Measurements of the production of W$^{\pm}$ and Z$^0$ bosons in pp collisions at $\sqrt{s} = 13$ TeV

This paper presents ALICE measurements of W$^{\pm}$ and Z$^0$ boson production cross sections in pp collisions at $\sqrt{s} = 13$ TeV via their electronic decay channels, comparing the results with perturbative QCD calculations and reporting the first LHC observation of W$^{\pm}$ production and associated hadrons as a function of charged-particle multiplicity.

The Gist

Imagine the Large Hadron Collider (LHC) as the world's most powerful particle smasher. Inside its giant ring, scientists crash protons (tiny building blocks of matter) together at speeds close to the speed of light. When these protons collide, they create a chaotic explosion of new particles, much like smashing two pocket watches together and watching the gears, springs, and glass fly out in every direction.

This paper from the ALICE collaboration is a report on what happens when they smash these protons together at a record-breaking energy level (13 TeV). Specifically, they are hunting for two very special, heavy "ghost" particles: the W boson and the Z boson.

Here is the breakdown of their findings, explained with some everyday analogies.

1. The Ghost Hunters: W and Z Bosons

Think of the W and Z bosons as the "heavyweights" of the particle world. They are so massive and unstable that they vanish almost instantly after being created, turning into other particles.

• The Z boson is like a shy ghost that splits into two electrons (a positive and a negative one) and disappears.
• The W boson is a bit more dramatic; it turns into an electron and a "neutrino" (a ghostly particle that barely interacts with anything).

Because these bosons don't hang around, the ALICE team couldn't see them directly. Instead, they acted like detectives looking for footprints. They looked for the specific electrons left behind by the Z boson and the specific electron patterns left by the W boson.

2. The Detective Work: Finding the Clues

To find these footprints, the scientists used a massive detector called ALICE, which acts like a high-speed, 3D camera surrounding the collision point.

• The Filter: They had to ignore billions of ordinary particles (like pions and protons) that are just "noise" in the background. They used special filters to spot only the high-energy electrons that looked like they came from a W or Z boson.
• The Result: They successfully counted how many W and Z bosons were created. They found that the number of these particles matched the predictions of our current best theories (called Quantum Chromodynamics or QCD). It's like checking a weather forecast and finding that the rain fell exactly where the models said it would. This confirms that our understanding of how the universe works at a fundamental level is solid.

3. The Big Mystery: The "Party Size" Effect

The most exciting part of this paper isn't just counting the bosons; it's looking at how many other particles are created alongside them.

Imagine a party.

• Scenario A (Low Multiplicity): A quiet dinner party with just a few people.
• Scenario B (High Multiplicity): A massive, raucous concert with thousands of people.

In particle physics, "multiplicity" is just a fancy word for how many particles are created in a single crash. The scientists asked a simple question: If we have a "loud" crash (many particles), does the production of W bosons increase in the same way?

They measured two things:

1. The W Bosons themselves: These are the "VIPs" of the crash.
2. The "Associated Hadrons": These are the "crowd" of other particles created in the same crash, specifically those flying in the opposite direction of the W boson.

The Surprising Discovery

• The VIPs (W Bosons): As the party got louder (more particles created), the number of W bosons increased in a straight, linear line. If you double the crowd size, you get double the W bosons. This makes sense because W bosons are "colorless" (they don't feel the strong nuclear force that binds quarks together). They are like independent guests who arrive and leave without getting involved in the group hugging and dancing.
• The Crowd (Associated Hadrons): However, the "crowd" particles behaved differently. As the party got louder, the number of these particles didn't just double; it exploded faster than linear. A small increase in the "loudness" of the crash led to a huge surge in these particles.

4. Why Does This Matter? (The "Color Reconnection" Analogy)

Why did the crowd grow so fast? The paper suggests a mechanism called Color Reconnection.

Think of the particles inside the proton as people holding hands with colored ribbons (representing "color charge").

• In a normal crash, people hold hands with their immediate neighbors.
• In a "Color Reconnection" scenario, when the crash is very crowded, people from different groups let go of their original ribbons and grab onto new ribbons from strangers to make the whole system more efficient. This creates a tangled web that produces way more particles than expected.

The W bosons, being "colorless," don't have ribbons to grab, so they don't get caught up in this tangle. They just do their own thing. But the other particles (hadrons) get swept up in this reconnection, causing that "faster-than-linear" explosion.

