Standard Model W, Z (+jet) at CMS and ATLAS

This paper reviews recent precision measurements of Standard Model W and Z boson production (including Z+jet and boosted W decays) by the ATLAS and CMS collaborations using Run 2 data, highlighting their role in rigorously testing perturbative QCD, electroweak theory, and parton distribution functions.

The Gist

Imagine the Large Hadron Collider (LHC) as the world's most powerful, high-speed particle smasher. Inside its massive ring, scientists crash protons together at nearly the speed of light, creating a chaotic explosion of subatomic debris. Among this chaos, two very special particles often appear: the W boson and the Z boson. You can think of them as the "messengers" of the weak nuclear force, the invisible glue that holds the universe together in specific ways.

This paper is a report card from two giant teams of scientists, ATLAS and CMS, who have been watching these messengers closely during the LHC's second major run of data collection (Run 2). They aren't just counting how many messengers show up; they are measuring their every move with incredible precision to see if the rules of the universe (the Standard Model) hold up or if there are cracks in the foundation.

Here is a breakdown of their four main investigations, explained with everyday analogies:

1. The "Forbidden Dance" Search (Charged Lepton Flavour Violation)

The Concept: In the Standard Model, particles have "flavors" (like electron, muon, and tau). Usually, a Z boson is like a strict bouncer at a club: it lets an electron in, but it won't let an electron turn into a muon right in front of it. This "flavor-changing" is strictly forbidden.
The Experiment: The CMS team looked through 138 trillion collisions (a massive dataset) to see if they could catch a Z boson breaking the rules—specifically, if it decayed into an electron and a muon at the same time. They also looked for a heavier, invisible cousin of the Z boson called a Z'.
The Result: The bouncer did his job perfectly. They found zero instances of this forbidden dance.
The Takeaway: While they didn't find new physics, they set a very strict "speed limit" on how often this could happen. It's like saying, "We checked the whole city, and if this crime happens, it's rarer than one in a billion." This puts huge pressure on theories that predict such events.

2. The "Spin and Wobble" Measurement (W-Boson Angular Coefficients)

The Concept: When a W boson is created, it doesn't just sit still; it spins and wobbles in specific directions before it decays. Think of a spinning top that is also being tossed through the air. The way it spins tells us about the invisible forces (QCD) that pushed it.
The Experiment: The ATLAS team used a special, low-crowd dataset (like taking a photo with a clear sky instead of a foggy one) to track the W boson's "wobble" (angular coefficients) and how fast it was moving sideways (transverse momentum).
The Result: They mapped out the wobble in extreme detail. The way the W boson spun matched the complex mathematical predictions of the Standard Model almost perfectly.
The Takeaway: It's like checking the aerodynamics of a new car model by watching how it drifts around a corner. The drift matched the engineers' simulations perfectly, confirming our understanding of how these particles interact with the "wind" of the quantum world.

3. The "Three-Dimensional Map" (Triple-Differential Z+Jet)

The Concept: Usually, scientists measure particles in one or two ways (like speed and direction). But the CMS team decided to measure the Z boson and its partner (a "jet" of particles) in three ways at once:

1. How hard the Z was hit (Transverse Momentum).
2. How far apart the Z and the jet were flying (Rapidity separation).
3. How fast the whole pair was zooming down the pipe (Boost).
   The Analogy: Imagine trying to understand a car crash. Most people just look at how fast the cars were going. These scientists looked at the speed, the angle of impact, and the speed of the wreckage sliding away, all at the same time.
   The Result: They created a 3D map of these collisions. The data matched the most advanced computer simulations (NNLO QCD) incredibly well.
   The Takeaway: This multi-angle view is like upgrading from a 2D photo to a 3D hologram. It gives scientists a much sharper picture of the "ingredients" inside the proton (parton distribution functions), helping them understand the proton's internal structure better than ever before.

