Measurements of the inclusive W and Z boson production cross sections and their ratios in proton-proton collisions at $\sqrt{s}$ = 13.6 TeV

This paper presents measurements of inclusive W and Z boson production cross sections and their ratios in proton-proton collisions at a center-of-mass energy of 13.6 TeV using 2022 data, yielding results that are in agreement with next-to-next-to-leading order quantum chromodynamic predictions.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful particle smasher. For years, it has been smashing protons together to see what happens. In this specific study, the CMS experiment (one of the giant detectors at the LHC) decided to turn up the dial to a new, record-breaking speed: 13.6 TeV. Think of this as upgrading a race car from a top speed of 130 mph to 136 mph. It's a small number on paper, but in the world of particle physics, it's a massive leap into uncharted territory.

The goal of this paper is to measure how often two specific, heavy particles—the W boson and the Z boson—are created when these protons collide. These particles are like the "messengers" of the weak nuclear force, one of the four fundamental forces of nature.

Here is a breakdown of what they did and found, using simple analogies:

1. The Setup: A Cosmic Coin Toss

The researchers didn't just look at every single collision. They focused on a very specific "signature" left behind: muons.

• The Analogy: Imagine a massive fireworks display (the proton collisions). Most of the time, you just see sparks and smoke. But sometimes, a specific type of bright, blue spark (a muon) flies out.
• The Strategy: The team looked at data collected in 2022. They filtered through billions of collisions to find the ones where they saw either one blue spark (indicating a W boson decayed) or two blue sparks flying in opposite directions (indicating a Z boson decayed).
• The Data: They analyzed a tiny slice of time, corresponding to about 5.01 inverse femtobarns of data. In everyday terms, this is like looking at a very specific, high-resolution snapshot of a storm that lasted only a few seconds, but that snapshot contained enough information to make incredibly precise measurements.

2. The Challenge: Finding a Needle in a Haystack

The universe is messy. When protons smash, they create a chaotic mess of particles. The W and Z bosons are rare, and they decay almost instantly.

• The Haystack: The "haystack" is the background noise of other particles (like jets of quarks or other heavy particles) that look similar to the muons the scientists are hunting.
• The Needle: The W and Z bosons are the needles.
• The Solution: The team used a sophisticated "filter" (a computer algorithm) to separate the real signals from the noise. They looked at the energy and direction of the muons. For the W boson, they also looked for "missing energy" (like a ghost that took some energy away), which happens because the W boson decays into a muon and a neutrino (a ghostly particle that doesn't leave a trace).

3. The Results: Counting the Particles

After cleaning up the data and removing the background noise, the team counted how many W and Z bosons they found.

• The Findings:
  • They measured the W+ boson production rate.
  • They measured the W- boson production rate.
  • They measured the Z boson production rate.
• The Precision: The results were incredibly precise. The uncertainty (the "fuzziness" of the measurement) was so small that it was dominated not by the number of particles they found, but by how well they knew the total amount of data they collected (the "luminosity"). It's like weighing a gold bar so precisely that the only thing you aren't 100% sure of is the exact calibration of the scale, not the weight of the gold itself.

4. The Ratios: Comparing the Weights

Instead of just counting the particles, the team also looked at the ratios.

• The Analogy: Imagine you are baking cookies. You want to know if you are making more chocolate chip cookies (W+) or oatmeal raisin cookies (W-). Instead of counting every single cookie in the world, you just compare the ratio of chocolate to oatmeal in your batch.
• Why do this? By comparing the ratios (e.g., W+ vs. W-, or W vs. Z), many of the potential errors cancel out. If your scale is slightly off, it affects both counts equally, so the ratio remains accurate. This allowed them to measure the relationship between these particles with even higher precision than the individual counts.

5. The Verdict: The Theory Holds Up

The most important part of the paper is the comparison with theory.

• The Prediction: Physicists have a "rulebook" called the Standard Model. Using complex math (Quantum Chromodynamics), they predicted exactly how many W and Z bosons should be created at this new energy level.
• The Result: The measurements from the CMS detector matched the theoretical predictions almost perfectly.
• The Metaphor: It's like a master chef following a recipe that says, "At this temperature, you should get exactly 100 cookies." The chef bakes them, counts them, and finds exactly 100. This confirms that the recipe (the Standard Model) is still correct, even at this new, higher speed.

Summary

In short, this paper is a "stress test" for our understanding of the universe. The CMS team turned the LHC up to a new speed, hunted for specific particle signatures, and found that the universe behaves exactly as our best theories predicted. They didn't discover a new particle or a new force; instead, they confirmed that our current map of the subatomic world is still accurate, even when we push the boundaries of energy to new heights.

The paper concludes that the CMS detector is performing beautifully after its recent upgrades, ready to tackle even more complex mysteries in the future.

Technical Summary

Technical Summary: Measurements of Inclusive W and Z Boson Production Cross Sections at $\sqrt{s} = 13.6$ TeV

Problem and Motivation
The massive W and Z bosons are fundamental components of the electroweak sector of the Standard Model (SM). Precise determination of their production cross sections in proton-proton (pp) collisions is critical for probing theoretical predictions, particularly at high orders of perturbative quantum chromodynamics (QCD). Furthermore, these measurements serve as essential background characterizations for searches for physics beyond the Standard Model. While previous analyses by the ATLAS, CMS, and LHCb Collaborations have reported results at center-of-mass energies ranging from 2.76 to 13 TeV, this paper addresses the need for precision measurements at the new, unprecedented energy regime of 13.6 TeV, which was reached by the LHC in 2022.

