Measurement of the cross-section for the production of a $W$ boson in association with $b$-jets in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector

Using 140 fb$^{-1}$ of 13 TeV proton-proton collision data collected by the ATLAS detector, this paper presents a measurement of the $W+b$-jet production cross-section that achieves a relative precision twice as good as previous results and is consistent with next-to-leading-order QCD predictions.

The Gist

The Big Picture: Catching a Ghost with a Heavy Friend

Imagine the Large Hadron Collider (LHC) as the world's most powerful particle smasher. It fires two beams of protons (tiny particles) at each other at nearly the speed of light. When they crash, they create a chaotic explosion of new particles, like shattering a vase and watching the pieces fly everywhere.

This paper is about a specific type of "shard" the ATLAS detector is looking for: a W boson (a heavy, unstable particle) that is born alongside a b-jet (a spray of particles created by a heavy bottom quark).

Think of the W boson as a "ghost." It decays almost instantly into a lepton (an electron or a muon) and a neutrino. The neutrino is invisible; it slips right through the detector like a ghost through a wall. We know the ghost was there because we see the lepton it left behind and we notice a "missing" amount of energy (the neutrino) in the balance sheet of the crash.

The b-jet is the "heavy friend." Bottom quarks are heavy and live just long enough to travel a tiny bit before decaying. This leaves a distinct "footprint" in the detector that allows scientists to identify them.

The goal of this paper is to count how often this specific duo (the ghost and the heavy friend) appears when protons smash together, and to measure exactly how much "oomph" (momentum) the heavy friend has.

The Setup: A Giant Camera and a Massive Dataset

The ATLAS detector is essentially a giant, 360-degree camera surrounding the collision point. It's layered like an onion:

• The Core: Tracks the paths of charged particles.
• The Middle: Measures the energy of particles that stop there (like electrons and photons).
• The Outer Shell: Catches the muons, which can pass through the inner layers.

The scientists used data collected between 2015 and 2018. This is a massive dataset, equivalent to 140 inverse femtobarns of collisions. To put that in perspective, if the previous measurement at 7 TeV was like taking a photo with a 4-megapixel camera, this new measurement is like taking a photo with a 120-megapixel camera. They have 30 times more data, which makes the picture much sharper.

The Challenge: Finding a Needle in a Haystack

The problem is that the "ghost + heavy friend" event is rare. Most of the time, the proton collisions produce other things:

1. The "Fake" Ghosts: Sometimes, a jet of particles is misidentified as an electron or muon.
2. The "Fake" Heavy Friends: Sometimes, a light quark or a charm quark is misidentified as a bottom quark.
3. The "Real" but Unwanted Guests: Events involving top quarks (which are even heavier) or multiple jets can look very similar to what the scientists want.

The signal (the W boson + b-jet) makes up only about 30% of the events that pass the initial filters. The other 70% are background noise.

The Detective Work: How They Separated the Signal

To find the real signal, the team used two main detective techniques:

1. The Matrix Method (The "Lie Detector" Test)
For the "fake" leptons (where a jet looks like an electron), they used a statistical trick called the Matrix Method. Imagine you have a group of people, some of whom are telling the truth and some are lying.

• You ask them a strict question (the "Tight" criteria).
• You ask them a loose question (the "Anti-Tight" criteria).
• By knowing how often truth-tellers and liars pass each test, you can mathematically solve for exactly how many liars are in the "Tight" group. This allowed them to subtract the fake leptons from their data.

2. The Flavor Fit (The "Fingerprint" Analysis)
For the "fake" b-jets (where a light jet is mistaken for a bottom quark), they looked at the "fingerprint" left by the b-tagging algorithm.

• Real bottom quarks leave a very specific, strong signal in the detector.
• Light quarks leave a weak or different signal.
• The scientists took the distribution of these signals from their data and compared it to what their computer simulations predicted for real b-jets, fake b-jets, and other backgrounds. They adjusted the numbers until the simulation matched the data perfectly. This "fit" told them exactly how many real W+b-jet events they had.

