Experimental review of the $\Upsilon(1S,2S,3S)$ physics at $e^+e^-$ colliders and the LHC

The three lowest-lying $\Upsilon$ states, i.e. $\Upsilon(1S)$, $\Upsilon(2S)$, and $\Upsilon(3S)$, composed of $b\bar b$ pairs and below the $B\bar B$ threshold, provide a good platform for the researches of hadronic physics and physics beyond the Standard Model. They can be produced directly in $e^+e^-$ colliding experiments, such as CLEO, Babar, and Belle, with low continuum backgrounds. In these experiments, many measurements of the exclusive $\Upsilon(1S)$ and $\Upsilon(2S)$ decays into light hadrons, which shed light on the "80\% rule" for the Okubo-Zweig-Iizuka suppressed decays in the bottomonium sector, were carried out. Meanwhile, many studies of the charmonium and bottomonium productions in $\Upsilon(1S,2S,3S)$ decays were performed, to distinguish different Quantum Chromodynamics (QCD) models. Besides, exotic states and new physics were also extensively explored in $\Upsilon(1S,2S,3S)$ decays at CLEO, BaBar, and Belle. The $\Upsilon(1S,2S,3S)$ states can also be produced in $pp$ collisions and in collisions involving heavy ions. The precision measurements of their cross sections and polarizations at the large hadron collider (LHC), especially in the CMS, ATLAS, and LHCb experiments, help to understand $\Upsilon$ production mechanisms in $pp$ collisions. The observation of the sequential $\Upsilon$ suppression in heavy ion collisions at CMS is of great importance for verifying the quark-gluon plasma predicted by QCD. In this article, we review the experimental results on $\Upsilon(1S,2S,3S)$ at $e^+e^-$ colliders and the LHC, and summarize their prospects at Belle II and the LHC.