Measurement of the jet mass in hadronic decays of boosted W bosons at 13 TeV and extraction of the W boson mass

Using 138 fb$^{-1}$ of 13 TeV proton-proton collision data collected by the CMS experiment, this paper presents the first unfolded double-differential cross-section measurements of boosted W+jets events to extract a W boson mass of 80.83 $\pm$ 0.55 GeV, achieving the smallest uncertainty to date for an all-jets final state at a hadron collider.

The Gist

Imagine you are a detective trying to identify a specific type of car (a W boson) speeding through a massive, chaotic traffic jam (the proton-proton collisions at CERN).

Usually, when this "car" breaks down, it splits into two smaller vehicles (quarks) that fly off in different directions. You can easily spot them as two separate cars. But sometimes, this "car" is moving so incredibly fast that when it breaks down, the two smaller vehicles are squeezed so tightly together they look like a single, giant, messy blob of debris.

This paper is about the CMS team at CERN learning how to identify that specific "giant blob" and measure exactly how heavy the original "car" was, even when it's moving at near-light speed.

Here is the story of how they did it, broken down into simple steps:

1. The Problem: The "Messy Blob"

When the W boson is moving slowly, it's easy to see its two parts. But when it's "boosted" (moving super fast), the two parts merge into one giant jet of particles.

• The Analogy: Imagine throwing a handful of confetti. If you throw it slowly, the pieces spread out. If you throw it with a giant fan blowing behind it, the confetti clumps into a tight, fast-moving ball.
• The Challenge: The detector sees this tight ball of confetti. But there are billions of other "balls of confetti" in the universe that aren't W bosons; they are just random garbage (quarks and gluons) created by the collision. The team needed a way to tell the "W boson ball" apart from the "garbage ball."

2. The Solution: The "Soft-Drop" Groomer

To find the W boson, the scientists needed to clean up the mess.

• The Analogy: Imagine you have a dirty, muddy snowball. You want to know how much pure snow is inside, but it's covered in mud and loose twigs. You shake the snowball gently. The loose mud and twigs (soft, wide-angle radiation) fall off, leaving you with a clean, dense core.
• The Tool: They used a computer algorithm called Soft-Drop. It acts like a digital snow-shaker. It strips away the loose, messy particles on the outside of the jet, leaving only the heavy, core particles. This makes the "mass" of the jet much clearer.

3. The "Two-Prong" Test

Even after cleaning the jet, how do you know it's a W boson and not just a random clump of garbage?

• The Analogy: Think of a W boson as a peanut. When it breaks, it splits into two distinct halves (two prongs). A random garbage jet is more like a single lump of clay.
• The Tool: The team used two different "detectors" to look for this peanut shape:
  1. N(1)2: A mathematical formula that counts how many "branches" the jet has.
  2. ParticleNet: An artificial intelligence (a neural network) trained to recognize the specific "fingerprint" of a peanut-shaped jet versus a clay-shaped jet.
  • Result: The AI (ParticleNet) was the better detective, finding the W bosons more accurately.

4. The Great Unfolding (The Magic Trick)

The data they collected was "blurry" because the detector isn't perfect, and the collisions are messy. They needed to "unblur" the picture to see what really happened at the particle level.

• The Analogy: Imagine taking a photo of a fast-moving car through a foggy window. The photo is blurry. To fix it, you use a mathematical "de-fogging" filter that knows exactly how the window distorts light. You apply this filter to the whole dataset to reconstruct the sharp, clear image of the car's speed and size.
• The Result: They created a "double-differential" map. This is like a 3D topographic map showing exactly how many W bosons exist at every specific speed and every specific mass.

5. The Big Discovery: Weighing the W Boson

Once they had the clean, unblurred map, they looked at the "peak" of the mountain.

• The Analogy: If you weigh a bag of apples, you expect the average weight to be around 5 lbs. If you weigh 1,000 bags and the average comes out to 5.05 lbs, you know the true weight of the apple.
• The Measurement: By looking at the mass of all these "peanut" jets, they calculated the mass of the W boson.
  • The Result: They found the mass to be 80.83 GeV (a unit of energy/mass).
  • The Uncertainty: They were off by only 0.55. This is incredibly precise for this type of measurement.

