Measurements of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>Z</mml:mi> </mml:math> -Boson Pair Entanglement in Decays of Higgs Bosons at the ATLAS Experiment

<jats:p> Entanglement is a key property of quantum systems. In this Letter the first measurements of quantum entanglement between spins in pairs of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>Z</a:mi> </a:math> bosons are reported, using proton-proton collision data from the Large Hadron Collider (LHC) at center-of-mass energies of 13 and 13.6 TeV, recorded with the ATLAS detector. Measurements of angular observables sensitive to <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>Z</c:mi> <c:msup> <c:mi>Z</c:mi> <c:mo>*</c:mo> </c:msup> </c:math> spin-density-matrix elements in the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mrow> <e:mi>H</e:mi> <e:mo stretchy="false">→</e:mo> <e:mi>Z</e:mi> <e:msup> <e:mrow> <e:mi>Z</e:mi> </e:mrow> <e:mrow> <e:mo>*</e:mo> </e:mrow> </e:msup> <e:mo stretchy="false">→</e:mo> <e:msup> <e:mrow> <e:mo>ℓ</e:mo> </e:mrow> <e:mrow> <e:mo>+</e:mo> </e:mrow> </e:msup> <e:msup> <e:mrow> <e:mo>ℓ</e:mo> </e:mrow> <e:mrow> <e:mo>−</e:mo> </e:mrow> </e:msup> <e:msup> <e:mrow> <e:mo>ℓ</e:mo> </e:mrow> <e:mrow> <e:mo>+</e:mo> </e:mrow> </e:msup> <e:msup> <e:mrow> <e:mo>ℓ</e:mo> </e:mrow> <e:mrow> <e:mo>−</e:mo> </e:mrow> </e:msup> </e:mrow> </e:math> process yield coefficients <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mrow> <i:msub> <i:mrow> <i:mi>C</i:mi> </i:mrow> <i:mrow> <i:mn>2</i:mn> <i:mo>,</i:mo> <i:mn>1</i:mn> <i:mo>,</i:mo> <i:mn>2</i:mn> <i:mo>,</i:mo> <i:mo>−</i:mo> <i:mn>1</i:mn> </i:mrow> </i:msub> <i:mo>=</i:mo> <i:mo>−</i:mo> <i:mn>0.71</i:mn> <i:mo>±</i:mo> <i:mn>0.45</i:mn> </i:mrow> </i:math> and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>C</k:mi> <k:mrow> <k:mn>2</k:mn> <k:mo>,</k:mo> <k:mn>2</k:mn> <k:mo>,</k:mo> <k:mn>2</k:mn> <k:mo>,</k:mo> <k:mo>−</k:mo> <k:mn>2</k:mn> </k:mrow> </k:msub> <k:mo>=</k:mo> <k:mn>0.08</k:mn> <k:mo>±</k:mo> <k:mn>0.44</k:mn> </k:math> , consistent with their Standard Model predictions. A complementary hypothesis test using the full angular distribution, and relying on several Standard Model assumptions in the decays, provides substantially higher sensitivity to quantum correlations and disfavors the separable-state hypothesis at a significance of 4.7 standard deviations (expected <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mn>4.9</m:mn> <m:mi>σ</m:mi> </m:math> ) relative to the entangled Standard Model hypothesis. These results provide strong evidence of quantum entanglement between massive bosons (spin qutrits) at the electroweak scale. </jats:p>