Probing entanglement and testing Bell inequality violation with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mrow><mml:mi>τ</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mi>τ</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math> at Belle II
K. Ehatäht, M. Fabbrichesi, Luca Marzola, Christian Veelken
Abstract
We present a feasibility study to probe quantum entanglement and Bell inequality violation in the process <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi mathvariant="normal">e</a:mi><a:mo>+</a:mo></a:msup><a:msup><a:mi mathvariant="normal">e</a:mi><a:mo>−</a:mo></a:msup><a:mo stretchy="false">→</a:mo><a:msup><a:mi>τ</a:mi><a:mo>+</a:mo></a:msup><a:msup><a:mi>τ</a:mi><a:mo>−</a:mo></a:msup></a:math> at a center-of-mass energy of <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mrow><f:msqrt><f:mrow><f:mi>s</f:mi></f:mrow></f:msqrt><f:mo>=</f:mo><f:mn>10.579</f:mn><f:mtext> </f:mtext><f:mtext> </f:mtext><f:mi>GeV</f:mi></f:mrow></f:math>. The sensitivity of the analysis is enhanced by applying a selection on the scattering angle <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>ϑ</h:mi></h:math> in the <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msup><j:mi>τ</j:mi><j:mo>+</j:mo></j:msup><j:msup><j:mi>τ</j:mi><j:mo>−</j:mo></j:msup></j:math> center-of-mass frame. We analyze events in which both <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi>τ</l:mi></l:math> leptons decay to hadrons, using a combination of decay channels <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:msup><n:mi>τ</n:mi><n:mo>−</n:mo></n:msup><n:mo stretchy="false">→</n:mo><n:msup><n:mi>π</n:mi><n:mo>−</n:mo></n:msup><n:msub><n:mi>ν</n:mi><n:mi>τ</n:mi></n:msub></n:math>, <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mrow><q:msup><q:mrow><q:mi>τ</q:mi></q:mrow><q:mrow><q:mo>−</q:mo></q:mrow></q:msup><q:mo stretchy="false">→</q:mo><q:msup><q:mrow><q:mi>π</q:mi></q:mrow><q:mrow><q:mo>−</q:mo></q:mrow></q:msup><q:msup><q:mrow><q:mi>π</q:mi></q:mrow><q:mrow><q:mn>0</q:mn></q:mrow></q:msup><q:msub><q:mrow><q:mi>ν</q:mi></q:mrow><q:mrow><q:mi>τ</q:mi></q:mrow></q:msub></q:mrow></q:math>, and <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:msup><t:mi>τ</t:mi><t:mo>−</t:mo></t:msup><t:mo stretchy="false">→</t:mo><t:msup><t:mi>π</t:mi><t:mo>−</t:mo></t:msup><t:msup><t:mi>π</t:mi><t:mo>+</t:mo></t:msup><t:msup><t:mi>π</t:mi><t:mo>−</t:mo></t:msup><t:msub><t:mi>ν</t:mi><t:mi>τ</t:mi></t:msub></t:math>. The spin orientation of the <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>τ</w:mi></w:math> leptons in these decays is reconstructed using the polarimeter-vector method. Assuming a dataset of 200 million <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msup><y:mi>τ</y:mi><y:mo>+</y:mo></y:msup><y:msup><y:mi>τ</y:mi><y:mo>−</y:mo></y:msup></y:math> events and accounting for experimental resolutions, we expect the observation of quantum entanglement and Bell inequality violation by the Belle-II experiment will be possible with a significance well in excess of five standard deviations. Published by the American Physical Society 2024