMS

This paper reviews recent multiboson and vector boson scattering measurements from the ATLAS and CMS collaborations at the LHC, including new results at 13.6 TeV, which collectively provide a comprehensive test of the Standard Model's electroweak sector and stringent constraints on anomalous gauge couplings.

The Gist

Imagine the Standard Model of physics as the ultimate "Rulebook" for how the universe works. For decades, scientists have been checking these rules, mostly by smashing particles together to see if they behave exactly as the book says they should.

This paper is a report card from two giant teams of scientists, ATLAS and CMS, working at the Large Hadron Collider (LHC) in Switzerland. They have spent years smashing protons together to study Multiboson and Vector Boson Scattering (VBS) events.

Here is the breakdown of what they did, explained with some everyday analogies.

1. The Big Picture: The "Party" Analogy

Think of the LHC as a massive, high-energy party where particles are the guests.

• Bosons are the "social butterflies" of this party. They are the messengers that carry forces (like the electromagnetic force or the weak nuclear force).
• Multiboson production is when these social butterflies get together in groups of two, three, or more to dance.
• Vector Boson Scattering (VBS) is a specific, rare type of dance where two bosons crash into each other, bounce off, and fly away, leaving behind two "jets" of debris (like two people bumping into each other at a crowded bar and scattering the drinks on the floor).

The scientists are checking: Do these particles dance exactly the way the Rulebook predicts? Or are they doing something weird that hints at a new, hidden rule?

2. The Main Goals: What Were They Looking For?

The scientists had three main jobs:

1. The Precision Check: Measure exactly how often these dances happen. (Is the attendance count correct?)
2. The "Spin" and "Mirror" Check: Look at the orientation of the particles (polarization) and check if they behave the same way in a mirror (CP-symmetry).
3. The "New Physics" Hunt: Look for tiny deviations. If the particles dance slightly differently than the Rulebook says, it might mean there is a "dimension-6 or dimension-8" operator at play—basically, a secret code in the universe we haven't cracked yet.

3. Key Discoveries (The Highlights)

A. The "Double-Check" (Diboson Measurements)

• The ZZ Production: ATLAS looked at pairs of Z-bosons. They measured how often they appear and how they move.
  • The Result: They matched the predictions perfectly. It's like checking a recipe and finding the cake rises exactly to the height the cookbook promised.
• The W and Photon (Wγ) Dance: ATLAS looked at a W-boson and a photon dancing together. They used a Neural Network (a type of AI) to act like a super-sleuth.
  • The Result: The AI found a new way to spot "mirror-image" violations (CP-sensitivity). It was so good it doubled the sensitivity of previous tests. The particles behaved exactly as the Standard Model predicted, but now we have a much sharper magnifying glass to look at them.

B. The "Bouncing" (Vector Boson Scattering - VBS)

This is the most exciting part. VBS is the "gold standard" for testing the Higgs boson's role in keeping the universe stable.

• The Semileptonic Breakthrough (ATLAS): Usually, these events are hard to see because they are messy. ATLAS looked for events where one boson decays into invisible particles and the other into visible jets.
  • The Result: Discovery! They saw this happen with a significance of 7.4 sigma. In science, 5 sigma is the "gold standard" for a discovery. This is like finding a needle in a haystack, but the needle is glowing.
• The "Missing Piece" (CMS): CMS finally observed Electroweak ZZ production. Before this, it was the last major boson pair combination that hadn't been clearly seen in this specific scattering mode.
  • The Result: Discovery! They combined different channels to get a 5.0 sigma confirmation. The puzzle is now complete.
• The Future Energy (Run 3): CMS started taking data at a higher energy (13.6 TeV). They saw these scattering events happen even faster and more frequently, confirming the rules hold up even at higher speeds.

C. The "Triple Threat" (Triboson Production)

This is when three bosons dance together. This is incredibly rare and hard to spot because the "noise" of the party is so loud.

