Search

The large constituent quark mass of bottomonium, the bottom quark/anti-quark bound state $(bbbar)$, affords a rich spectroscopy in which the perturbative (non-relativistic) limit of Quantum Chromodynamics may be theoretically described and experimentally investigated. The radial excitations of bottomonia---with radial quantum number $n$, one unit of total angular momentum $(J=1)$, and orbital angular momentum $L=0$, labeled $Upsilon(nS)$---are copiously produced in electron--positron $(epem)$ collisions. The Belle Collaboration is a high energy physics experiment located at the KEKB B-Factory epem collider, based at KEK in Tsukuba, Japan. Belle has accumulated a large dataset near the FourS and ThreeS resonances, collectively containing more than 28 million ThreeS and 556 million FourS. Some of these decay to other bbbar states---with one unit of orbital angular momentum and total angular momentum $J=0,1,2$, labeled cbj{n} ---via the emission of a photon, with subsequent transition to the OneS with the emission of one or more gluons, which hadronize to form an om meson. This dissertation presents an analysis of the hadronic transitions $chi_{bJ}(nP) rightarrow omega Upsilon(1S)$, where $Upsilon(1S) rightarrow ell^{+}ell^{-}$ with $ell=e,mu$, at Belle. The transitions of the $n=2$ triplet states provide a unique laboratory in which to study nonrelativistic quantum chromodynamics (NRQCD), as the kinematic threshold for production of an $omega$ and $Upsilon(1S)$ lies between the $J=0$ and $J=1$ states. The results presented herein constitute the first confirmation measurement of the $omega$ transitions of the $chi_{bJ}(2P)$ states since their discovery in 2004, with evidence---in excess of three standard deviations---for the sub-threshold transition of the $J=0$ state. The branching fraction $mathcal{B}big( chi_{b0}(2P) rightarrow omega Upsilon(1S) big)$ is found to be as large as the corresponding rate for the $J=2$ transition. The ratio of the $J=2$ to $J=1$ transitions is also measured and compared with the expectation from NRQCD, which we compute, revealing a $3.3sigma$ tension between experiment and theory. This work is leveraged to perform a search for radiative transitions of the $Upsilon(4S)$ to the $chi_{bJ}(2P)$ and $chi_{bJ}(3P)$ states, which are reconstructed in an inclusive $omega Upsilon(1S)$ final state. With no significant signal seen, limits are set on the corresponding branching fractions.