Why Does This Matter?

• It's a New Record: This is the most precise measurement of the W boson mass ever made using only jets (the messy debris). Previous records used "clean" signals like electrons or muons.
• Testing the Universe: The Standard Model (our rulebook for physics) predicts what this mass should be. If our measurement is slightly off, it could mean there is "New Physics" hiding in the shadows—perhaps a new particle we haven't discovered yet.
• Future Proofing: This experiment proves that we can measure these heavy particles with high precision even when they are moving at extreme speeds. This sets the stage for the "High-Luminosity LHC" in the future, where we will have even more data to hunt for new physics.

In a nutshell: The CMS team took a chaotic, high-speed crash, used a digital "snow-shaker" to clean up the debris, used an AI to spot the "peanut-shaped" wreckage, and used math to unblur the photo. The result? They weighed the W boson with the highest precision ever achieved using this specific method, giving us a sharper picture of how the universe works.

Technical Summary

1. Problem Statement

The W boson mass ($m_W$) is a fundamental parameter of the Standard Model (SM). While previous measurements using leptonic decay channels (e.g., $W \to \ell\nu$) at LEP, Tevatron, and the LHC have achieved high precision, measurements in the all-jets final state ($W \to q\bar{q}'$) have historically suffered from large uncertainties due to the overwhelming background of Quantum Chromodynamics (QCD) multijet production and imperfect modeling of jet substructure.

At the Large Hadron Collider (LHC), W bosons produced with high transverse momentum ($p_T \gg m_W$) undergo significant Lorentz boosting. In this regime, the decay products (quark-antiquark pair) are highly collimated and reconstructed as a single large-radius jet rather than two separate jets. The challenge lies in distinguishing these "boosted W jets" from the vast background of quark- and gluon-initiated jets and accurately modeling the jet mass distribution to extract $m_W$.

2. Methodology

Data and Simulation

• Dataset: Proton-proton collisions at $\sqrt{s} = 13$ TeV collected by the CMS experiment during 2016–2018, corresponding to an integrated luminosity of 138 fb$^{-1}$.
• Trigger: Events were selected using triggers requiring an anti-$k_T$ jet ($R=0.8$) with $p_T > 450$ or $500$ GeV.
• Simulation: Signal ($W(qq')$+jets) and background processes were simulated using **MADGRAPH5_aMC@NLO** interfaced with **PYTHIA 8** (CP5 tune) for parton showering and hadronization. Alternative samples used **HERWIG 7** to estimate hadronization model uncertainties. Top quark ($t\bar{t}$) and Z+jets backgrounds were simulated using POWHEG and MADGRAPH respectively.

Jet Reconstruction and Grooming

• Jet Algorithm: Jets were clustered using the anti-$k_T$ algorithm with a distance parameter $R=0.8$.
• Pileup Mitigation: The PUPPI (Pileup Per Particle Identification) algorithm was applied to weight particles based on their likelihood of originating from the primary vertex.
• Soft-Drop Grooming: To mitigate the effects of soft, wide-angle radiation (which broadens the jet mass distribution), the Soft-Drop (SD) algorithm was applied. This removes soft subjets that do not satisfy the condition:
  $$\frac{\min(p_{T,1}, p_{T,2})}{p_{T,1} + p_{T,2}} > z_{cut} \left( \frac{\Delta R_{12}}{R} \right)^{\beta_{sd}}$$
  with default parameters $z_{cut}=0.1$ and $\beta_{sd}=0$. The jet $p_T$ used for measurement was taken from the ungroomed jet, while the mass ($m_{SD}$) was calculated from the groomed jet.

