Testing Bell inequalities and probing quantum entanglement at CEPC

We study quantum entanglement and test violation of Bell-type inequality at the Circular Electron Positron Collider (CEPC), which is one of the most attractive future collides. It is a promising particle collider designed to search new physics, make Standard Model (SM) precision measurements, and serving as a Higgs factory. Our study is based on a fast simulation of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>Z</a:mi></a:math> boson pair production from Higgs boson decay at <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msqrt><c:mi>s</c:mi></c:msqrt><c:mo>=</c:mo><c:mn>250</c:mn><c:mtext> </c:mtext><c:mtext> </c:mtext><c:mi>GeV</c:mi></c:math>. The detector effects are also included in the simulation. The spin density matrix of the joint <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>Z</e:mi><e:mi>Z</e:mi></e:math> system is parametrized using irreducible tensor operators and reconstructed from the spherical coordinates of the decay leptons. To test Bell inequalities, we construct observable quantities for the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>H</g:mi><g:mo stretchy="false">→</g:mo><g:mi>Z</g:mi><g:mi>Z</g:mi><g:mo>*</g:mo></g:math> process in CEPC by using the Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality, whose value is determined from the density matrix of the Z boson pairs. The sensitivity of the Bell inequality violation is observed with more than <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mrow><j:mn>1</j:mn><j:mi>σ</j:mi></j:mrow></j:math> and the presence of the quantum entanglement is probed with more than <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mrow><l:mn>2</l:mn><l:mi>σ</l:mi></l:mrow></l:math> confidence level.