Top quark spin and quantum entanglement in the ATLAS experiment

The ATLAS experiment utilized top quark pair spin correlation measurements from 13 TeV proton-proton collisions at the LHC to observe quantum entanglement, a fundamental property of quantum mechanics.

The Gist

Imagine the universe as a giant, high-speed dance floor where particles are the dancers. For a long time, physicists have been watching the "Top Quark," the heaviest and most energetic dancer in the show. Because this dancer is so heavy, it spins out of the dance floor (decays) almost instantly, before it can even grab a partner or form a stable group.

This paper is a report from the ATLAS experiment, a massive detector at the Large Hadron Collider (LHC) in Europe, describing how they watched these top quarks dance and discovered something magical about their connection.

Here is the story in simple terms:

1. The "Spinning Top" Connection

Top quarks are born in pairs: a top quark and an anti-top quark. Even though they are tiny, they have a property called "spin," which you can imagine like a spinning top or a dancer twirling.

When these two are created, their spins are linked. If you know which way one is spinning, you instantly know something about the other, even if they fly apart in opposite directions. The ATLAS team spent years measuring these spins. In the past, they checked this using data from 2011–2012 (when the collider was running at lower speeds) and confirmed that the spins were indeed linked, just as the standard rules of physics predicted.

2. The Big Question: Are They "Entangled"?

The paper moves beyond just checking if they are linked to asking a deeper question: Are they "quantum entangled"?

Think of quantum entanglement like a pair of magic dice. If you roll one in New York and it lands on a 6, the other die in Tokyo instantly becomes a 1, no matter how far apart they are. They aren't just correlated; they share a single, invisible quantum identity.

To prove this, the scientists needed to look at a specific "dance move." They focused on a specific region where the top quark pairs were created with relatively low energy (a "low mass" region). In this zone, the laws of quantum mechanics suggest the dancers should be in a "spin-singlet" state—a very tight, inseparable bond where their spins are perfectly opposite.

3. The "Magic Angle" (The Observable D)

How did they prove this? They didn't look at the quarks directly (they decay too fast). Instead, they looked at the "footprints" the quarks left behind: the electrons and muons (lighter particles) they produced when they fell apart.

The team measured a specific angle between the paths of these footprints. They called this measurement Observable D.

• The Analogy: Imagine two people throwing darts at a board. If they are just throwing randomly, the darts will land all over. But if they are "entangled," their throws will follow a strict, secret pattern.
• The scientists calculated a number based on this pattern. If the number was below a certain "magic line" (specifically, less than -1/3), it would prove that the particles were truly entangled.

4. The Result: Magic Confirmed!

Using data from 2015 to 2018 (the full "Run 2" of the LHC), the ATLAS team analyzed over a million events.

• They found that the measured number was -0.537.
• The "magic line" for proving entanglement was -0.322.

Because -0.537 is significantly lower than -0.322, the result was a resounding YES. The top quark pairs were indeed quantum entangled. The team was more than 5 standard deviations sure of this, which in science is like being 99.9999% certain.

5. A Small Glitch in the Matrix

The paper notes one interesting hiccup. While the data proved entanglement, the exact numbers didn't perfectly match the computer simulations (the "theory") for the low-energy region.

• The Reason: The scientists suspect this is because the computer models don't fully account for a weird, sticky force that happens when the particles are moving very slowly near the "threshold" of creation. It's like a dance floor that gets sticky right at the entrance, affecting how the dancers move before they even start their routine.

The Bottom Line

This paper is a milestone. It confirms that the strange, spooky rules of quantum mechanics (entanglement) aren't just for tiny atoms in a lab; they happen with the heaviest particles in the universe, created in the most violent collisions we can make.

The authors conclude that this is just the beginning. With even more data coming in the future, we might enter a new era where we use the LHC not just to find new particles, but to study the very nature of quantum information itself.

Technical Summary

Technical Summary: Top Quark Spin and Quantum Entanglement in the ATLAS Experiment

Problem and Motivation
The top quark, distinguished by its large mass ($m_t \approx 172.57$ GeV), decays prior to forming bound states or undergoing spin decorrelation. Consequently, the spin correlation between a top quark and an antitop quark ($t\bar{t}$) produced in pairs is preserved and transferred to their decay products. While the ATLAS experiment has previously measured these spin correlations using LHC Run 1 data ($\sqrt{s} = 7$ and $8$ TeV) and partial Run 2 data ($\sqrt{s} = 13$ TeV), recent theoretical proposals suggest that specific measurements of $t\bar{t}$ correlations can probe fundamental aspects of quantum mechanics, specifically quantum entanglement, at the energy scales of the Large Hadron Collider (LHC). This paper summarizes ATLAS's progression from measuring the full spin density matrix to observing quantum entanglement in $t\bar{t}$ production.