• The Result: ATLAS observed VVZ (two Ws and a Z, or two Zs and a W) for the first time (6.4 sigma). CMS found evidence for WWZ at the new higher energy.
• Why it matters: This tests the "Quartic Gauge Couplings." Think of this as testing the rules of a three-way handshake. If the handshake is weird, the whole Rulebook might need rewriting. So far, the handshake is perfect.

4. The Verdict: "Everything is Normal... For Now"

The most important takeaway from this paper is: The Standard Model is still winning.

Every single measurement—from the simplest pair of bosons to the complex triple-boson dances—matches the predictions of the Standard Model within the margin of error.

• No "New Physics" Found Yet: They didn't find the "glitch" that would prove the existence of new particles or forces.
• But the Net is Tighter: While they didn't find a ghost, they have tightened the net so much that if a ghost does exist, it has to be very small or very shy. They have ruled out many theories that predicted big deviations.

5. What's Next?

The LHC is moving into Run 3, which means more data (more party guests) and higher energy (louder music).

• Precision Era: We are moving from "Did we see it?" to "Exactly how does it behave?"
• The High-Luminosity Future: With even more data coming, these measurements will become the most sensitive indirect tests for "Beyond Standard Model" (BSM) physics in the world.

In a nutshell: The scientists checked the universe's rulebook with the most precise tools ever built. The book is still correct, but the margin for error is now so tiny that any future discovery will be undeniable. The hunt for the "new physics" continues, but the foundation of our current understanding is rock solid.

Technical Summary

1. Problem and Motivation

The paper addresses the need to rigorously test the non-Abelian gauge structure of the Standard Model (SM), specifically the electroweak sector. The primary objectives are:

• Testing Gauge Couplings: Verifying Triple Gauge Couplings (TGC) and Quartic Gauge Couplings (QGC) predicted by the SM.
• Probing Unitarity: Investigating Vector Boson Scattering (VBS) processes, where the cancellation between gauge and Higgs exchange diagrams ensures perturbative unitarity at high energies.
• Searching for New Physics: Detecting deviations from SM predictions that could indicate Beyond the Standard Model (BSM) physics, parametrized via Effective Field Theory (EFT) using dimension-6 and dimension-8 operators.
• Precision Era: Transitioning from discovery-phase measurements to precision cross-section measurements and enhanced EFT sensitivity using the full Run 2 dataset ($\sqrt{s}=13$ TeV) and initial Run 3 data ($\sqrt{s}=13.6$ TeV).

2. Methodology

The review synthesizes results from the ATLAS and CMS collaborations, utilizing datasets up to $140 \text{ fb}^{-1}$ (Run 2) and initial Run 3 datasets ($171\text{--}280 \text{ fb}^{-1}$). Key methodological approaches include:

• Event Selection:
  • VBS Topology: Events are selected by requiring two vector bosons and two energetic forward jets with large dijet invariant mass ($m_{jj}$) and large rapidity separation ($\Delta\eta_{jj}$) to suppress QCD-induced backgrounds.
  • Final States: Analyses cover fully leptonic, semileptonic (one boson decaying hadronically, one leptonically), and inclusive channels.
• Advanced Statistical & Machine Learning Techniques:
  • Neural Networks (NN): Used for signal extraction and background suppression. Specific applications include:
    • RNN (Recurrent NN): Used by ATLAS for semileptonic VBS discriminants.
    • GNN (Graph NN): Used by CMS for $ZZ$ VBS signal extraction.
    • CP-Sensitive NN: A novel observable ($O_{NN}$) constructed from multiclass NN outputs to separate linear interference terms from squared contributions for CP-odd EFT operators in $W\gamma$ production.
  • BDT (Boosted Decision Trees): Used for $WZ$ VBS discrimination in Run 3.
  • Simultaneous Fits: CMS employs simultaneous fits across multiple channels (fully leptonic and semileptonic) and center-of-mass energies (13 TeV and 13.6 TeV) to extract independent signal strengths.
• Theoretical Comparisons: Measured cross-sections and differential distributions are compared against state-of-the-art theoretical predictions, including NNLO QCD (Geneva+PY8) and virtual NLO electroweak corrections.

