Precision measurement of the muon charge asymmetry from $W$-boson decays in $pp$ collisions at $\sqrt{s}$ = 13 TeV in the forward region

Using 5.1 fb⁻¹ of proton-proton collision data at 13 TeV collected by the LHCb detector, this study presents the most precise measurement to date of the muon charge asymmetry from W-boson decays in the forward region, which aligns excellently with next-to-next-to-leading-order perturbative QCD predictions.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful particle smasher. It takes two beams of protons (tiny building blocks of matter) and smashes them together at nearly the speed of light. When they collide, they create a shower of new particles, including a heavy, short-lived particle called the W boson.

This paper is like a high-precision report card from the LHCb experiment, one of the detectors watching these collisions. Specifically, they are looking at how the W boson decays into a muon (a heavy cousin of the electron) and a neutrino.

Here is the breakdown of what they did and why it matters, using some everyday analogies:

1. The Big Question: Why is there more "Left" than "Right"?

In our everyday world, things usually look the same whether you look at them in a mirror or not. But in the subatomic world, nature has a favorite side.

• The Analogy: Imagine a factory that makes red and blue balls. The factory is made of two types of workers: "Up" workers and "Down" workers. Because the factory has more "Up" workers than "Down" workers, it accidentally produces more red balls than blue balls.
• The Physics: Protons are made of quarks. Specifically, they have two "Up" quarks and one "Down" quark. When protons smash together, the "Up" quarks are more likely to team up to create a W+ boson (which decays into a positive muon), while the "Down" quarks create a W- boson (which decays into a negative muon).
• The Result: Because there are more "Up" quarks, the LHC produces more positive muons than negative ones, especially when they fly off at a specific angle. This difference is called the Charge Asymmetry.

2. The Detective Work: Catching the Muons

The LHCb detector is like a giant, high-speed camera that only looks in one direction (the "forward" region). The scientists looked at 5.1 billion collisions (represented by 5.1 inverse femtobarns of data) collected between 2016 and 2018.

• The Filter: They didn't look at every single muon. They set strict rules:
  • The muon must be fast enough (high momentum).
  • It must fly at a specific angle (between 2.0 and 4.5 on a scale called "pseudorapidity").
  • It must be "clean" (not surrounded by too much debris).
• The Count: After filtering, they counted about 6.3 million positive muons and 4.4 million negative muons.

3. The "Recipe" Check: Testing the Theory

Scientists have a "recipe book" for how these particles should behave, based on a theory called Quantum Chromodynamics (QCD). This recipe relies on something called Parton Distribution Functions (PDFs).

• The Metaphor: Think of a proton not as a solid marble, but as a busy bag of marbles (quarks and gluons) moving around inside. The PDFs are a map that tells you: "If you reach into the bag, what is the chance you'll grab a red marble versus a blue marble?"
• The Problem: For a long time, the map was a bit fuzzy in the "forward" direction (where the LHCb detector looks).
• The Test: The scientists measured the actual ratio of positive to negative muons and compared it to the predictions from the recipe book.

4. The Result: A Perfect Match

The paper reports that their measurement is the most precise ever taken in this specific direction.

• The Outcome: The real-world data matched the theoretical predictions almost perfectly.
• Why it matters: This confirms that our "map" of the proton (the PDFs) is accurate. It tells us exactly how the quarks are distributed inside the proton.
• The Future: If the data had not matched the theory, it would have been a huge discovery, suggesting "New Physics" (something we don't know yet). Since it matched, it means our current understanding of the universe's building blocks is solid, but now we have a much sharper, more detailed map for future experiments.

Summary in One Sentence

The LHCb team acted like super-accurate accountants, counting millions of particle collisions to prove that our current understanding of how protons are built is correct, refining the "map" of the subatomic world with unprecedented precision.

Technical Summary

1. Problem and Motivation

The production of $W$ bosons in proton-proton ($pp$) collisions is a fundamental process for testing the Standard Model and constraining Parton Distribution Functions (PDFs). The proton is composed of two valence $u$ quarks and one valence $d$ quark. Consequently, $W^+$ production (via $u\bar{d}$) is more frequent than $W^-$ production (via $d\bar{u}$) at the Large Hadron Collider (LHC).

This imbalance creates a measurable muon charge asymmetry ($A$) in the pseudorapidity ($\eta_\mu$) distribution of the decay leptons.

• Scientific Goal: Precise measurements of this asymmetry are essential for global PDF fits, particularly for determining the ratio of $u$ and $d$ quark distributions and the light-flavor sea quark components.
• Gap: While ATLAS and CMS have measured this in the central region, the forward region ($2 < \eta < 5$) offers unique sensitivity to PDFs at both small and large Bjorken-$x$ ($10^{-4} < x < 10^{-1}$). Previous LHCb measurements lacked the granularity and precision of the current dataset.

2. Methodology

Data Sample and Detector

• Dataset: Data collected by the LHCb detector during Run 2 (2016, 2017, 2018) at a center-of-mass energy of $\sqrt{s} = 13$ TeV.
• Integrated Luminosity: $5.1 \text{ fb}^{-1}$.
• Kinematic Region: Muons with transverse momentum $25 < p_T < 55$ GeV and pseudorapidity $2.0 < \eta_\mu < 4.5$.
• Detector: LHCb is a single-arm forward spectrometer, optimized for this specific kinematic range.

