Measurements of polarization and spin correlation and observation of entanglement in top quark pairs using <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>lepton</mml:mi><mml:mo>+</mml:mo><mml:mtext>jets</mml:mtext></mml:mrow></mml:math> events from proton-proton collisions at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msqrt><mml:mi>s</mml:mi></mml:msqrt><mml:mo>=</mml:mo><mml:mn>13</mml:mn><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mi>TeV</mml:mi></mml:math>

Measurements of the polarization and spin correlation in top quark pairs (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>t</a:mi><a:mover accent="true"><a:mi>t</a:mi><a:mo stretchy="false">¯</a:mo></a:mover></a:math>) are presented using events with a single electron or muon and jets in the final state. The measurements are based on proton-proton collision data from the LHC at <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msqrt><e:mi>s</e:mi></e:msqrt><e:mo>=</e:mo><e:mn>13</e:mn><e:mtext> </e:mtext><e:mtext> </e:mtext><e:mi>TeV</e:mi></e:math> collected by the CMS experiment, corresponding to an integrated luminosity of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mn>138</g:mn><g:mtext> </g:mtext><g:mtext> </g:mtext><g:msup><g:mi>fb</g:mi><g:mrow><g:mo>−</g:mo><g:mn>1</g:mn></g:mrow></g:msup></g:math>. All coefficients of the polarization vectors and the spin correlation matrix are extracted simultaneously by performing a binned likelihood fit to the data. The measurement is performed inclusively and in bins of additional observables, such as the mass of the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>t</i:mi><i:mover accent="true"><i:mi>t</i:mi><i:mo stretchy="false">¯</i:mo></i:mover></i:math> system and the top quark scattering angle in the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>t</m:mi><m:mover accent="true"><m:mi>t</m:mi><m:mo stretchy="false">¯</m:mo></m:mover></m:math> rest frame. The measured polarization and spin correlation are in agreement with the standard model. From the measured spin correlation, conclusions on the <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>t</q:mi><q:mover accent="true"><q:mi>t</q:mi><q:mo stretchy="false">¯</q:mo></q:mover></q:math> spin entanglement are drawn by applying the Peres-Horodecki criterion. The standard model predicts entangled spins for <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>t</u:mi><u:mover accent="true"><u:mi>t</u:mi><u:mo stretchy="false">¯</u:mo></u:mover></u:math> states at the production threshold and at high masses of the <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mi>t</y:mi><y:mover accent="true"><y:mi>t</y:mi><y:mo stretchy="false">¯</y:mo></y:mover></y:math> system. Entanglement is observed for the first time in events at high <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi>t</cb:mi><cb:mover accent="true"><cb:mi>t</cb:mi><cb:mo stretchy="false">¯</cb:mo></cb:mover></cb:math> mass, where a large fraction of the <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:mi>t</gb:mi><gb:mover accent="true"><gb:mi>t</gb:mi><gb:mo stretchy="false">¯</gb:mo></gb:mover></gb:math> decays are spacelike separated, with an expected and observed significance of above 5 standard deviations. © 2024 CERN, for the CMS Collaboration 2024 CERN