Improved tests of entanglement and Bell inequalities with LHC tops

<jats:title>Abstract</jats:title><jats:p>We discuss quantum entanglement in top pair production at the LHC. Near the <jats:inline-formula><jats:alternatives><jats:tex-math>$$t {\bar{t}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>t</mml:mi> <mml:mover> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> threshold, entanglement observables are enhanced by suppressing the contribution of <jats:inline-formula><jats:alternatives><jats:tex-math>$$q {\bar{q}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>q</mml:mi> <mml:mover> <mml:mrow> <mml:mi>q</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> subprocesses, which is achieved by a simple cut on the velocity of the <jats:inline-formula><jats:alternatives><jats:tex-math>$$t {\bar{t}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>t</mml:mi> <mml:mover> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> system in the laboratory frame. Furthermore, we design new observables that directly measure the relevant combinations of <jats:inline-formula><jats:alternatives><jats:tex-math>$$t{\bar{t}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>t</mml:mi> <mml:mover> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> spin correlation coefficients involved in the measurement of entanglement and Bell inequalities. As a result, the statistical sensitivity is enhanced, up to a factor of 7 for Bell inequalities near threshold.</jats:p>