Recent electroweak measurements from the CMS experiment

This paper summarizes recent electroweak measurements from the CMS experiment at the Large Hadron Collider, highlighting high-precision determinations of key parameters and process rates at 13.6 TeV that often match or exceed the precision of previous lepton collider results.

The Gist

Imagine the universe is built like a giant, incredibly complex Lego set. For decades, scientists have had a "rulebook" called the Standard Model that explains how the pieces (particles) snap together and interact. Two of the most important forces in this rulebook are Electromagnetism (which makes magnets stick and lights turn on) and the Weak Force (which makes the sun shine and allows radioactive decay).

This paper is a report card from the CMS experiment, a massive, high-tech detective agency built inside the Large Hadron Collider (LHC) in Switzerland. The CMS team is like a team of master mechanics who smash protons together at nearly the speed of light to see how the "Lego bricks" of the universe behave.

Here is what they found, explained simply:

1. The Machine: A Giant Particle Microscope

Think of the CMS detector as a 360-degree, high-speed camera the size of a cathedral. Inside, there is a super-strong magnet (like a giant donut) that bends the paths of particles. When protons smash together, they create a shower of new particles. The CMS camera catches these particles, measuring their speed, energy, and direction with incredible precision.

The paper covers data from two "seasons" of smashing:

• Run 2: Smashing at 13 TeV (a very high energy).
• Run 3: Smashing at an even higher 13.6 TeV (the current record).

2. The Precision Frontier: Checking the Rulebook

The first part of the paper is about checking the math. Scientists have very precise predictions about how often certain particles should appear. It's like predicting exactly how many times a coin will land on heads if you flip it a million times.

• The W and Z Bosons: These are the "messengers" of the weak force. The team counted how many W and Z particles were created. The numbers matched the rulebook perfectly.
  • Analogy: Imagine you run a bakery and predict you'll sell 1,000 croissants a day. If you actually sell 1,000, your recipe is perfect. If you sell 1,200, something is wrong with your recipe (or you have a secret ingredient). The CMS team found the "croissant count" was exactly as predicted.
• The "Mixing Angle": This is a specific number that describes how the weak force and electromagnetism mix together. The team measured this angle with such precision that it rivals the best measurements ever made by older machines that used electrons instead of protons.
  • Analogy: It's like measuring the exact shade of blue in a paint mixture. They found the shade is exactly what the rulebook said it should be, down to the millionth of a percent.
• The Tau Lepton: This is a heavy cousin of the electron. The team watched how these particles spin (polarization) and how they interact with light. They found that the "spin" matches the rulebook perfectly, setting new, stricter limits on how "magnetic" these particles can be.

3. The Energy Frontier: Breaking the Rules to Find New Ones

The second part of the paper is about pushing the limits. Scientists smash particles together at higher and higher energies to see if the rulebook breaks. If the rules break, it means there is "New Physics" hiding underneath—something we don't know about yet.

• Multiboson Production: Usually, particles are born in pairs. The team looked for rare events where three or four force-carrying particles were born at once (like a triple or quadruple play in baseball).
  • Analogy: Imagine a pool table where you hit the cue ball, and instead of just two balls scattering, you suddenly see three or four balls flying off in perfect formation. The team saw this happen (specifically, three particles: W, W, and a photon) for the first time in a proton collider. It was a "5-sigma" discovery, which in science means "we are 99.9999% sure this isn't a fluke."
• Vector Boson Scattering: This is like watching two force-carrying particles bounce off each other. The team used advanced AI (neural networks) to find these rare bounces in a sea of background noise. They found no evidence of "New Physics" here either; the particles bounced exactly as the Standard Model predicted.

4. The Big Conclusion: The Rulebook is Still King

So, what does it all mean?

• The Good News: The Standard Model is incredibly robust. Every time the CMS team looked, the universe behaved exactly as the rulebook predicted. The measurements are so precise that they are now as good as, or even better than, the best measurements from the old days of electron colliders.
• The Challenge: Because the rulebook is so perfect, it's getting harder to find cracks in it. The team is now saying, "We need even better math from the theorists!" They are asking for predictions that are even more precise so they can spot the tiniest possible deviations.

In a nutshell: The CMS team took the universe apart, piece by piece, at the highest energies ever achieved. They found that the universe is still playing by the rules we wrote down 50 years ago. While they didn't find "new physics" (like dark matter or extra dimensions) yet, they proved that our current understanding is rock-solid, and they set the stage for the next generation of experiments to finally find what's hiding in the shadows.

Technical Summary

1. Problem and Motivation

The paper addresses the need to rigorously test the Standard Model (SM) of particle physics, specifically the unified electroweak (EW) theory. The motivation is twofold:

• Precision Frontier: To compare highly precise experimental measurements of EW parameters (e.g., $W$ boson mass, effective leptonic mixing angle) against theoretical predictions. Deviations could indicate New Physics (NP) contributions via virtual loops.
• Energy Frontier: To explore high-energy regimes (up to 13.6 TeV) where deviations from gauge cancellations might reveal NP, such as anomalous couplings, Effective Field Theory (EFT) operators, or Axion-Like Particles (ALPs).
• Context: While lepton colliders (like LEP) provided legacy precision, the Large Hadron Collider (LHC) offers unprecedented center-of-mass energies and high production rates of gauge bosons, though it faces challenges from high pileup and QCD backgrounds.

2. Methodology

The study utilizes data from the Compact Muon Solenoid (CMS) detector at the LHC, covering Run 2 (13 TeV, 2015–2018) and Run 3 (13.6 TeV, 2022–ongoing).