The Results: A Precise Measurement

After cleaning up the data and removing the background noise, they measured the cross-section. In particle physics, the cross-section is basically a measure of "how likely" this event is to happen. It's like measuring the size of a target: a larger cross-section means the target is bigger and easier to hit.

• The Measurement: They found the probability of this event to be 16.6 ± 1.9 picobarns (a picobarn is a tiny unit of area).
• The Comparison: They compared this result to two different computer theories (Sherpa and MGaMC+Py8).
  • The Sherpa theory predicted 16.8 ± 2.3 pb. The measurement matches this almost perfectly.
  • The MGaMC+Py8 theory predicted 13.9 ± 1.3 pb. The measurement is slightly higher than this, by about one standard deviation (a small statistical wiggle room).

Why This Matters

This isn't just about counting particles; it's about testing the rules of the universe.

• Testing the Rules: The Standard Model (our current rulebook for physics) predicts how these particles should behave. By measuring this process with high precision, scientists are checking if the rulebook is correct.
• The "Heavy" Factor: This process involves heavy quarks (bottom quarks). Understanding how they interact with the W boson helps refine our understanding of the strong nuclear force (Quantum Chromodynamics).
• Background for New Physics: The W+b-jet process is a major "background" noise for searching for the Higgs boson or new, unknown particles. To find a new needle in the haystack, you must first know exactly how big the haystack is. This measurement helps sharpen the search for new physics.

The Bottom Line

The ATLAS collaboration has taken a massive dataset from the LHC and used sophisticated statistical tricks to isolate a rare particle interaction. They found that the universe produces W bosons with bottom quarks at a rate that matches our best current theories (specifically the Sherpa model) very closely. The measurement is twice as precise as the previous attempt, thanks to having 30 times more data and better tools. It's a successful confirmation of our current understanding of how heavy quarks behave in high-energy collisions.

Technical Summary

Technical Summary: Measurement of the Cross-section for the Production of a W Boson in Association with b-jets in pp Collisions at √s = 13 TeV with the ATLAS Detector

Problem and Motivation
This paper presents a measurement of the production cross-section for a $W$ boson in association with one or two jets, where at least one jet originates from a $b$-quark ($W + b$-jets). This process is a critical probe of perturbative quantum chromodynamics (pQCD) involving heavy quarks. In the Standard Model, the dominant contribution arises from gluon splitting into a $b\bar{b}$ pair ($W + g(\to b\bar{b})$), while next-to-leading-order (NLO) contributions depend on the treatment of $b$-quark production, specifically distinguishing between the four-flavour number scheme (4FNS) and the five-flavour number scheme (5FNS).

Precise measurements of this cross-section are essential for refining theoretical calculations and validating Monte Carlo (MC) techniques. Furthermore, the $W + b$-jets process constitutes a significant background for Higgs boson production measurements (specifically $WH$ and $ZH$ with $H \to b\bar{b}$) and serves as an irreducible background in searches for physics beyond the Standard Model and in single top-quark production measurements. Previous measurements at the Tevatron and at the LHC (ATLAS at 7 TeV and CMS at 7/8 TeV) have shown varying levels of tension with NLO theoretical predictions, motivating a higher-precision measurement using the full Run 2 dataset.

Methodology
The analysis utilizes proton-proton collision data collected by the ATLAS detector at $\sqrt{s} = 13$ TeV, corresponding to an integrated luminosity of 140 fb$^{-1}$ (2015–2018). The $W$ boson is reconstructed via its leptonic decay ($W \to e\nu$ or $W \to \mu\nu$).