4. The "Heavy Suitcase" and the W-Boson's Weight (Jet Mass)

The Concept: When a W boson is created with massive energy, it moves so fast that its decay products (the pieces it breaks into) get squished together into a single, giant blob of particles called a "jet." It's like a suitcase that is so heavy and packed that it looks like one solid block.
The Experiment: The CMS team looked at these "heavy suitcases" and used a special digital "grooming" tool (soft-drop algorithm) to trim away the loose dust and fluff, revealing the true weight of the suitcase.
The Result: By weighing these suitcases, they calculated the mass of the W boson to be 80.77 GeV.
The Takeaway: This is the first time anyone has weighed the W boson using only these messy, all-jet collisions. It's like weighing a person by looking at the shadow they cast in a foggy room, rather than putting them on a scale. It proves that even in the messiest, most chaotic environments, we can still get precise measurements.

The Big Picture

Why does this matter?
Think of the Standard Model as a massive, intricate clockwork machine that has kept perfect time for 50 years. These experiments are like master watchmakers taking the machine apart, measuring every gear and spring with laser precision.

• The Good News: The gears are turning exactly as predicted. The machine works.
• The Exciting Part: Because the measurements are so precise, even the tiniest, almost invisible "wobble" in the gears could hint at a new, hidden mechanism (New Physics) that we haven't discovered yet.

With more data coming from the LHC's future runs (Run 3 and the High-Luminosity LHC), these scientists will be able to see even deeper into the clockwork, potentially revealing secrets that have been hidden for decades.

Technical Summary

Based on the provided paper, here is a detailed technical summary of the recent Standard Model $W$ and $Z$ boson production measurements by the ATLAS and CMS Collaborations.

1. Problem and Motivation

The paper addresses the need for high-precision tests of the Standard Model (SM), specifically focusing on perturbative Quantum Chromodynamics (QCD) and Electroweak (EW) theory. While $W$ and $Z$ bosons are produced with large cross-sections at the Large Hadron Collider (LHC), precise measurements of their production and decay properties are essential for:

• Testing Theory: Validating calculations at Next-to-Next-to-Leading Order (NNLO) and beyond.
• Constraining PDFs: Improving Parton Distribution Functions (PDFs), which are critical for modeling proton-proton collisions.
• Searching for New Physics: Probing for Charged Lepton Flavour Violation (CLFV) and deviations from SM predictions that could indicate Beyond-the-Standard-Model (BSM) scenarios.
• Precision Mass Extraction: Determining the $W$ boson mass ($m_W$) in challenging hadronic final states.

The authors leverage the large datasets from Run 2 ($\sqrt{s} = 13$ TeV) to perform multi-differential measurements that were previously statistically limited, offering enhanced sensitivity to underlying parton dynamics.

2. Methodology

The paper reviews four distinct analyses performed by ATLAS and CMS, utilizing different decay channels and statistical techniques:

• CLFV Search (CMS):

  • Dataset: 138 fb$^{-1}$ of $pp$ collision data.
  • Channels: Searched for $Z \to e\mu$, $Z \to e\tau$, $Z \to \mu\tau$, and heavy $Z' \to e\mu$.
  • Technique: Signal extraction relied on the invariant mass of the dilepton system. For channels involving $\tau$ leptons (where neutrinos degrade mass resolution), a Boosted Decision Tree (BDT) was used as the primary discriminant.
  • Limits: Set 95% Confidence Level (CL) upper limits on branching fractions and production cross-sections.

• $W$-Boson Angular Coefficients (ATLAS):

  • Dataset: 338 pb$^{-1}$ of dedicated low pile-up data to improve hadronic recoil reconstruction.
  • Technique: Measured the full set of eight angular coefficients ($A_i$) describing the lepton decay angles. These coefficients encode the helicity structure of the process.
  • Analysis: A profile likelihood fit was used to extract coefficients in bins of the $W$-boson transverse momentum ($p_T^W$).