Tagging and Background Estimation

• Substructure Taggers: Two strategies were employed to distinguish W jets (characterized by a "two-prong" substructure) from QCD background ("one-prong"):
  1. $N^{(1)}_2$: An energy correlation function ratio, theoretically well-defined.
  2. PARTICLENET: A Graph Neural Network (GNN) classifier.
  • To avoid bias in the mass measurement, mass-decorrelated versions of these taggers were constructed using the Design Decorrelated Tagger (DDT) technique, ensuring constant selection efficiency for QCD jets across the phase space.
• Control Regions: Events were categorized into Signal (Pass) and Control (Fail) regions based on the tagger output.
• Background Modeling: The QCD multijet background shape was estimated directly from data in the Fail region using a transfer factor method. A two-dimensional transfer function depending on jet $p_T$ and $\rho_{SD}$ (log of $m_{SD}^2/p_T^2$) was fitted using Bernstein polynomials to extrapolate the background shape to the Signal region.

Unfolding and Extraction

• Unfolding: A maximum-likelihood template fit was performed to unfold detector effects, correcting the measured distributions to the particle level. The response matrix was derived from simulation, and Tikhonov regularization was applied to stabilize the unfolding.
• Mass Extraction: The W boson mass was extracted by fitting the unfolded $m_{SD}$ distribution in the peak region ($70 < m_{SD} < 90$ GeV) using templates generated with PYTHIA at various input $m_W$ values (79.0, 80.0, 80.385, 81.0, 82.0 GeV).

3. Key Contributions

1. First Double-Differential Measurement: This paper presents the first unfolded measurement of the double-differential $W$+jets cross section as a function of jet transverse momentum ($p_T$) and soft-drop mass ($m_{SD}$) for boosted W bosons.
2. Advanced Background Estimation: Implementation of a robust, data-driven QCD background estimation using mass-decorrelated taggers and a flexible transfer function, minimizing reliance on simulation for the dominant background.
3. Precision in All-Jets Channel: Achieved the smallest uncertainty to date for an $m_W$ measurement in the all-jets final state at a hadron collider, demonstrating the viability of this channel for future high-luminosity studies.
4. Substructure Validation: Provided a critical testbed for jet substructure modeling (parton showering and hadronization) in a regime where the W boson is not color-connected to the rest of the event (unlike in $t\bar{t}$ events).

4. Results

Jet Mass Distribution

• The unfolded double-differential cross sections ($d\sigma/dm_{SD}dp_T$) were measured for $p_T > 650$ GeV.
• The data showed good agreement with theoretical predictions (MADGRAPH5_aMC@NLO+PYTHIA with NLO QCD and EW corrections) within total uncertainties.
• A slight shift in the peak position was observed in the highest $p_T$ bins compared to simulation, covered by the total uncertainty.

W Boson Mass Extraction

• Using the template fit to the unfolded data in the peak region:
  $$m_W = 80.81 \pm 0.55 \text{ GeV (total)}$$
• Breaking down the uncertainty:
  • Statistical + Background: $\pm 0.36$ GeV
  • Other Systematics: $\pm 0.41$ GeV
• Systematic Dominance: The largest uncertainties arose from the W tagging efficiency, V+jets QCD NLO corrections, Final State Radiation (FSR), and the Hadronization model. The Jet Energy Scale (JES) was a significant contributor to the shape uncertainty.
• Renormalization Scheme: Converting to the on-shell renormalization scheme (adding 27 MeV):
  $$m_W = 80.83 \pm 0.55 \text{ GeV}$$

5. Significance

• Competitiveness: While the current uncertainty ($\sim 0.55$ GeV) is larger than the most precise leptonic measurements ($\sim 0.01$ GeV), this result represents a major milestone. It proves that the all-jets channel can yield a precise $m_W$ measurement, which is crucial for cross-checking the SM and probing new physics where leptonic channels might be suppressed or biased.
• Future Prospects: The analysis serves as a proof-of-concept for the High-Luminosity LHC (HL-LHC). With the anticipated increase in integrated luminosity (factor of 10-20), statistical uncertainties will decrease significantly, potentially making the all-jets channel competitive with leptonic channels.
• Modeling Insights: The measurement highlights specific areas where QCD modeling (particularly hadronization and FSR) needs improvement to reduce systematic uncertainties in future high-precision measurements.

In conclusion, this paper establishes a rigorous framework for measuring boosted W boson properties in the all-jets channel, delivering the most precise $m_W$ extraction from this final state to date and laying the groundwork for future precision physics at the HL-LHC.