First measurements of vector boson scattering in W$^\pm$W$^{\pm}$ and WZ production in all-leptonic final states at $\sqrt{s}$ = 13.6 TeV

Using 171 fb$^{-1}$ of proton-proton collision data at $\sqrt{s}$ = 13.6 TeV collected by the CMS detector, this paper reports the first measurements of W$^\pm$W$^\pm$ and WZ vector boson scattering cross sections in all-leptonic final states, achieving a significance greater than five standard deviations for both processes.

The Gist

The Great Particle Brawl: A Look Inside the CMS Experiment

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful, high-speed particle racetrack. In this paper, the CMS Collaboration (a massive team of scientists) reports on a specific type of "race" they observed between 2022 and 2024. They smashed protons together at record-breaking speeds and watched what happened when two heavy force-carriers, called W bosons or a W and a Z boson, were created alongside two jets of debris.

Here is the story of what they found, explained simply.

1. The Goal: Watching the "Scattering"

In the Standard Model of physics (our best rulebook for how the universe works), particles usually interact by exchanging other particles. But sometimes, two force-carrying particles (like W bosons) can crash into each other directly. This is called Vector Boson Scattering (VBS).

Think of it like this:

• Normal Interaction: Two people (particles) throw a ball (a force carrier) back and forth to push each other away.
• Vector Boson Scattering: Two people are already holding balls, and they crash into each other's balls directly.

The scientists wanted to watch these direct crashes happen. Why? Because the rules of this crash are very sensitive. If the "Higgs field" (the invisible field that gives particles mass) behaves differently than we think, or if there are hidden new forces, the way these particles scatter would change. It's like checking the structural integrity of a bridge by watching how it sways in a storm; if the sway is weird, the bridge might have a hidden flaw.

2. The Setup: The "All-Leptonic" Filter

The collision produces a chaotic mess of debris. To find the specific "scattering" events they wanted, the scientists had to act like detectives looking for a very specific clue.

They looked for events where the W and Z bosons decayed into leptons (lightweight particles like electrons and muons).

• The W±W± Channel: They looked for two particles with the same electric charge (like two positive ions) flying out, plus some missing energy (carried away by invisible neutrinos). This is a rare signature because most background noise produces opposite charges.
• The WZ Channel: They looked for three charged particles (two from the Z, one from the W) and missing energy.

To make sure they weren't just seeing random noise, they applied strict filters:

• The "Forward Jet" Rule: The two bosons must be accompanied by two jets of debris that are shot far apart in opposite directions (like two skiers jumping off a ramp in opposite directions). This specific geometry is the "fingerprint" of the scattering process.
• The "Mass" Rule: The two jets must have a very high combined mass, ensuring the collision was energetic enough to be interesting.

3. The Data: A Massive Dataset

The team analyzed data equivalent to 171 inverse femtobarns of collisions. To put that in perspective, if a femtobarn is a tiny speck of dust, they collected a mountain of them. This corresponds to the data collected during the LHC's 2022–2024 run at a collision energy of 13.6 TeV (tera-electronvolts), which is the highest energy the LHC has ever reached.

4. The Results: "Five Sigma" Discovery

After sifting through billions of collisions, the team found exactly what they were looking for.

• The Signal: They observed the production of these boson pairs (W±W± and WZ) with a statistical certainty of greater than five standard deviations.
• What that means: In the world of particle physics, "five sigma" is the gold standard for a discovery. It means there is less than a one-in-a-million chance that what they saw was just a random fluke or background noise. They have officially "seen" these scattering events happening.

They also measured how often these events happened (the cross-section) and how the energy was distributed. They compared their measurements to the predictions of the Standard Model (the current rulebook).

The Verdict: The measurements matched the Standard Model predictions very well. The "sway" of the bridge was exactly as expected. This confirms that our current understanding of how these particles interact is correct, at least at these energy levels.

5. Why This Matters (According to the Paper)

The paper does not claim to have found "new physics" (like dark matter or new particles). Instead, it claims to have confirmed the rules of the game.

• It proves that the "electroweak" force (the force responsible for radioactivity and electricity) behaves exactly as the theory predicts when these heavy particles scatter.
• It sets a new baseline. Now that we know the "normal" behavior at 13.6 TeV, if we see something weird in the future, we will know it's truly new and not just a miscalculation.

In Summary:
The CMS team built a high-speed camera, took a massive number of photos of protons smashing together, and successfully identified the rare, specific moment when two force-carrying particles crashed into each other. They confirmed that the universe is playing by the rules we wrote down in the Standard Model. It's a victory for confirmation, ensuring our map of the subatomic world is accurate before we try to explore the uncharted territories beyond it.