Methodology
The analysis utilizes data collected by the CMS detector during the 2022 LHC run, corresponding to an integrated luminosity of $5.01 \pm 0.07 \text{ fb}^{-1}$. The study focuses on events with one or two identified muons in the final state.

• Event Selection:
  • W Boson Candidates: Events are selected with exactly one "tight" muon ($p_T > 25$ GeV, $|\eta| < 2.4$) and large missing transverse momentum ($p_T^{\text{miss}}$) arising from the undetected neutrino. Events with a second "loose" muon are rejected to reduce Z boson contamination. The transverse mass ($m_T$) is used as the primary discriminant between signal and background.
  • Z Boson Candidates: Events are selected with two "tight" muons of opposite electric charge. The invariant mass of the dimuon pair ($m_{\mu\mu}$) is required to be in the range of 60–120 GeV.
• Signal Extraction: A simultaneous binned maximum likelihood fit is performed on the $m_T$ distributions in the single-muon regions ($\mu^+$ and $\mu^-$) and the $m_{\mu\mu}$ distribution in the double-muon region. The fit includes signal templates for $W^+$, $W^-$, and Z bosons, as well as background templates for top quark production ($t\bar{t}$ and single top), electroweak (EWK) processes, and QCD multijet production.
• Background Modeling:
  • $t\bar{t}$, single top, and diboson backgrounds are modeled using Monte Carlo (MC) simulations generated at Next-to-Leading Order (NLO) or Next-to-Next-to-Leading Order (NNLO) using POWHEG and MADGRAPH5 aMC@NLO.
  • The QCD multijet background, which is a significant contributor to the single-muon signal regions, is modeled using a data-driven approach. A QCD-enriched control region is defined by inverting the muon isolation requirement. The shape of the $m_T$ distribution is extrapolated to the signal region using linear and quadratic fits to the dependence on muon relative isolation.
• Corrections and Calibration:
  • Pileup: Simulated events are reweighted to match the pileup distribution observed in data.
  • Muon Efficiency: Scale factors are derived using a tag-and-probe method to correct for differences in muon identification, isolation, and reconstruction efficiencies between data and simulation.
  • Momentum Scale and Resolution: Corrections are applied to the muon momentum scale and resolution in data to align the Z boson peak position and width with simulation.
  • Recoil: Corrections based on the Z boson recoil are applied to improve the modeling of $p_T^{\text{miss}}$.
• Cross Section Calculation: Fiducial cross sections are measured within the experimentally accessible phase space. Total inclusive cross sections are derived by extrapolating the fiducial results using kinematic acceptance corrections calculated at NNLO QCD with NNLL $q_T$ resummation using the DYTURBO program and NNPDF 3.1 parton distribution functions (PDFs).

Key Contributions and Results
The paper presents the first measurements of inclusive W and Z boson production cross sections at $\sqrt{s} = 13.6$ TeV. Despite the relatively small dataset and the focus on muonic final states, the precision of the results exceeds that of previous measurements, largely attributed to a more precise determination of the integrated luminosity.

• Measured Cross Sections: The products of the total inclusive cross sections and branching fractions for muonic decays are reported as:

  • $W^+$: $11.93 \pm 0.08 \text{ (syst)} \pm 0.17 \text{ (lumi)} {}^{+0.07}_{-0.07} \text{ (acceptance)}$ nb.
  • $W^-$: $8.86 \pm 0.06 \text{ (syst)} \pm 0.12 \text{ (lumi)} {}^{+0.05}_{-0.06} \text{ (acceptance)}$ nb.
  • $Z$ (60–120 GeV): $2.021 \pm 0.009 \text{ (syst)} \pm 0.028 \text{ (lumi)} {}^{+0.011}_{-0.013} \text{ (acceptance)}$ nb.
  • Statistical uncertainties are negligible for all measurements.

• Cross Section Ratios: Ratios are provided with higher precision than individual cross sections due to the cancellation of systematic uncertainties, particularly the luminosity uncertainty.

  • $R_{W^+/Z} = 5.906 \pm 0.004 \text{ (stat)} \pm 0.040 \text{ (syst)} {}^{+0.022}_{-0.028} \text{ (acceptance)}$.
  • $R_{W^-/Z} = 4.382 \pm 0.003 \text{ (stat)} \pm 0.029 \text{ (syst)} {}^{+0.023}_{-0.016} \text{ (acceptance)}$.
  • $R_{W^+/W^-} = 1.348 \pm 0.001 \text{ (stat)} \pm 0.005 \text{ (syst)} {}^{+0.006}_{-0.007} \text{ (acceptance)}$.

• Theoretical Comparison: All measured values are in agreement with theoretical predictions calculated at next-to-next-to-leading order (NNLO) accuracy in QCD plus next-to-next-to-leading logarithmic (NNLL) $q_T$ resummation.

Significance
The authors claim that the high precision of these measurements highlights the excellent performance of the CMS detector following the Long Shutdown 2 (2018–2022) and its operation at the new center-of-mass energy of 13.6 TeV. The results underscore the potential value of dedicated differential measurements for refining the description of parton distribution functions (PDFs) and enhancing the understanding of QCD processes in the future. The paper emphasizes that these measurements provide a robust baseline for background estimation in searches for new physics at the LHC.