• Triple-Differential $Z$+jet Measurement (CMS):

  • Dataset: 138 fb$^{-1}$ in the dimuon final state.
  • Observables: Measured the cross-section differentially in three variables:
    1. $p_T^Z$: Transverse momentum of the $Z$ boson.
    2. $y^*$: Half the rapidity separation between the $Z$ and the leading jet (probes scattering angle).
    3. $y_b$: Boost of the $Z$+jet system (probes parton momentum fractions).
  • Technique: Unfolded simultaneously in all three observables to correct for detector effects.

• Boosted $W$ Jet Mass and $m_W$ Extraction (CMS):

  • Dataset: Full Run 2 dataset (138 fb$^{-1}$).
  • Selection: Focused on highly boosted $W$ bosons ($p_T > 650$ GeV) decaying hadronically, reconstructed as single large-radius jets.
  • Technique: Used soft-drop grooming to remove soft, wide-angle radiation and improve mass resolution. Jet substructure (two-prong topology) was used to suppress QCD background.
  • Extraction: The $W$ mass was extracted from the measured jet mass distribution using a maximum-likelihood approach.

3. Key Contributions and Results

A. Charged Lepton Flavour Violation (CLFV)

• Result: No significant deviation from the SM was observed.
• Limits Set:
  • $\mathcal{B}(Z \to e\mu) < 1.9 \times 10^{-7}$ (The most stringent direct constraint to date).
  • $\mathcal{B}(Z \to e\tau) < 1.38 \times 10^{-5}$.
  • $\mathcal{B}(Z \to \mu\tau) < 1.20 \times 10^{-5}$.
• Significance: These limits significantly constrain BSM scenarios predicting CLFV. The sensitivity is currently limited by the available data sample size.

B. $W$-Boson Angular Coefficients

• Result: Several coefficients (specifically $A_0$ and $A_{2-4}$) were found to be significantly non-zero, confirming sensitivity to QCD dynamics.
• Comparison: Results showed overall good agreement with state-of-the-art NNLO QCD predictions including resummation effects.
• Significance: This is the first measurement of the full set of angular coefficients in $pp$ collisions, providing direct information on $W$-boson polarization.

C. Triple-Differential $Z$+jet Production

• Result: The cross-section was measured up to $p_T^Z = 1$ TeV with experimental uncertainties of 1.5%–5% in the central phase space.
• Comparison: Data agreed well with NNLO QCD predictions supplemented with electroweak and non-perturbative corrections.
• Significance: The triple-differential approach provides stronger constraints on PDFs than inclusive or single-differential measurements by probing the kinematics of the underlying $2 \to 2$ scattering process more granularly.

D. Jet Mass and $W$ Boson Mass Extraction

• Result: The jet mass distribution was well-described by Monte Carlo generators including higher-order corrections.
• Mass Extraction: A $W$ boson mass of $m_W = 80.77 \pm 0.57$ GeV was extracted from the fully hadronic final state.
• Significance: This represents the first determination of $m_W$ in an all-jets final state at a hadron collider, demonstrating the viability of jet substructure techniques for precision measurements in complex environments.

4. Significance and Outlook

The collective results highlight a shift toward multi-differential precision measurements enabled by the large Run 2 datasets.

• Theoretical Validation: The agreement with NNLO predictions validates current theoretical frameworks but also provides data to refine Monte Carlo modeling and theoretical calculations where small discrepancies exist.
• PDF Constraints: The enhanced sensitivity to parton distribution functions, particularly through the triple-differential $Z$+jet measurement, is crucial for reducing uncertainties in future LHC physics.
• Future Prospects:
  • Run 3 and HL-LHC: Larger datasets will further reduce statistical uncertainties and extend kinematic reach.
  • Low Pile-up Data: Dedicated low pile-up runs (expected ~1 fb$^{-1}$) at the end of Run 3 are identified as crucial for measurements currently limited by the statistical precision of low pile-up samples (such as the $W$ angular coefficient measurement).

In conclusion, these measurements demonstrate that precision studies of $W$ and $Z$ bosons, combined with advanced experimental techniques (like jet substructure and low pile-up data), serve as stringent tests of the Standard Model and powerful tools for probing the limits of current theoretical understanding.