Golden Probe of the di$-\Upsilon$ Threshold

Recent studies indicate that the ground state of a QCD four bottom quark system may form a resonance in the range $\sim 18 -19$ GeV, near the di-$\Upsilon$ threshold, which may be observable at the LHC in the four lepton final state. These studies also predict a variety of possible resonances associated with the various excited states and allow for a number of possible spin and $CP$ quantum numbers. Of course, even if a resonance is observed in four leptons in the predicted mass range, it will be prudent to experimentally confirm its four bottom quark QCD nature or whether it is perhaps something more exotic. We initiate an investigation in this direction by exploring the ability of the \emph{normalized} fully differential decay width for decays to four leptons to probe the underlying nature of a putative resonance including $CP$ and tensor properties. We assume the first observed state is a spin-0 boson decaying to at least one on-shell $\Upsilon$, but allow for decays to four leptons through $\Upsilon\Upsilon,\,\Upsilon\gamma$, and $\Upsilon Z$ vector boson pairs. We consider a range of resonance masses around the di-$\Upsilon$ threshold and find excellent prospects at the LHC for establishing its $CP$ and tensor properties, perhaps not long after a discovery depending on (unknown) production cross sections and the exact resonance mass.