Measurements of $t\bar{t}$ in association with charm quarks at 13 TeV with the ATLAS experiment

Using the full Run 2 dataset at 13 TeV, the ATLAS Collaboration performed its first measurement of the inclusive cross-section for top-quark pair production in association with charm quarks, finding that while the results largely agree with various simulation predictions, all models underpredict the observed values.

The Gist

Imagine the Large Hadron Collider (LHC) as the world's most powerful particle smasher. When scientists crash protons together at nearly the speed of light, they create a chaotic explosion of new particles, much like smashing two watches together and watching the gears, springs, and glass fly everywhere.

Most of the time, physicists are looking for the "rare gems" in this debris—exotic particles that might reveal new laws of physics. However, there is a very common, messy background noise that makes finding these gems difficult: Top quark pairs.

The Problem: The "Top Quark" Traffic Jam

Top quarks are the heaviest known elementary particles. When they are produced in pairs (called $t\bar{t}$), they almost always decay into other particles. Sometimes, this process accidentally creates extra heavy particles called charm quarks or bottom quarks.

Think of a top quark pair event as a busy highway. Usually, you expect to see just the main cars (the top quarks). But sometimes, the highway gets clogged with extra delivery trucks (charm quarks). These trucks are a nuisance because they look very similar to the rare "gems" scientists are trying to find (like the Higgs boson). If you don't know exactly how many trucks are usually on the road, you can't tell if a new truck is just normal traffic or a special delivery.

The Mission: Counting the "Charm" Trucks

This paper describes the first time the ATLAS experiment team has tried to count exactly how many charm quarks appear alongside top quark pairs.

Before this, scientists had good maps (theoretical predictions) for how often top quarks appear with bottom quarks, but they had very vague guesses for charm quarks. It was like trying to navigate a city with a perfect map for the main roads but no map for the side streets.

The Detective Work: The "Flavor-Tagging" Goggles

To solve this, the team needed a way to tell the difference between the different types of "trucks" (jets of particles) flying out of the collision.

• The Challenge: Standard tools are great at spotting bottom quarks but terrible at spotting charm quarks.
• The Solution: The team built a custom "flavor-tagging" algorithm. Imagine putting on a pair of high-tech goggles that can instantly label every particle jet as "Light," "Charm," or "Bottom" with high confidence. This allowed them to sort the debris into specific piles:
  1. Events with two or more charm jets.
  2. Events with exactly one charm jet.

The Experiment: Sorting the Debris

The team analyzed a massive amount of data collected between 2015 and 2018 (140 "inverse femtobarns" of data, which is a fancy way of saying "a huge pile of collisions"). They looked for specific patterns where top quarks decayed into electrons or muons (lighter cousins of electrons) and then checked the remaining debris for those charm tags.

They set up a "control room" with different zones:

• Signal Regions: Where they expected to find the charm-heavy events.
• Control Regions: Where they knew not to find charm, just to make sure their background noise estimates were correct.

The Results: The Map Was Close, But Off

After crunching the numbers, the team found:

1. They found the charm: They successfully measured the rate of top quark pairs appearing with charm quarks for the first time.
2. The predictions were close, but low: The theoretical models (the "maps") predicted how often this happens, and they were in the right ballpark. However, every single model predicted fewer events than what was actually observed.
   • Think of it like a weather forecast that says "there's a 20% chance of rain," but it actually rains 30% of the time. The forecast isn't wrong about that it rains, but it underestimates how much.

The measured "cross-section" (a measure of how likely the event is to happen) was:

• Top + 2 Charm: 1.28 picobarns.
• Top + 1 Charm: 6.4 picobarns.

Why This Matters

This isn't just about counting particles; it's about cleaning up the noise. Because these "charm-heavy" top quark events are a major source of background noise for other rare discoveries, having an accurate count helps physicists filter out the fake signals.

The paper concludes that while our current computer simulations are doing a decent job, they are consistently underestimating the number of charm quarks produced. This tells the theorists: "Your maps need to be updated; there are more charm trucks on the highway than you thought."

In short: The ATLAS team used custom software to count how often heavy "charm" particles appear with top quarks. They found that current theories are slightly too pessimistic, predicting fewer events than reality actually shows. This new data will help refine the models used to search for even rarer physics in the future.

Technical Summary

Technical Summary: Measurements of $t\bar{t}$ in Association with Charm Quarks at 13 TeV with the ATLAS Experiment

Problem and Motivation
Top-quark pair production ($t\bar{t}$) accompanied by additional heavy-flavour jets constitutes a significant irreducible background for numerous rare Standard Model (SM) processes, such as $t\bar{t}H$ production with $H \to b\bar{b}$ decays and four-top quark production. While theoretical computations for $t\bar{t} + b\bar{b}$ exist at next-to-leading order (NLO) accuracy in quantum chromodynamics (QCD), uncertainties regarding renormalisation and factorisation scales remain substantial. Crucially, no dedicated NLO computations are currently available for $t\bar{t} + c\bar{c}$ production. This theoretical gap necessitates experimental measurements to refine the understanding of these final states, where additional heavy-flavour jets arise from gluon splitting into $b\bar{b}$ or $c\bar{c}$ pairs, or from initial-state radiation.

