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CMS-TOP-23-001 ; CERN-EP-2024-137
Observation of quantum entanglement in top quark pair production in proton-proton collisions at $ \sqrt{s}= $ 13 TeV
Rep. Prog. Phys. 87 (2024) 117801
Abstract: Entanglement is an intrinsic property of quantum mechanics and is predicted to be exhibited in the particles produced at the Large Hadron Collider. A measurement of the extent of entanglement in top quark-antiquark ($ \mathrm{t} \bar{\mathrm{t}} $) events produced in proton-proton collisions at a center-of-mass energy of 13 TeV is performed with the data recorded by the CMS experiment at the CERN LHC in 2016, and corresponding to an integrated luminosity of 36.3 fb$ ^{-1} $. The events are selected based on the presence of two leptons with opposite charges and high transverse momentum. An entanglement-sensitive observable $ D $ is derived from the top quark spin-dependent parts of the $ \mathrm{t} \bar{\mathrm{t}} $ production density matrix and measured in the region of the $ \mathrm{t} \bar{\mathrm{t}} $ production threshold. Values of $ D {<} -$1/3 are evidence of entanglement and $ D $ is observed (expected) to be $-$0.480$ ^{+0.026}_{-0.029} $ ($-$0.467$ ^{+0.026}_{-0.029} $) at the parton level. With an observed significance of 5.1 standard deviations with respect to the non-entangled hypothesis, this provides observation of quantum mechanical entanglement within $ \mathrm{t} \bar{\mathrm{t}} $ pairs in this phase space. This measurement provides a new probe of quantum mechanics at the highest energies ever produced.
Summary CMS Publications
Summary
Entanglement is an intrinsic property of quantum mechanics and its measurement utilizes elementary particles to test quantum mechanics. Recently, the ATLAS Collaboration reported the first observation of entanglement in the top quark-antiquark ($ \mathrm{t} \bar{\mathrm{t}} $) system [21] wih a result indicating slight deviation from MC simulation. The measurement of the entanglement of $ \mathrm{t} \bar{\mathrm{t}} $ pairs performed with CMS data exploits the spin correlation variable $ D $, which at the $ \mathrm{t} \bar{\mathrm{t}} $ production threshold, and in absence of BSM contributions, provides access to the full spin correlation information. This result contrasts with the ATLAS Collaboration's findings in several key ways. We directly measure entanglement at the parton level, whereas ATLAS reports their observable at the particle level. Additionally, our analysis is the first to consider non-relativistic bound-state effects in the production threshold by including the ground state of toponium, $\eta$t, which were not included in the ATLAS result. Unlike ATLAS, the CMS result is derived from a binned likelihood fit to extract the entanglement proxy, rather than using a calibration curve. The $ D $ variable represents an entanglement proxy, where less than $ -1/ $ 3 signals the presence of entanglement. This proxy is measured using events containing two oppositely charged electrons or muons produced in pp collisions at a center-of-mass energy of 13 TeV. The modeling of the data is improved when including the additional predicted contribution of the ground state of toponium, $\eta$t, and is utilized in a combined signal model of $ {\mathrm{t}\bar{\mathrm{t}}} {+} {\eta}$t in the measurement. The extent to which $ \mathrm{t} \bar{\mathrm{t}} $ pairs are entangled is measured by means of a binned profile likelihood fit of the parameter of interest $ D $ directly from the distribution of $ \cos\varphi $, where $ \varphi $ is the angle between the two charged decay leptons in their respective parent top quark rest frames. In the most sensitive kinematic phase space of the relative velocity between the lab and $ \mathrm{t} \bar{\mathrm{t}} $ reference frames $ \beta_z({\mathrm{t}\bar{\mathrm{t}}} ) < $ 0.9, and of the invariant mass of the top quark pair 345 $ < m({\mathrm{t}\bar{\mathrm{t}}} ) < $ 400 GeV, the fit of the $ \cos\varphi $ distribution yields an observed value of $ D=-$0.480$^{+0.026}_{-0.029} $ and an expected value of $ D=-$0.467$ ^{+0.026}_{-0.029} $ including the predicted $\eta$t state. This result has an observed (expected) significance of 5.1 (4.7) $ \sigma $, corresponding to the observation of top quark entanglement. The measured value of $ D $ is in good agreement with the MC modeling in this phase space when including the expected $\eta$t bound state contribution.
Compact Muon Solenoid
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