3. Key Contributions and Results

A. Precision Diboson Measurements

• Differential $ZZ$ Production (ATLAS): Measured $ZZ \to \ell\ell\nu\nu$ and $ZZjj$ at 13 TeV.
  • Results: $\sigma_{\text{fid}}(ZZ) = 21.0 \pm 1.0$ fb and $\sigma_{\text{fid}}(ZZjj) = 0.96^{+0.18}_{-0.16}$ fb.
  • Significance: Differential distributions up to $p_T^{ZZ} = 1.5$ TeV agree with NLO predictions, allowing constraints on neutral anomalous TGC operators.
• $W\gamma$ Production (ATLAS):
  • Polarization: Measured double-differential cross-sections in decay angles ($\phi_\ell, \theta_\ell$), confirming SM spin-density matrix predictions.
  • CP Sensitivity: Introduced $O_{NN}$, a CP-sensitive observable that improves expected limits on CP-odd dimension-6 operators by a factor of two compared to traditional angular observables.

B. Vector Boson Scattering (VBS)

• Semileptonic VBS Observation (ATLAS): First observation of electroweak $WW/WZ/ZZ$ production in semileptonic channels ($\ell\ell qq, \ell\nu qq, \nu\nu qq$).
  • Result: Signal strength $\mu_{\text{EWK}} = 1.28^{+0.23}_{-0.21}$ with an observed significance of 7.4 $\sigma$.
• CMS VBS Combination: A 7-channel combination (4 fully leptonic, 3 semileptonic) at 13 TeV.
  • Result: All signal strengths are consistent with the SM (unity), providing a coherent baseline for EFT interpretations.
• Electroweak $ZZ$ Observation (CMS): First establishment of EW $ZZ$ production in the $\ell\ell\nu\nu jj$ channel.
  • Result: Combined significance of 5.0 $\sigma$ (combining 4-lepton and $\ell\ell\nu\nu$ channels).
• Run 3 Measurements (CMS): First VBS measurements at $\sqrt{s} = 13.6$ TeV.
  • Results: Observed $W^\pm W^\pm jj$ ($>5\sigma$) and $WZjj$($\approx 7\sigma$) with cross-sections of $3.81 \pm 0.38$ fb and $1.43 \pm 0.26$ fb, respectively.

C. Triboson Production

• $VVZ$ Observation (ATLAS): First observation of inclusive $VVZ$($V=W,Z$) production.
  • Result: $\sigma(pp \to VVZ) = 660^{+93}_{-90} \text{ (stat)} ^{+88}_{-81} \text{ (syst)}$ fb with 6.4 $\sigma$ significance.
  • Evidence: Specific evidence for $WWZ$($4.4 \sigma$).
• Triboson at 13.6 TeV (CMS): First evidence for triboson production at the new energy.
  • Result: Simultaneous measurement of non-resonant $WWZ$ and Higgsstrahlung $ZH$. The 13.6 TeV signal shows 3.8 $\sigma$ significance.

4. Significance and Outlook

• Validation of the SM: All measured cross-sections and signal strengths are consistent with SM expectations within uncertainties, providing a comprehensive test of the electroweak gauge sector.
• EFT Constraints: The results provide stringent constraints on anomalous gauge couplings (aQGC) and EFT Wilson coefficients, particularly in the high-$m_{jj}$ and high-$p_T$ tails where BSM effects are enhanced.
• Technological Advancement: The successful deployment of advanced ML techniques (RNN, GNN, CP-sensitive NN) demonstrates their critical role in isolating rare electroweak signals from overwhelming QCD backgrounds.
• Future Prospects: The transition to Run 3 ($\sqrt{s}=13.6$ TeV, up to $300 \text{ fb}^{-1}$) and the eventual High-Luminosity LHC (HL-LHC) will transform multiboson physics into a precision probe. This will offer indirect constraints on BSM physics at the TeV scale that are complementary to direct searches and Higgs coupling measurements.

In summary, the paper documents the completion of the Run 2 VBS discovery program and the successful initiation of the precision era in Run 3, confirming the SM's non-Abelian gauge structure with unprecedented statistical significance and experimental sophistication.