5. The "Autocorrelation" Twist

The paper also considers a simpler explanation: Self-Reference.
Imagine you are counting how many people are at a party by counting the number of people you know. If you are the host, and you invite more people, your count goes up. But if you are just a guest, your count might not change as much.
In the experiment, the "multiplicity" (the total number of particles) is measured using the same particles that are being studied. This creates a mathematical "echo" or autocorrelation. The paper suggests that while the "Color Reconnection" theory is strong, this self-referencing effect might also be making the numbers look bigger than they really are.

The Bottom Line

This paper is a victory lap for our current understanding of physics.

1. We are right: The number of W and Z bosons created matches our complex math models perfectly.
2. We found a new pattern: In small, high-energy crashes, the "crowd" of particles grows much faster than the "VIPs" (W bosons).
3. The mystery deepens: This suggests that in these tiny, high-energy collisions, the particles are interacting in complex ways (like the Color Reconnection) that we are still learning to fully understand.

It's like realizing that in a massive crowd, the people holding hands (the hadrons) create a chain reaction that grows exponentially, while the people walking alone (the W bosons) just keep walking at a steady pace. This helps scientists understand how the "soup" of the early universe behaved right after the Big Bang.

Technical Summary

1. Problem and Motivation

The primary goal of this research is to investigate the production mechanisms of electroweak bosons ($W^\pm$ and $Z^0$) in proton-proton (pp) collisions at the Large Hadron Collider (LHC) and to understand their relationship with the charged-particle multiplicity.

• Context: In high-energy heavy-ion collisions, the Quark-Gluon Plasma (QGP) is formed, characterized by strong suppression of high-$p_T$ particles and azimuthal anisotropy. However, similar "collective-like" behaviors (e.g., non-zero elliptic flow $v_2$) have been observed in high-multiplicity small systems (pp, p-A, d-A).
• The Debate: It remains unclear whether these effects in small systems arise from:
  1. Final-state interactions (hydrodynamic evolution of a medium).
  2. Initial-state effects such as Multi-Parton Interactions (MPI) and Color Reconnection (CR).
  3. Autocorrelations: Artificial correlations between the measured particle and the event multiplicity estimator.
• The Probe: Electroweak bosons ($W^\pm, Z^0$) are ideal probes because they are produced via the Drell-Yan process, are colorless, and do not interact via the strong force. Therefore, they are expected to be insensitive to final-state effects and Color Reconnection. Comparing their multiplicity dependence against that of hadrons allows physicists to disentangle MPI/CR effects from autocorrelations.

2. Methodology

The analysis utilizes pp collision data recorded by the ALICE detector at a center-of-mass energy of $\sqrt{s} = 13$ TeV (collected from 2016–2018).

• Data Sample: The analysis uses a sample of $\approx 60$ million events triggered by the Electromagnetic Calorimeter (EMCal) with an integrated luminosity of $7.8 \text{ pb}^{-1}$.
• Detector Setup:
  • Tracking: Inner Tracking System (ITS) and Time Projection Chamber (TPC) for charged particle reconstruction.
  • Calorimetry: EMCal for electron energy measurement and triggering.
  • Multiplicity Estimation: Charged-particle multiplicity is estimated using tracklets in the Silicon Pixel Detector (SPD) within $|\eta| < 1$.
• Reconstruction Strategy:
  • $Z^0$ Bosons: Reconstructed via the dielectron decay channel ($Z^0 \to e^+e^-$). The invariant mass of the pair is required to be in the range $60 < m_{ee} < 108 \text{ GeV}/c^2$. One electron must satisfy tight kinematic cuts ($30 < p_T < 60 \text{ GeV}/c$, $|y| < 0.6$), while the partner has looser requirements.
  • $W^\pm$ Bosons: Reconstructed via the single electron decay channel ($W^\pm \to e^\pm \nu$). Since the neutrino is undetected, the signal is extracted from the transverse momentum ($p_T$) distribution of isolated electrons.
• Particle Identification (PID): Electrons are identified using:
  • Specific ionization energy loss ($dE/dx$) in the TPC.
  • Energy-to-momentum ratio ($E/p$) in the EMCal.
  • Shower shape variables ($\sigma^2_{long}$).
  • Isolation: A relative isolation energy $E_{iso} < 0.1$ within a cone $R=0.3$ is applied to suppress background from heavy-flavor decays and QCD jets.
• Background Subtraction:
  • $Z^0$: Background is estimated using like-sign ($e^+e^+$ and $e^-e^-$) pairs.
  • $W^\pm$: Backgrounds from heavy-flavor hadron decays ($c, b$), $Z^0$ decays, photon conversions, and Dalitz decays are estimated using data-driven templates and Monte Carlo simulations (PYTHIA 8, POWHEG) and statistically subtracted.
• Multiplicity Dependence: The yields of $W^\pm$ and associated hadrons are measured as a function of the self-normalized charged-particle multiplicity ($dN_{ch}/d\eta / \langle dN_{ch}/d\eta \rangle$). Associated hadrons are defined as particles with $p_T > 10 \text{ GeV}/c$ azimuthally correlated with the $W^\pm$ electron.

