Top quark spin and quantum entanglement in the ATLAS experiment

Top quark pair spin correlation measurements performed by the ATLAS experiment using $pp$ collisions at the CERN Large Hadron Collider are summarized. Moreover, the measurement of a specific observable $D$ related to top quark pair spin correlations is presented using the full LHC Run 2 data taking at the center-of-mass energy of $\sqrt{s} = 13$ TeV. This allowed the ATLAS experiment to observe the quantum entanglement, one of the fundamental property of the quantum mechanics.

💡 Research Summary

The ATLAS Collaboration has performed a comprehensive program of top‑antitop (t t̄) spin‑correlation measurements and, for the first time at a hadron collider, used these correlations to demonstrate quantum entanglement between the two top quarks. Because the top quark decays before hadronising (τ ≈ 5 × 10⁻²⁵ s), its spin information is transferred directly to its decay products – principally the W boson and the b‑quark, and subsequently to the charged leptons (e, µ) from the W decays. By reconstructing the angular distributions of these leptons in the rest frames of their parent top quarks, one can infer the original spin state of the t t̄ system.

The spin density matrix of a t t̄ pair is fully described by 15 real parameters: three components of the top polarisation vector B⁺, three of the antitop polarisation vector B⁻, and a 3 × 3 correlation matrix C. In the helicity basis (axes (\hat{k},\hat{n},\hat{r})) the coefficients are obtained from simple averages of cosine of angles between the lepton direction and each axis:
(B^{a}{\pm}=3\langle\cos\theta^{a}{\pm}\rangle),
(C(a,b)=-9\langle\cos\theta^{a}{+}\cos\theta^{b}{-}\rangle).

Run 1 (8 TeV, 20.2 fb⁻¹).
ATLAS measured the full spin density matrix using the dilepton channels (ee, µµ, eµ). The neutrino‑weighting method was employed to reconstruct the t t̄ kinematics. All three polarisation components were found to be compatible with the Standard Model (SM) expectation of zero. The nine correlation coefficients C(k,k), C(n,n), C(r,r) and the six off‑diagonal terms were extracted at both parton and stable‑particle levels. The uncertainties range from 3–5 % for polarisation to 9–19 % for the correlation terms, and all results lie within one standard deviation of the SM predictions (see Fig. 1 of the paper).

Run 2 (13 TeV, 36 fb⁻¹).
A simplified analysis focused on the e µ channel and measured only the azimuthal angle difference Δφ(l⁺, l⁻) between the two leptons. By fitting the unfolded Δφ distribution with templates corresponding to SM spin correlation (POWHEG) and the no‑spin hypothesis, ATLAS obtained a spin‑correlation strength of (f_{\text{SM}} = 1.25^{+0.09}_{-0.11}). This is slightly higher than the NLO POWHEG prediction but compatible with recent NNLO calculations.

Quantum‑entanglement measurement.
Theoretical work has shown that in the low‑invariant‑mass region (m_{t t̄} < 380 GeV) the t t̄ spin density matrix satisfies a sufficient entanglement condition (\text{Tr}