Measurements of top quark asymmetries

This paper summarizes the latest experimental results from the ATLAS and CMS Collaborations regarding top quark asymmetries measured at the LHC, which serve to probe subtle differences in top quark and antiquark production predicted by the Standard Model.

The Gist

Imagine the Large Hadron Collider (LHC) as the world's most powerful, high-speed particle factory. Its most famous product? The top quark. It's the heaviest known elementary particle, and the LHC has produced hundreds of millions of them. Because they are so heavy and short-lived, they are like "heavyweights" in a boxing ring that vanish instantly after the bell rings.

Scientists at the LHC (specifically the ATLAS and CMS teams) are trying to understand the rules of the game by watching how these top quarks behave. This paper is a report card on a specific type of behavior: Asymmetry.

Here is the breakdown of what they found, explained with simple analogies.

1. The Core Mystery: The "Mirror" Problem

In a perfect, symmetrical world, if you smash two protons together, the resulting top quarks and their antimatter twins (antiquarks) should behave exactly like mirror images of each other. If the top quark flies slightly to the left, the antiquark should fly slightly to the right with the exact same intensity.

However, the Standard Model (the rulebook of physics) predicts a tiny, subtle crack in this mirror. It says that top quarks might have a slight "preference" to fly in one direction compared to their antimatter twins. This is called Charge Asymmetry.

The Analogy: Imagine a dance floor where couples (proton collisions) spin around. The rulebook says the male dancer (top quark) might take a slightly wider step forward than the female dancer (antiquark) steps backward. It's a tiny difference, but if you watch millions of dances, you can spot the pattern.

2. Why Measure This?

Measuring these tiny differences is hard because of "noise" (systematic uncertainties). It's like trying to hear a whisper in a hurricane.

• The Problem: Usually, when scientists measure things, the "noise" of the equipment and the theory calculations messes up the precision.
• The Solution: Asymmetry is special. Because the "noise" affects the top quark and the antiquark in almost the exact same way, it cancels out when you compare them. It's like weighing two identical suitcases on a shaky scale; if you look at the difference in their weight, the shaking of the scale doesn't matter as much. This allows scientists to test the "rulebook" (Standard Model) with extreme precision.

3. The Three Experiments

A. The Main Event: Top Quark Pairs ($t\bar{t}$)

The teams looked at the most common collisions where a top quark and an antiquark are born together.

• What they found: They confirmed the "whisper." The top quarks do have a slight preference to fly further out than the antiquarks.
• The Result: The ATLAS team measured this with high confidence (4.7 sigma, which is like saying, "We are 99.999% sure this isn't a fluke").
• The Verdict: The data matches the Standard Model perfectly. The "rulebook" is holding up. No new, mysterious physics was found here yet.

B. The "Flashlight" Effect: Top Quarks + Photon ($t\bar{t}\gamma$)

To make the asymmetry easier to see, scientists tried to add a "flashlight" (a photon) to the mix. The idea was that if a photon is shot off early, it might make the asymmetry bigger.

• The Challenge: It's like trying to find a specific needle in a haystack, but the haystack is also on fire. The signal is very weak, and it's hard to tell if the photon came from the initial crash or from a decaying top quark later.
• The Result: Both teams looked at this, but the data was too "fuzzy" (large uncertainties) to say anything definitive. The results were compatible with "no difference," but they couldn't prove or disprove anything new yet.

C. The "Three-Way" Dance: Top Quarks + W Boson ($t\bar{t}W$)

Here, they added a W boson (a heavy particle) to the mix. This makes the final state very complex, with three "leptons" (like electrons) flying out.

• The Challenge: It's like trying to figure out which of three dancers is leading the dance. It's hard to tell which lepton came from which top quark.
• The Result:
  • ATLAS: Saw nothing unusual; it matched the rulebook.
  • CMS: Saw a tiny hint of something interesting (a deviation of about 1 sigma). It's like hearing a faint, strange sound in the music. It's not loud enough to be a new discovery, but it's enough to make scientists say, "Hmm, let's keep an eye on that."

D. The "Angle" Game: Top Quarks + Jet ($t\bar{t}j$)

Finally, they looked at collisions where a third particle (a "jet" of particles) is kicked out. They measured two things:

1. Energy Asymmetry: Do the top quarks have different energy levels depending on the angle?
2. Incline Asymmetry: Do they tilt at different angles?

• The Result: Both teams saw small deviations from zero (around 2 to 2.7 sigma).
• The Catch: While these numbers look exciting, they are still in the "maybe" zone. It's like a coin landing on its edge a few times in a row. It could be a new physics phenomenon, but it could also just be a statistical fluke. More data is needed to know for sure.

The Bottom Line

This paper is a status report from the world's best particle detectives.

• Good News: The Standard Model is still the champion. The tiny asymmetries they predicted are real, and the LHC has finally seen them clearly.
• The Search Continues: They haven't found "New Physics" (like Dark Matter or extra dimensions) yet. The "whispers" they heard were exactly what the old rulebook predicted.
• Future Hope: The "hints" of deviation (like the 2.7 sigma result) are tantalizing. As the LHC collects more data (more "dances"), these whispers might turn into a shout, revealing a crack in the Standard Model that leads to a deeper understanding of the universe.

In short: The LHC is a top quark factory, and so far, the products are coming out exactly as the manual says they should. But the scientists are still looking very closely, hoping to find the one tiny glitch that will rewrite the manual.

Technical Summary

Based on the provided paper, here is a detailed technical summary of the measurements of top quark asymmetries by the ATLAS and CMS Collaborations.

1. Problem Statement and Motivation

The Large Hadron Collider (LHC) has produced hundreds of millions of top quarks, earning it the title of a "top quark factory." However, precision measurements in the top quark sector are increasingly limited by systematic uncertainties from both experimental and theoretical sources.