Methodology
The analysis relies on characterizing the $t\bar{t}$ spin state using a spin density matrix defined by 15 coefficients: three polarization vectors for the top and antitop quarks and a $3\times3$ correlation matrix ($C$). These coefficients are extracted by measuring the angular distributions of decay products, specifically the angles ($\theta$) between lepton directions in the parent top quark rest frames and specific helicity axes ($\vec{k}, \vec{n}, \vec{r}$).

The paper details three distinct measurement phases:

1. Run 1 ($\sqrt{s} = 8$ TeV): A full spin density matrix measurement using the complete dataset ($20.2 \text{ fb}^{-1}$) across all dilepton channels ($ee, \mu\mu, e\mu$). The neutrino weighting method was employed for reconstruction, with distributions corrected to the truth level (stable-particle and parton levels).
2. Run 2 Partial ($\sqrt{s} = 13$ TeV): A simplified measurement using $36 \text{ fb}^{-1}$ of the $e\mu$ channel, focusing on the azimuthal angle difference ($\Delta\phi$) between leptons. A template fit compared data against Standard Model (SM) predictions generated by POWHEG at next-to-leading order (NLO).
3. Run 2 Full ($\sqrt{s} = 13$ TeV): A dedicated measurement of quantum entanglement using the full Run 2 dataset ($140 \text{ fb}^{-1}$, 2015–2018) in the $e\mu$ channel. The analysis focused on the low invariant mass region ($340 < m_{t\bar{t}} < 380$ GeV), where gluon-gluon fusion dominates and the $t\bar{t}$ system is expected to be in a spin-singlet state.
   • Event Selection: Requires one electron and one muon with opposite charges and $p_T > 25\text{--}28$ GeV, plus at least two jets ($p_T > 25$ GeV) with at least one $b$-tagged. No cut on missing transverse momentum was applied.
   • Reconstruction: A combination of methods was used to reconstruct top momenta, primarily the "Ellipse" method (85% efficiency), supplemented by the neutrino weighting method and simple pairing.
   • Entanglement Observable: The analysis utilizes the observable $D$, defined as $D = \text{Tr}[C]/3 = -3\langle \cos\phi \rangle$, where $\phi$ is the angle between lepton directions in their respective rest frames. Quantum entanglement is theoretically established if $D < -1/3$.

Key Results

• Spin Correlations (Run 1): The measured polarization coefficients were consistent with the SM prediction of zero. Most correlation coefficients agreed with theory within one standard deviation, with uncertainties ranging from 3–5% for polarization to 9–19% for cross-terms.
• Spin Correlations (Run 2 Partial): The measured fraction of spin correlations relative to the NLO POWHEG prediction was $1.25^{+0.09}_{-0.11}$, indicating slightly higher correlations than the NLO prediction, though this discrepancy diminishes when compared to next-to-next-to-leading order (NNLO) predictions.
• Quantum Entanglement (Run 2 Full):
  • The measured value of the observable $D$ at the particle level in the signal region ($340 < m_{t\bar{t}} < 380$ GeV) was $-0.537 \pm 0.002 \text{ (stat.)} \pm 0.019 \text{ (syst.)}$.
  • This result is significantly below the entanglement threshold of $-0.322 \pm 0.009$ (derived from POWHEG+PYTHIA 8 predictions), representing a deviation of more than 5 standard deviations.
  • The analysis confirms the observation of quantum entanglement in $t\bar{t}$ pair production.
  • Discrepancies were noted between data and predictions in the low $m_{t\bar{t}}$ region, potentially due to non-relativistic QCD effects (e.g., Coulomb bound state effects) near the production threshold, which are not fully accounted for in current simulations.

Significance and Claims
The paper claims that the ATLAS experiment has successfully observed quantum entanglement, a fundamental property of quantum mechanics, within the high-energy environment of the LHC. By measuring the specific observable $D$ in the low invariant mass region, the experiment demonstrated that the $t\bar{t}$ system exists in an entangled state.

The authors note that while the observation is robust, the modeling of $t\bar{t}$ production remains a limiting factor, particularly regarding the differences in predictions between Monte Carlo generators (POWHEG+PYTHIA vs. POWHEG+HERWIG) and the treatment of non-relativistic effects near the threshold. The paper concludes that this measurement marks the beginning of an era of quantum information measurements at the LHC, with the expectation that the full LHC program will provide up to 20 times more data, potentially stimulating further progress in theoretical modeling and experimental precision.