Tripartite entanglement in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>H</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>Z</mml:mi><mml:mi>Z</mml:mi><mml:mo>,</mml:mo><mml:mi>W</mml:mi><mml:mi>W</mml:mi></mml:math> decays
J. A. Aguilar–Saavedra
Abstract
The decays of the Higgs boson produce a state in which the spins of the decay products and the orbital angular momentum (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>L</a:mi></a:math>) are highly entangled. We obtain the tripartite density operator, as well as reduced operators, for the decay into two weak bosons. For <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>H</c:mi><c:mo stretchy="false">→</c:mo><c:mi>Z</c:mi><c:mi>Z</c:mi></c:math> in the four-lepton final state we also estimate the statistical sensitivity at the Large Hadron Collider and future upgrades, using a binned method to reconstruct the density operators from distributions. With the expected Run 3 data, establishing genuine tripartite entanglement would be possible beyond the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mn>5</f:mn><f:mi>σ</f:mi></f:math> level. The violation of Bell inequalities involving the spins of the two weak bosons could also be established beyond the <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mn>5</h:mn><h:mi>σ</h:mi></h:math> level. Published by the American Physical Society 2024