Inclusive top cross sections in ATLAS

The ATLAS collaboration reports inclusive cross-section measurements for single-top and $t\overline{t}$ production at various LHC center-of-mass energies, along with derived observables like $V_{tb}$ and nuclear modification factors, all of which show good agreement with Standard Model predictions.

The Gist

Imagine the Large Hadron Collider (LHC) as the world's most powerful particle smasher. Inside, it smashes protons together at incredible speeds, creating a chaotic storm of energy. In this storm, the top quark is the "heavyweight champion" of the particle world. It is the heaviest elementary particle we know, and because it's so heavy, it's like a rare, giant fish in a very crowded ocean.

This paper is a report card from the ATLAS experiment, one of the giant detectors at the LHC. The scientists are checking their math by counting how many of these "heavyweight fish" they catch and comparing their numbers to the "Standard Model" (the official rulebook of physics).

Here is a breakdown of what they found, using simple analogies:

1. The Two Ways to Catch Top Quarks

The paper looks at two main ways these heavy particles appear:

• The "Double Trouble" (Top-Antitop pairs): Usually, the strong force of nature creates top quarks in pairs (a top and an anti-top), like a dance couple. This is the most common way they appear.
• The "Solo Act" (Single Top): Sometimes, the weak force creates just one top quark on its own. This is rarer and happens in two specific "channels" (ways of interacting):
  • The t-channel: Like a billiard ball hitting another and knocking a third one out.
  • The tW channel: Like a top quark being born while holding hands with a W boson (another particle).

2. The Main Goal: Counting the Catch

The scientists didn't just look at the data; they counted the "cross-section." Think of a cross-section not as a physical slice, but as a target size. If a particle has a large cross-section, it's an easy target to hit. If it's small, it's hard to catch.

The team measured these target sizes at different energy levels (how hard they smashed the particles):

• 13 TeV and 13.6 TeV: The main, high-energy runs.
• 5.02 TeV: A special, lower-energy run with very few "background" particles (like a quiet room vs. a noisy party).
• 8.16 TeV (Proton-Lead): Smashing protons into heavy lead nuclei to see how the "crowded" environment of a heavy atom affects the creation of top quarks.

3. The Results: The Rulebook Holds Up

In every single case, the scientists compared their actual counts to the predictions made by the Standard Model (the rulebook).

• The Verdict: The numbers matched almost perfectly.
• The Analogy: Imagine you predict that a specific vending machine will dispense exactly 100 chocolate bars if you put in $100. You try it 10 times, and every time you get between 99 and 101 bars. The machine is working exactly as the manual says it should.

4. Specific Measurements (The "Side Quests")

While counting the main catch, the scientists also measured some interesting side details:

• The "Vtb" Element: The top quark is connected to a "mixing matrix" (a kind of cosmic recipe book) that tells us how particles change flavors. The scientists measured this specific ingredient (called $V_{tb}$) and found it to be exactly what the recipe predicted (a value of 1).
• The Ratios: They compared how often they caught a "top" versus an "anti-top." It's like checking if a coin is fair. They found the ratio was exactly what physics expected.
• The Heavy-Ion Test: In the proton-lead collisions, they checked if the heavy lead nucleus acted like a "traffic jam" for the particles. They calculated a "nuclear modification factor." The result was 1.09, which is very close to 1. This means the heavy lead didn't significantly change the rules of the game; the top quarks behaved normally even in the crowded environment.

5. The Tools They Used

To get these numbers, the scientists had to be very clever:

• Filtering the Noise: The collision data is messy. They used "Boosted Decision Trees" (a type of smart computer algorithm) to act like a bouncer at a club, letting only the "real" top quark events in and kicking out the background noise.
• Fitting the Curve: They used statistical "fits" to squeeze the most accurate number out of the data, accounting for things like how well their detectors measure energy (like checking if a scale is slightly off).

Summary

The paper is essentially a confirmation that our current understanding of the universe is solid. The ATLAS team caught thousands of the heaviest known particles, measured how often they appeared in different scenarios, and found that everything matches the Standard Model predictions.

There are no "new physics" discoveries here (like finding a particle that breaks the rules). Instead, it's a victory lap for the current theory, proving that our "rulebook" is still accurate even when we look at the universe with extreme precision.

Technical Summary

Technical Summary: Inclusive Top Cross Sections in ATLAS

Problem and Scope
This report presents a comprehensive set of inclusive cross-section measurements for top quark production performed by the ATLAS collaboration at the Large Hadron Collider (LHC). The study addresses the need for precision tests of the Standard Model (SM) by measuring top quark observables at next-to-next-to-leading-order (NNLO) precision in Quantum Chromodynamics (QCD). The analysis covers two dominant production modes: top-antitop ($t\bar{t}$) pair production via the strong interaction, and single-top production via the electroweak interaction. The measurements span multiple center-of-mass energies ($\sqrt{s} = 5.02, 8.16, 13,$ and $13.6$ TeV) and collision systems ($pp$ and $p$+Pb). Beyond nominal cross-sections, the report investigates specific observables including the $|V_{tb}|$ element of the Cabibbo-Kobayashi-Maskawa (CKM) matrix, cross-section ratios ($tq$ vs. $\bar{t}q$, $t\bar{t}$ vs. $Z \to \ell\ell$), and the nuclear modification factor in heavy-ion collisions.

Methodology
The analysis utilizes data from ATLAS Run 2 (13 TeV, 140 fb$^{-1}$; 5.02 TeV, 255 pb$^{-1}$) and Run 3 (13.6 TeV, 29 fb$^{-1}$), as well as proton-lead ($p$+Pb) collision data at $\sqrt{s_{NN}} = 8.16$ TeV (165 nb$^{-1}$).