Technical Summary

Technical Summary: First Measurements of Vector Boson Scattering in W±W± and WZ Production in All-Leptonic Final States at √s = 13.6 TeV

Problem and Motivation
The observation of the Higgs boson established the scalar field responsible for electroweak (EW) symmetry breaking, yet further insight into the mechanism is required to test the Standard Model (SM) and probe for physics beyond it. Vector boson scattering (VBS) processes are critical for this purpose, as they are sensitive to the self-interactions of gauge bosons (triple and quartic gauge couplings) and potential modifications to Higgs couplings. While VBS interactions involving $W^\pm W^\pm$ and $WZ$ boson pairs have been previously observed at $\sqrt{s} = 8$ and $13$ TeV, this paper presents the first measurements of these processes at the higher center-of-mass energy of $\sqrt{s} = 13.6$ TeV. The study focuses on the leptonic decay modes to minimize backgrounds and isolate the electroweak production component from the dominant Quantum Chromodynamics (QCD) induced diboson production.

Methodology
The analysis utilizes proton-proton collision data collected by the CMS detector during the 2022–2024 LHC operating periods, corresponding to an integrated luminosity of $171 \text{ fb}^{-1}$. The study targets two specific channels:

1. Same-sign $W^\pm W^\pm$ production: Decaying to $\ell^\pm \nu \ell'^\pm \nu$ (where $\ell, \ell' = e, \mu$).
2. $WZ$ production: Decaying to $\ell^\pm \nu \ell'^\pm \ell'^\mp$.

Event Selection and Reconstruction:

• Triggers: Events are selected using single-lepton and dilepton triggers with transverse momentum ($p_T$) thresholds of 27 and 24 GeV, respectively, ensuring high efficiency for offline selection.
• Object Definition: Electrons and muons are reconstructed using a particle-flow algorithm. Jets are clustered using the anti-$k_T$ algorithm ($R=0.4$) with $p_T > 50$ GeV and $|\eta| < 4.7$. Missing transverse momentum ($p_T^{miss}$) is calculated using PUPPI to mitigate pileup effects.
• Signal Regions (SR): Candidate events require two or three isolated leptons, at least two jets, and specific kinematic cuts to isolate the VBS topology:
  • $W^\pm W^\pm$ SR: Two same-sign leptons ($p_T > 25/20$ GeV), $m_{\ell\ell} > 20$ GeV, $p_T^{miss} > 30$ GeV, dijet mass $m_{jj} > 500$ GeV, and pseudorapidity separation $\Delta\eta_{jj} > 2.5$. A Zeppenfeld variable cut ($\max(z^*_\ell) < 0.75$) is applied.
  • $WZ$ SR: Three leptons with a Z-boson candidate ($|m_{\ell\ell} - m_Z| < 15$ GeV) and a third lepton from the W boson. Similar jet and $p_T^{miss}$ requirements apply, with a Zeppenfeld cut of $\max(z^*_\ell) < 1.0$.
• Background Suppression: Top quark backgrounds are reduced by vetoing $b$-tagged jets. Non-prompt lepton backgrounds are estimated using a "pass-fail" method in data, while $tZq$ and other backgrounds are constrained using dedicated control regions (CRs).
• Analysis Strategy: A binned maximum-likelihood fit is performed simultaneously across the SRs and CRs. For the $WZ$ channel, where QCD production dominates, a Gradient Boosted Decision Tree (BDT) discriminator is trained to separate EW signal from QCD background. The fit extracts normalization factors for signal and background processes, treating systematic uncertainties as nuisance parameters.

Key Contributions and Results

• Observation: The electroweak production of both $W^\pm W^\pm$ and $WZ$ boson pairs is observed with a statistical significance exceeding five standard deviations from the background-only hypothesis. The observed significance for the EW $WZ$ signal is approximately seven standard deviations.
• Cross Section Measurements: Inclusive fiducial cross sections for EW $W^\pm W^\pm$, EW+QCD $W^\pm W^\pm$, EW $WZ$, and EW+QCD $WZ$ are measured. The results are consistent with SM predictions calculated using MADGRAPH5_aMC@NLO and SHERPA generators, including next-to-leading order (NLO) corrections.
  • The measured EW $W^\pm W^\pm$ cross section is $3.81 \pm 0.38$ fb.
  • The measured EW $WZ$ cross section is $1.43 \pm 0.26$ fb.
• Differential Measurements: Differential fiducial cross sections are measured as functions of $m_{jj}$, $m_{\ell\ell}$, jet multiplicity ($n_j$), $\Delta\eta_{jj}$, and $\Delta\phi_{jj}$. These distributions show good agreement with theoretical predictions within experimental and theoretical uncertainties.
• Systematics: The total uncertainty on the signal strength is approximately 10.7% for $W^\pm W^\pm$ and 20.4% for $WZ$. The larger uncertainty in the $WZ$ channel is attributed to the difficulty in disentangling the EW and QCD components.

Significance
This paper reports the first measurements of VBS in $W^\pm W^\pm$ and $WZ$ channels at $\sqrt{s} = 13.6$ TeV. By utilizing the increased center-of-mass energy and a substantial dataset of $171 \text{ fb}^{-1}$, the analysis confirms the Standard Model description of electroweak symmetry breaking and gauge boson self-interactions in a new energy regime. The results provide stringent constraints on anomalous quartic gauge couplings and serve as a baseline for future searches for new physics in the electroweak sector. The measurements are consistent with SM predictions, reinforcing the validity of the current theoretical framework while offering improved precision over previous 13 TeV results.