• Event Selection: Candidate events are required to have exactly one high-$p_T$ electron or muon, missing transverse momentum ($E_T^{miss}$) consistent with a neutrino, and exactly one or two reconstructed jets. In the "1j1b" category, the single jet must be $b$-tagged. In the "2j1b" category, exactly one of the two jets must be $b$-tagged. Events with additional $b$-jets or three or more jets are rejected to suppress top-quark backgrounds.
• Object Reconstruction: Electrons and muons are selected with tight identification and isolation criteria. Jets are reconstructed using the anti-$k_t$ algorithm ($R=0.4$) with particle-flow inputs. $b$-tagging is performed using the DL1r deep neural network discriminant at a 60% working point.
• Background Estimation:
  • Multijet Background: Estimated using a data-driven "matrix method" to separate prompt and non-prompt (fake) leptons.
  • $W + c$-jets and $W +$ light-jets: These dominant backgrounds, which mimic the signal kinematics, are estimated using a data-driven "flavour-fit" method. This involves a simultaneous $\chi^2$ fit to the distribution of the $b$-tagging discriminant (DL1r score) in two bins (0–20% and 20–60% efficiency regions) to extract the signal yield and the combined $W +$ other-jets background.
  • Other Backgrounds: Contributions from $t\bar{t}$, single top, diboson, $Z$+jets, and $W \to \tau\nu$ are estimated using fully simulated MC samples (Sherpa, Powheg+Pythia, MadGraph5_aMC@NLO).
• Cross-section Extraction: The measured yields are corrected for detector effects (efficiency, resolution, acceptance) to obtain fiducial cross-sections. An unfolding procedure (iterative Bayesian technique) is applied to correct for bin-to-bin migrations and extrapolate the results to a defined particle-level fiducial region. The results for electron and muon channels are combined using the Best Linear Unbiased Estimate (BLUE) method.

Key Contributions

• Dataset: This is the first measurement of the $W + b$-jets cross-section by ATLAS using the full Run 2 dataset (140 fb$^{-1}$), representing a significant increase in statistics compared to the previous 7 TeV measurement (4.6 fb$^{-1}$).
• Differential Measurement: The paper provides differential cross-sections as a function of the leading $b$-jet transverse momentum ($p_T$) in four bins (25–30, 30–40, 40–60, and 60–140 GeV) for both the 1-jet and 2-jet signal regions.
• Flavour-Fit Technique: The application of the flavour-fit method to simultaneously extract signal and dominant $W +$ light/$c$-jet backgrounds directly from data reduces reliance on theoretical modeling for these specific background components.
• Theoretical Comparison: Results are compared against two NLO theoretical predictions: Sherpa (5FNS) and MadGraph5_aMC@NLO + Pythia (5FNS).

Results
The measured inclusive fiducial cross-section for $W + b$-jets (combined electron and muon channels) is:
$$\sigma_{\text{fid}} = 16.6 \pm 1.9 \text{ pb}$$
This value is consistent with the Sherpa NLO prediction of $16.8 \pm 2.3$ pb. The measurement is approximately one standard deviation higher than the MadGraph5_aMC@NLO + Pythia prediction of $13.9 \pm 1.3$ pb.

The breakdown of the cross-section by jet multiplicity is:

• 1-jet region: $9.1 \pm 0.9$ pb
• 2-jet region: $7.5 \pm 1.1$ pb

The differential cross-sections show good agreement with the Sherpa prediction across all $p_T$ bins. The MGaMC+Py8 FxFx prediction exhibits a systematic deficit of approximately one standard deviation relative to the data.

Uncertainties and Precision
The total uncertainty on the inclusive cross-section is approximately 10%, dominated by systematic uncertainties (primarily $b$-tagging calibration and top-quark background modeling in the 2-jet region). The statistical uncertainty is approximately 1%. The relative precision of this measurement is improved by a factor of two compared to the previous ATLAS measurement at $\sqrt{s} = 7$ TeV. This improvement is attributed to the larger dataset (30 times more data) and improved jet and $b$-tagging performance.

Significance
The paper claims that this measurement provides a stringent test of pQCD in the presence of heavy quarks and offers improved constraints on theoretical calculations and MC modeling. The results are consistent with the Sherpa NLO prediction within uncertainties, while the slight tension with the MGaMC+Py8 FxFx prediction highlights the need for continued refinement of theoretical models. The high precision achieved serves as a valuable input for reducing background uncertainties in Higgs boson coupling measurements and searches for new physics.