3. Key Contributions

1. First ALICE Measurement: This is the first measurement by ALICE of $W^\pm$ and $Z^0$ production via the (di)electronic decay channel at midrapidity ($|y| < 0.6$) in pp collisions at $\sqrt{s} = 13$ TeV.
2. Multiplicity Dependence of $W^\pm$: The paper presents the first measurement at the LHC of the production of $W^\pm$ bosons and their associated hadrons as a function of charged-particle multiplicity.
3. Comparison with Theory: The results are compared with perturbative QCD (pQCD) calculations using various Parton Distribution Functions (PDFs: CT14NNLO, CT18NLO, NNPDF4.0) and Monte Carlo models (PYTHIA 8) incorporating MPI and Color Reconnection (CR).

4. Results

A. Production Cross Sections

• $Z^0$ Boson: The fiducial production cross section for $Z^0 \to e^+e^-$ (with one electron in $30 < p_T < 60 \text{ GeV}/c$ and $|y| < 0.6$) is measured to be:
  $$\sigma^{\text{fid}}_{Z^0 \to e^+e^-} = 203 \pm 22 (\text{stat.}) \pm 22 (\text{sys.}) \pm 11 (\text{lumi.}) \text{ pb}$$
  This result is consistent with NLO pQCD calculations using POWHEG + PYTHIA 8 and various PDF sets.
• $W^\pm$ Bosons: The $p_T$-differential and $p_T$-integrated production cross sections for electrons from $W^-$ and positrons from $W^+$ are measured in the range $30 < p_T < 60 \text{ GeV}/c$.
  • $d\sigma/dy (W^-) = 0.68 \pm 0.04 (\text{stat.}) \pm 0.09 (\text{sys.}) \pm 0.04 (\text{lumi.}) \text{ nb}$
  • $d\sigma/dy (W^+) = 0.72 \pm 0.05 (\text{stat.}) \pm 0.09 (\text{sys.}) \pm 0.04 (\text{lumi.}) \text{ nb}$
  • The ratio $W^+/W^-$ is consistent with theoretical predictions, showing a slight enhancement of $W^+$ over $W^-$ due to the $u\bar{d}$ vs $d\bar{u}$ production asymmetry.
  • All cross-section measurements agree well with theoretical predictions within uncertainties.

B. Multiplicity Dependence

• $W^\pm$ Yield: The production of $W^\pm$ bosons increases approximately linearly with the charged-particle multiplicity. This confirms the expectation that colorless bosons are not significantly affected by Color Reconnection mechanisms.
• Associated Hadrons: In contrast, the yield of hadrons produced in association with $W^\pm$ (recoil jets) exhibits a faster-than-linear increase with multiplicity, particularly at high multiplicities.
• Interpretation:
  • The linear behavior of $W^\pm$ suggests they are not subject to the same final-state or CR effects that enhance hadron production.
  • The faster-than-linear rise of associated hadrons is qualitatively described by PYTHIA 8 calculations including MPI and CR effects.
  • The study also compares these results with $J/\psi$ production. While midrapidity $J/\psi$ shows a faster-than-linear trend (likely due to autocorrelations with soft particles), forward rapidity $J/\psi$ does not. The linear trend of $W^\pm$ supports the hypothesis that the observed non-linear trends in other probes are driven by autocorrelations (where the probe contributes to the multiplicity estimator) or MPI/CR effects, rather than a universal hydrodynamic medium in small systems.

5. Significance

• Constraint on QCD Models: The measurements provide stringent constraints on Parton Distribution Functions (PDFs) and the modeling of MPI and Color Reconnection in Monte Carlo event generators.
• Understanding Small Systems: The distinct behavior between the linear $W^\pm$ yield and the non-linear associated hadron yield provides crucial evidence that the "collective-like" behavior observed in high-multiplicity pp collisions is likely driven by initial-state effects (MPI/CR) and autocorrelations, rather than the formation of a thermalized QGP medium affecting all particles equally.
• Benchmark for Future Runs: These results serve as a baseline for future high-statistics measurements with the upgraded ALICE detector during LHC Run 3 and Run 4, which will allow for more precise differential studies.