• Detector Capabilities: The analysis relies on the CMS detector's high-performance reconstruction of electrons, muons, and photons, with efficiencies >95% for electrons/photons and >96% for muons. Neutrinos are inferred via missing transverse momentum.
• Data Selection:
  • Cross Sections: Dedicated runs with reduced instantaneous luminosity were used to minimize pileup. Cross sections were extracted using binned maximum likelihood fits on transverse mass ($W$) and dilepton invariant mass ($Z$).
  • Asymmetry Measurements: The forward-backward asymmetry ($A_{FB}$) in Drell-Yan production was measured using the Collins-Soper reference frame. Two methods were employed: direct angular-weighted asymmetry and template fits to $A_{FB}$ as a function of dilepton mass and rapidity.
  • Tau Physics: Tau leptons were reconstructed from leptonic and hadronic decay modes. Specific selections included back-to-back azimuthal topology for photon-photon fusion and helicity analysis for $Z \to \tau\tau$.
  • Multiboson & Scattering: Events were selected based on specific final states (e.g., 3 leptons for $WZ$, 2 leptons + photon for $WW\gamma$). Deep neural networks (DNNs) were utilized to discriminate signal from backgrounds in Vector Boson Scattering (VBS) channels.
• Theoretical Framework: Results are compared against SM predictions at Next-to-Next-to-Leading Order (NNLO) for QCD and Next-to-Leading Order (NLO) for EW corrections. Parton Distribution Functions (PDFs), specifically the CT18Z set, were profiled to assess uncertainties.

3. Key Contributions and Results

A. Precision Frontier Results

• $W$ and $Z$ Cross Sections:
  • Measured inclusive cross sections at 5.02 TeV and 13 TeV with reduced systematic uncertainties.
  • New Result: A precise measurement of the $Z$ production cross section at 13.6 TeV (Run 3) using $Z \to \mu\mu$ decays: $\sigma = 2.010 \pm 0.001(\text{stat}) \pm 0.018(\text{syst}) \pm 0.046(\text{lumi}) \pm 0.007(\text{theo})$ nb.
  • Results agree with NNLO QCD predictions.
• Decay Branching Fractions & Asymmetries:
  • $Z \to 4l$: Measured the inclusive branching fraction $B(Z \to 4l) = (4.67 \pm 0.21) \times 10^{-6}$ (precision $\sim 3\%$), the best to date.
  • $W$ Hadronic Decays: Measured the ratio $R_c^W = B(W \to cq)/B(W \to q\bar{q}') = 0.489 \pm 0.020$, improving world precision by a factor of two.
  • Effective Leptonic Mixing Angle ($\sin^2\theta_{\text{eff}}^l$): Derived from $A_{FB}$ in Drell-Yan production using 138 fb$^{-1}$ of data.
    • Result: $\sin^2\theta_{\text{eff}}^l = 0.23157 \pm 0.00031$.
    • Significance: This is the best measurement at a hadron collider, reaching the precision of legacy lepton collider results and helping resolve discrepancies between LEP lepton and $b$-quark results.
• Tau Lepton Properties:
  • First Observation: Observed $\gamma\gamma \to \tau\tau$ production at a proton-proton collider with 5.3$\sigma$ significance.
  • Constraints: Set the most stringent limit on the tau anomalous magnetic moment ($a_\tau$) and electric dipole moment ($|d_\tau| < 2.9 \times 10^{-17} e \cdot \text{cm}$).
  • Polarization: Measured $Z \to \tau\tau$ polarization as $P_\tau = -0.144 \pm 0.015$, the most precise at a hadron collider, yielding an independent $\sin^2\theta_{\text{eff}}^l = 0.2319 \pm 0.0019$.

B. Energy Frontier Results

• Multiboson Production:
  • $WZ$ Production: Measured cross section at 13.6 TeV: $\sigma_{WZ} = 55.2 \pm 1.2(\text{stat}) \pm 1.2(\text{syst}) \pm 0.8(\text{lumi}) \pm 0.1(\text{theo})$ pb.
  • $WW\gamma$ Production: Achieved the first observation of $WW\gamma$ production at a proton-proton collider (5.6$\sigma$ significance) with $\sigma_{WW\gamma} = 5.9 \pm 1.3$ fb.
  • $WZ\gamma$ Production: Set limits on anomalous quartic gauge couplings and photophobic ALP models.
• Vector Boson Scattering (VBS):
  • Performed the first study of same-sign $W$ boson scattering with a hadronic tau decay channel.
  • Measured cross section: $1.44^{+0.63}_{-0.56}$ times the SM prediction.
  • Interpreted via EFT; no deviations from SM expectations were found.

4. Significance

• Precision Benchmarking: The CMS experiment has successfully established its role as a precision instrument for EW physics. Several measurements (specifically $\sin^2\theta_{\text{eff}}^l$ and tau polarization) now match or surpass the precision of results from legacy lepton colliders (LEP, SLC).
• New Physics Constraints: The absence of deviations from the SM in high-precision parameters and high-energy multiboson/VBS channels places stringent constraints on New Physics models, including EFT operators, anomalous couplings, and ALPs.
• Future Directions: The high precision of current results highlights a growing need for even higher-order theoretical predictions (e.g., N$^3$LO QCD) to fully exploit the experimental capabilities.
• Operational Success: The results demonstrate the CMS detector's ability to operate effectively in the challenging high-pileup environment of the LHC, utilizing advanced reconstruction techniques and machine learning (DNNs) to isolate rare electroweak signals.

In conclusion, the paper summarizes a comprehensive program where CMS has validated the Standard Model across both precision and energy frontiers, setting new benchmarks for hadron collider physics and providing critical inputs for future theoretical developments.