Observation of quantum entanglement in top quark pair production in proton–proton collisions at<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msqrt><mml:mi>s</mml:mi></mml:msqrt><mml:mo>=</mml:mo><mml:mn>13</mml:mn></mml:mrow></mml:math> TeV
CMS Collaboration, Aram Hayrapetyan, A. Tumasyan, Wolfgang Adam, Janik Walter Andrejkovic, Thomas Bergauer, S. Chatterjee, K. Damanakis, M. Dragicevic, André H. Hoang, Priya Sajid Hussain, Jeitler, Manfred, Natascha Krammer, Ang Li, D. Liko, Ivan Mikulec, J. Schieck, Schöfbeck, Robert, D. Schwarz, M. Sonawane, Sebastian Templ, W. Waltenberger, Claudia-Elisabeth Wulz, X. Janssen, T. Van Laer, P. Van Mechelen, Nordin Breugelmans, Jorgen d'Hondt, Soumya Dansana, A. De Moor, M. Delcourt, Felix Heyen, S. Lowette, I. Makarenko, D. Müller, Stefaan Tavernier, M. Tytgat, G. P. Van Onsem, S. Van Putte, D. Vannerom, B. Bilin, B. Clerbaux, Aloke Kumar Das, G. De Lentdecker, Hugues Evard, L. Favart, P. Gianneios, J. Jaramillo, Ali Khalilzadeh, Khan, Fakhri Alam, Kyeongpil Lee, M. Mahdavikhorrami, A. Malara, S. Paredes, Muhammad Aamir Shahzad, Laurent Thomas, Vanden Bemden, Max, Vander Velde, Catherine, Pascal Vanlaer, M. De Coen, Dobur, Didar, Gokbulut, Gul, Yanwen Hong, J. Knolle, Luka Lambrecht, David Marckx, Mota Amarilo, Kevin, Amrutha Samalan, K. Skovpen, N. Van Den Bossche, Jan van der Linden, Liam Wezenbeek, Anna Benecke, A. Bethani, Giacomo Bruno, C. Caputo, De Favereau De Jeneret, Jerome, C. Delaere, Donertas, Izzeddin Suat, A. Giammanco, Ahmet Oguz Guzel, Sandhya Jain, V. Lemaitre, Jindrich Lidrych, Paola Mastrapasqua, T. T. Tran, S. Wertz, G. A. Alves, Alves Gallo Pereira, Miguel, E. Coelho, Correia Silva, Gilson, C. Hensel, Menezes De Oliveira, Thales, Mora Herrera, Clemencia, A. Moraes, Rebello Teles, Patricia, Mariana Soeiro, Vilela Pereira, Antonio, Aldá Júnior, Walter Luiz, Barroso Ferreira Filho, Mapse
Abstract
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 ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mrow><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mover></mml:mrow></mml:mrow></mml:math> ) 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mrow><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mover></mml:mrow></mml:mrow></mml:math> production density matrix and measured in the region of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mrow><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mover></mml:mrow></mml:mrow></mml:math> production threshold. Values of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mrow><mml:mi>D</mml:mi><mml:mo><</mml:mo><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:math> are evidence of entanglement and D is observed (expected) to be <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mrow><mml:mo>−</mml:mo><mml:msubsup><mml:mn>0.480</mml:mn><mml:mrow><mml:mo>−</mml:mo><mml:mn>0.029</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mn>0.026</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math> ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mrow><mml:mo>−</mml:mo><mml:msubsup><mml:mn>0.467</mml:mn><mml:mrow><mml:mo>−</mml:mo><mml:mn>0.029</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mn>0.026</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math> ) 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mrow><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mover></mml:mrow></mml:mrow></mml:math> pairs in this phase space. This measurement provides a new probe of quantum mechanics at the highest energies ever produced.