• Single-Top ($tW$ channel, 13 TeV): Selected in the dileptonic channel ($e^\pm\mu^\mp$) with at least one $b$-tagged jet. Events are categorized into three orthogonal signal regions based on jet multiplicity ($1j1b, 2j1b, 2j2b$). A Boosted Decision Tree (BDT) distinguishes signal from the dominant $t\bar{t}$ background. A binned profile likelihood fit is applied to the BDT response distribution within a restricted range to mitigate double-counting uncertainties between single-top and $t\bar{t}$ samples.
• Single-Top ($t$-channel, 13 TeV): Selected in the lepton+jets channel with exactly one lepton, two jets (one $b$-tagged), and cuts on missing transverse momentum ($E_T^{miss}$) and $W$ transverse mass ($m_T(W)$). Signal regions are defined by lepton charge ($\ell^+$ and $\ell^-$). A neural network ($D_{nn}$) combining kinematic observables separates signal from background. A profile likelihood fit extracts cross-sections for $tq$ and $\bar{t}q$ separately.
• Single-Top ($t$-channel, 5.02 TeV): Utilizes a low pileup environment ($\langle \mu \rangle \approx 2$) to provide an independent test of the SM. Selection criteria mirror the 13 TeV analysis. Uncertainties are estimated using the 5.02 TeV sample or extrapolated from 13 TeV data.
• Top-Antitop ($t\bar{t}$, 13.6 TeV): Measures inclusive $t\bar{t}$ and $Z \to \ell\ell$ cross-sections and their ratio ($R_{t\bar{t}/Z}$). Selection requires two oppositely charged leptons and one or two $b$-jets for $t\bar{t}$, and same-flavor lepton pairs with invariant mass $66 < m_{\ell\ell} < 116$ GeV for $Z$. A profile likelihood fit is applied to event yields across four signal regions.
• Top-Antitop ($p$+Pb, 8.16 TeV): Defines dileptonic and semileptonic signal regions. Dileptonic events require two oppositely charged leptons and at least two jets (one $b$-tagged), excluding the $Z$-boson mass window. Semileptonic events require one lepton and at least four jets. Signal yields are extracted via a profile likelihood fit to the scalar sum of transverse momenta ($H_T^{\ell,j}$).

Systematic uncertainties are treated as nuisance parameters in the fits. Dominant uncertainties vary by channel, including $t\bar{t}$ modeling, Jet Energy Scale (JES), $E_T^{miss}$ reconstruction, and luminosity.

Key Results
All measured cross-sections are compared to SM predictions calculated at (N)NLO in QCD.

• $tW$ Production (13 TeV): Measured $\sigma_{tW} = 75 \pm 1(\text{stat}) +15_{-14}(\text{syst}) \pm 1(\text{lumi})$ pb, consistent with the SM prediction of $79.3^{+2.9}_{-2.8}$ pb. The extracted $|f_{LV}V_{tb}| = 0.97 \pm 0.10$ agrees with the SM expectation of unity.
• $t$-channel Production (13 TeV): Measured $\sigma(tq) = 137 \pm 8$ pb and $\sigma(\bar{t}q) = 84^{+6}_{-5}$ pb. These align with SM predictions of $134.2^{+2.6}_{-1.7}$ pb and $80.0^{+6}_{-5}$ pb, respectively. The ratio $R_t = \sigma(tq)/\sigma(\bar{t}q) = 1.636^{+0.036}_{-0.034}$ is reported, and $|f_{LV}V_{tb}| = 1.015 \pm 0.031$.
• $t$-channel Production (5.02 TeV): Measured $\sigma(tq) = 19.8^{+3.9}_{-3.1}(\text{stat}) +2.9_{-2.2}(\text{syst})$ pb and $\sigma(\bar{t}q) = 7.3^{+3.2}_{-2.1}(\text{stat}) +2.8_{-1.5}(\text{syst})$ pb. While consistent with SM predictions, uncertainties are larger (up to 58% relative) due to limited statistics.
• $t\bar{t}$ Production (13.6 TeV): Measured $\sigma_{t\bar{t}} = 850 \pm 3(\text{stat}) \pm 18(\text{syst}) \pm 20(\text{lumi})$ pb and $\sigma_{Z\to\ell\ell} = 744 \pm 11(\text{stat}+\text{syst}) \pm 16(\text{lumi})$ pb. The ratio $R_{t\bar{t}/Z} = 1.145 \pm 0.003(\text{stat}) \pm 0.021(\text{syst}) \pm 0.002(\text{lumi})$ is consistent with the SM prediction within one standard deviation.
• $t\bar{t}$ in $p$+Pb (8.16 TeV): Measured inclusive cross-section $\sigma_{t\bar{t}} = 58.1 \pm 2.0(\text{stat}) +4.8_{-4.4}(\text{syst})$ nb. The nuclear modification factor $R_{pA} = 1.090 \pm 0.039(\text{stat}) +0.094_{-0.087}(\text{syst})$ is consistent with the SM prediction of unity.

Significance and Claims
The paper claims that these results provide stringent tests of the Standard Model, specifically probing perturbative QCD limits at NNLO precision. The measurements serve to constrain Monte Carlo generator parameters, thereby improving the modeling of SM backgrounds involving top quarks. The report emphasizes that all presented results, including cross-sections, ratios, and the $|V_{tb}|$ element, are in good agreement with SM predictions. The inclusion of the $t\bar{t}$ to $Z$ ratio and the nuclear modification factor highlights the capability of these measurements to constrain Parton Distribution Functions (PDFs), particularly the gluon-to-quark ratio and nuclear PDFs in heavy-ion collisions. The consistency across different collision energies and systems reinforces the robustness of the SM description of top quark production.