The paper addresses the need to probe subtle differences between top quark ($t$) and top antiquark ($\bar{t}$) production. The study of asymmetries offers a solution because systematic uncertainties often cancel out when comparing $t$ and $\bar{t}$, as they affect both particles similarly. This approach allows for:

• Testing Standard Model (SM) predictions derived from higher-order Quantum Chromodynamics (QCD).
• Searching for Beyond the Standard Model (BSM) contributions using Effective Field Theory (EFT) approaches.

2. Methodology

The analysis utilizes proton-proton collision data at a center-of-mass energy of $\sqrt{s} = 13$ TeV. The methodology focuses on defining and measuring various asymmetry observables across different production channels:

• Charge Asymmetry ($A_C^{t\bar{t}}$): Defined based on the rapidity difference ($\Delta|y_{t\bar{t}}| = |y_t| - |y_{\bar{t}}|$) between the top quark and antiquark.
  • Definition: $A_C^{t\bar{t}} = \frac{N(\Delta|y_{t\bar{t}}| > 0) - N(\Delta|y_{t\bar{t}}| < 0)}{N(\Delta|y_{t\bar{t}}| > 0) + N(\Delta|y_{t\bar{t}}| < 0)}$.
  • Context: Unlike the Tevatron (proton-antiproton), where asymmetry causes a shift in rapidity, the LHC (proton-proton) manifests asymmetry as a broader rapidity distribution for top quarks compared to antiquarks.
• Associated Production Channels: To enhance asymmetry magnitude (which is suppressed by the dominance of gluon-gluon initial states), the authors analyze:
  • $t\bar{t}\gamma$: Top pair production with an isolated photon.
  • $t\bar{t}W$: Top pair production with a $W$ boson. Here, the asymmetry is defined by the rapidity difference of the leptons rather than the top quarks due to the complexity of assigning leptons to specific $W$ bosons.
• Energy and Incline Asymmetries ($t\bar{t}j$):
  • Energy Asymmetry ($A_E$): Based on the scattering angle ($\theta_j$) between initial partons and the additional jet, comparing events where the energy difference ($\Delta E$) is positive vs. negative.
  • Incline Asymmetry ($A_I$): Based on the angle ($\phi$) between the planes defined by initial and final state momenta.

Statistical Techniques:

• ATLAS: Utilizes a Fully Bayesian Unfolding technique to obtain parton-level inclusive values.
• CMS: Focuses on specific topologies (e.g., boosted topologies in lepton+jets) to enhance sensitivity to BSM physics.

3. Key Contributions and Results

A. Inclusive Top Quark Pair Production ($t\bar{t}$)

• ATLAS: Measured the charge asymmetry in lepton+jets, dilepton, and combined channels.
  • Result: Obtained an inclusive parton-level value of $A_C^{t\bar{t}} = 0.0068 \pm 0.0015$.
  • Significance: This is 4.7$\sigma$ against the no-asymmetry scenario, representing the first evidence of top quark charge asymmetry at the LHC.
  • Comparison: The result is compatible with the SM prediction ($0.0064^{+0.0005}_{-0.0006}$). Differential measurements across the invariant mass of the $t\bar{t}$ system showed no significant deviations from the SM.
• CMS: Focused on boosted topologies in the lepton+jets channel.
  • Result: No significant deviations from the SM or the no-asymmetry scenario were observed.

B. Associated Production with Vector Bosons ($t\bar{t}\gamma$ and $t\bar{t}W$)

• $t\bar{t}\gamma$ (Photon):
  • ATLAS (lepton+jets): Measured $A_C = -0.003 \pm 0.029$.
  • CMS (dilepton): Measured $A_C = (-1.2 \pm 4.2)\%$.
  • Conclusion: Both results are compatible with no asymmetry and theoretical predictions.
• $t\bar{t}W$ (W Boson):
  • ATLAS: Results at reconstruction and particle levels are compatible with no asymmetry and SM predictions.
  • CMS: Measured a lepton charge asymmetry of $A_C^l = -0.19^{+0.16}_{-0.18}$. This shows a deviation from zero of slightly more than 1$\sigma$, but remains consistent with SM expectations within uncertainties.

C. Associated Production with a Jet ($t\bar{t}j$)

• Energy Asymmetry ($A_E$):
  • ATLAS: No significant deviations from theory; the most significant bin showed a 2.1$\sigma$ difference from zero.
  • CMS: Found a significance of 2.7$\sigma$ against no asymmetry in the most significant bin ($A_E = -6.3 \pm 2.3\%$). However, this also represents a 2$\sigma$ deviation from theoretical predictions.
• Incline Asymmetry ($A_I$):
  • CMS: Measured $A_I = (2.5 \pm 2.3)\%$. While less significant, this value deviates from zero and from slightly negative theoretical predictions.

4. Significance and Conclusion

• First Evidence at LHC: The paper highlights the first experimental evidence ($4.7\sigma$) of the top quark charge asymmetry at the LHC, confirming SM predictions regarding higher-order QCD effects.
• Systematic Uncertainty Mitigation: The study validates the utility of asymmetry measurements as a tool to cancel systematic uncertainties, providing a cleaner probe of the top quark sector than inclusive cross-section measurements.
• BSM Sensitivity: While current results are largely consistent with the Standard Model, the differential measurements and associated production channels ($t\bar{t}\gamma$, $t\bar{t}W$, $t\bar{t}j$) provide stringent constraints on BSM EFT operators.
• Future Outlook: While inclusive measurements are now limited by systematic uncertainties, the sensitivity of associated production channels is currently limited by statistical power (data volume). Future improvements are expected as more data is recorded at the LHC.