Studies of $Z$ boson decay into double $\Upsilon$ mesons at the NLO QCD accuracy

TL;DR

This study uses nonrelativistic QCD at NLO accuracy to analyze Z boson decay into double Upsilon mesons, highlighting the importance of QED diagrams and feed-down effects, and providing a precise branching ratio prediction.

Contribution

First comprehensive NLO QCD analysis of Z boson decay into double Upsilon mesons including QED effects and feed-down contributions.

Findings

QED diagrams are essential for accurate results.

QCD corrections significantly improve the predictions.

Predicted branching ratio is around 10^{-11}, below experimental limits.

Abstract

In this paper, we employ the nonrelativistic QCD factorization to conduct a comprehensive examination of the $Z$ boson decay into a pair of $\Upsilon$ mesons, achieving accuracy at the next-to-leading-order (NLO) in $\alpha_s$. Our calculations demonstrate that the QED diagrams are indispensable in comparison to the pure QCD diagrams, and the implementation of QCD corrections markedly enhance the QCD results, whereas it substantially diminish 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 $\mathcal{B}_{Z \to \Upsilon(nS)+\Upsilon(mS)} \sim 10^{-11}$, which is notably lower than the upper limits set by CMS.