Event Selection and Reconstruction

• Signal: Reconstructed $W \to \mu\nu$ decays.
• Selection Criteria:
  • Muon momentum $p_\mu < 2$ TeV.
  • Relative momentum uncertainty $< 6\%$.
  • Originating from the primary vertex (PV) with good track-fit quality.
  • Isolation: Scalar sum of $p_T$ of other particles within $\Delta R < 0.5$ must be $< 3$ GeV.
  • Z-veto: Events with secondary muons consistent with $Z \to \mu\mu$ are rejected.
• Yields: Approximately $6.3 \times 10^6$ $W^+$ and $4.4 \times 10^6$ $W^-$ candidates retained, with purities of $\sim 85\%$ and $\sim 80\%$, respectively.

Background Estimation

• Dominant Background: Hadrons misidentified as muons (QCD background).
• Other Backgrounds: Heavy-flavor ($b\bar{b}, c\bar{c}, t\bar{t}$) and electroweak processes ($W \to \tau\nu, Z \to \mu\mu, WW$, etc.).
• Modeling: Backgrounds are estimated using simulated samples calibrated with $Z \to \mu\mu$ data. The ratio of $p_T$ distributions between data and simulation is used to reweight events to match the observed hadronic composition.

Analysis Technique

• Signal Extraction: A binned likelihood fit is performed separately for $W^+$ and $W^-$ in 18 $\eta_\mu$ intervals.
  • Signal and QCD background fractions are free parameters.
  • Electroweak and heavy-flavor fractions are fixed to theory predictions.
  • Statistical uncertainties in templates are handled via the Beeston–Barlow lite prescription.
• Efficiency Corrections:
  • Determined using the tag-and-probe method on $Z \to \mu\mu$ and $\Upsilon(1S) \to \mu\mu$ samples.
  • Factorized into tracking, muon identification (ID), and trigger efficiencies.
  • Corrections are applied as weights in 18 $\eta_\mu$ bins with independent $p_T$ parameterizations.
• Systematic Corrections:
  • Charge Bias: Corrected using the pseudomass method with $Z \to \mu\mu$ data to remove curvature biases.
  • FSR: Final-state radiation corrections applied using Photos.
  • Simulation Weighting: Leading-order Pythia events are weighted to NNLO calculations from DYTurbo to account for higher-order QCD effects.

3. Key Contributions

1. Unprecedented Precision: This represents the most precise determination of the muon charge asymmetry in the forward region to date.
2. Granularity: The measurement utilizes 18 bins in pseudorapidity, offering significantly finer granularity than previous LHCb results.
3. Comprehensive Uncertainty Budget: The analysis provides a complete breakdown of systematic uncertainties (reconstruction, generator modeling, smearing, selection, QCD background, and FSR) and offers the full covariance matrix for future PDF fits.
4. Validation of NNLO QCD: The results serve as a rigorous test of Next-to-Next-to-Leading-Order (NNLO) perturbative QCD predictions in the forward kinematic regime.

4. Results

• Measurement: The charge asymmetry $A(\eta_\mu)$ is measured across the range $2.0 < \eta_\mu < 4.5$.
  • The asymmetry is positive in the lower $\eta$ range (peaking around $\eta \approx 2.6$) and becomes negative at higher $\eta$ (down to $\approx -177 \times 10^{-3}$ at $4.25 < \eta < 4.5$).
  • Values range from approximately $261 \times 10^{-3}$ to $-177 \times 10^{-3}$.
• Comparison with Theory:
  • Results are compared against predictions from Powheg (using CT18 PDFs) and ResBos 2 (using MSHT20, NNPDF40, and CT18 PDFs).
  • Agreement: The measured values show excellent agreement with NNLO QCD predictions.
• Uncertainty Analysis:
  • Experimental uncertainties (statistical + systematic) are comparable in magnitude to the theoretical uncertainties arising from PDF sets (MSHT20, NNPDF40, CT18) and scale variations.
  • This indicates that the measurement is now precise enough to meaningfully constrain and improve global PDF fits.

5. Significance

• PDF Constraints: The high-precision forward data provides critical constraints on the valence quark PDFs and the light-flavor sea in the Bjorken-$x$ range of $10^{-4}$ to $10^{-1}$. This complements central detector measurements (ATLAS/CMS) which probe different $x$ ranges.
• New Physics Searches: Improved PDF knowledge reduces theoretical uncertainties in Standard Model predictions, which is a prerequisite for sensitive searches for New Physics at the LHC.
• Future Impact: The release of the full covariance matrix and FSR corrections allows the global PDF fitting groups (e.g., NNPDF, MSHT, CT) to directly incorporate this dataset, leading to more accurate models of proton structure for future high-energy physics experiments.

In summary, this paper establishes a new benchmark for forward $W$-boson physics, demonstrating that LHCb can deliver precision measurements that rival central detectors in their specific kinematic domain, thereby significantly advancing our understanding of proton structure.