Studies of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Z</mml:mi></mml:math> boson decay into double <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">ϒ</mml:m

In this paper, we employ the nonrelativistic quantum chromodynamics (QCD) factorization to conduct a comprehensive examination of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>Z</a:mi></a:math> boson decay into a pair of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi mathvariant="normal">ϒ</c:mi></c:math> mesons, achieving accuracy at the next-to-leading-order (NLO) in <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:msub><f:mi>α</f:mi><f:mi>s</f:mi></f:msub></f:math>. Our calculations demonstrate that the quantum electrodynamics (QED) diagrams are indispensable in comparison to the pure QCD diagrams, and the implementation of QCD corrections markedly enhances the QCD results, whereas it substantially diminishes the QED results. To ensure consistency with the experimental methodology, we have taken into account the feed-down transitions originating from higher excited states, which exhibit significant relevance. Combining all the contributions, we arrive at the NLO prediction of <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mrow><h:msub><h:mrow><h:mi mathvariant="script">B</h:mi></h:mrow><h:mrow><h:mi>Z</h:mi><h:mo stretchy="false">→</h:mo><h:mi mathvariant="normal">ϒ</h:mi><h:mo stretchy="false">(</h:mo><h:mi>n</h:mi><h:mi>S</h:mi><h:mo stretchy="false">)</h:mo><h:mo>+</h:mo><h:mi mathvariant="normal">ϒ</h:mi><h:mo stretchy="false">(</h:mo><h:mi>m</h:mi><h:mi>S</h:mi><h:mo stretchy="false">)</h:mo></h:mrow></h:msub><h:mo>∼</h:mo><h:msup><h:mrow><h:mn>10</h:mn></h:mrow><h:mrow><h:mo>−</h:mo><h:mn>11</h:mn></h:mrow></h:msup></h:mrow></h:math>, which is notably lower than the upper limits set by CMS. Published by the American Physical Society 2024