Methodology
This analysis utilizes the full Run 2 proton–proton collision dataset collected by the ATLAS experiment at $\sqrt{s} = 13$ TeV between 2015 and 2018, corresponding to an integrated luminosity of 140 fb$^{-1}$. The measurement targets $t\bar{t}$ events containing one or two charged leptons ($e$ or $\mu$) and at least one additional jet.

• Simulation and Modelling: Signal and background processes are modelled using Monte Carlo (MC) simulations. Inclusive $t\bar{t} + \ge 1c$ and $t\bar{t} + \text{light}$ processes are simulated using the five-flavor scheme (5FS) with POWHEG BOX 2 interfaced to PYTHIA 8 for parton showering and hadronisation. $t\bar{t} + b\bar{b}$ processes utilize a four-flavor scheme (4FS) matrix element approach. Events are categorized at the stable particle level into four distinct groups: $t\bar{t} + \ge 2c$, $t\bar{t} + 1c$, $t\bar{t} + \ge 2b$, and $t\bar{t} + \text{light}$.
• Flavour-Tagging: A custom "b/c-tagger" algorithm was developed to simultaneously identify $b$-jets and $c$-jets, as standard ATLAS algorithms lack dedicated $c$-tagging working points. The algorithm outputs a two-dimensional discriminant defining five bins: two for $c$-jets (at 11% and 22% efficiency), two for $b$-jets (at 60% and 70% efficiency), and one for untagged jets.
• Event Selection and Fitting: The analysis employs single-electron and single-muon triggers to select events with one or two leptons. The single-lepton channel requires $\ge 5$ jets, while the dilepton channel requires $\ge 3$ jets (with at least three passing specific tagging criteria). The 19 orthogonal control regions (CRs) and signal regions (SRs) defined by the b/c-tagger bins are used to extract signal strengths via a profile likelihood fit. Systematic uncertainties, including those related to modelling, the flavour-tagging algorithm, and detector effects, are treated as nuisance parameters.

Key Contributions
This work presents the first measurement of the inclusive cross-section for $t\bar{t}$ production in association with charm quarks by the ATLAS Collaboration. The primary contribution is the simultaneous extraction of separate fiducial cross-sections for:

1. $t\bar{t} + \ge 2c$ (events with at least two $c$-jets, primarily targeting $t\bar{t} + c\bar{c}$).
2. $t\bar{t} + 1c$ (events with exactly one additional $c$-jet, originating from $t\bar{t} + 1c$, $t\bar{t} + c\bar{c}$ with one jet outside acceptance, or $t\bar{t} + c\bar{c}$ where jets are clustered).

Results
The analysis demonstrates good agreement between data and simulation, with a fit compatibility of 98%. The measured fiducial cross-sections are:

• $\sigma_{\text{fid}}(t\bar{t} + \ge 2c) = 1.28^{+0.27}_{-0.24}$ pb
• $\sigma_{\text{fid}}(t\bar{t} + 1c) = 6.4^{+1.0}_{-0.9}$ pb

The dominant sources of uncertainty are the modelling of $t\bar{t} + \ge 1c$, $t\bar{t} + \ge 1b$, and $t\bar{t} + \text{light}$ processes (specifically NLO matching and parton showering), uncertainties in the b/c-tagger performance, and data statistics.

When compared to various NLO+PS predictions from inclusive $t\bar{t} + \text{jets}$ and $t\bar{t} + b\bar{b}$ simulations:

• All theoretical predictions underpredict the observed values.
• The POWHEG BOX 2 + PYTHIA 8 predictions agree with the measurement within 1.1 standard deviations when considering scale and PDF variations.
• POWHEG BOX 2 + HERWIG 7 and MADGRAPH5_AMC@NLO + HERWIG 7 predictions show agreement within 1.2 to 2.0 standard deviations.

Additionally, the ratios of $t\bar{t} + \ge 2c$ and $t\bar{t} + 1c$ cross-sections to the total inclusive $t\bar{t} + \text{jets}$ cross-section were measured in both fiducial and inclusive volumes, finding consistency with NLO+PS simulations at a level similar to the absolute cross-section measurements.

Significance
The paper claims significance primarily through the provision of the first experimental constraints on $t\bar{t} + \text{charm}$ production cross-sections. These measurements address a gap in theoretical calculations (specifically the lack of dedicated $t\bar{t} + c\bar{c}$ computations) and improve the understanding of heavy-flavour jet backgrounds. While the results are largely consistent with existing simulation models, the observation that all models underpredict the data highlights areas for potential refinement in QCD modelling, particularly regarding gluon splitting into $c\bar{c}$ pairs. The precision of the measurement is currently limited by modelling uncertainties and the statistical power of the dataset.