Heavy quarkonium production is not fully understood, but often described by two different models, the Color Singlet Model (CSM), and the Color Octet Model (COM). Previous measurements at the Tevatron collider by the CDF and D0 experiments are not fully in agreement with predicted observables from either model. The Relativistic Heavy Ion Collider (RHIC), and the Solenoidal Tracker At RHIC (STAR) is well suited to further explore heavy quarkonium production. The Heavy Flavor program in STAR encompasses various heavy-flavor analyses, taking advantage of its large solid-angle acceptance, including measurements that explore the properties of heavy quarkonium production using J/ψ and Upsilon (Υ) reconstructions via the di-electron channel, in p+p, d+Au, Cu+Cu, and Au+Au collision systems. This thesis presents results of reconstructed Upsilon (Υ) to study the Upsilon(nS) [n = 1, 2, 3] line- shape and measurements of the production-related observables of spin-alignment (‘polarization’) and Upsilon + hadron correlations (Υ + h) to investigate the Upsilon production mechanism, using triggered data from Run-8 (2008) d+Au and Run-9 (2009) p+p collisions at sqrt(sN N) = 200 GeV, detected at STAR. The result of the spin-alignment measurement is α = 1 ± 0.3 with χ^2 /n.d.f. = 18.71/7 indicating a large (transverse) polarization. The measurement of hadronic activity near the vicinity of an Upsilon, within current uncertainties, is in reasonable agreement with both CSM and COM predictions from PYTHIA, but slightly favors the COM prediction for the near-side Υ + h correlation.

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. / Doctor of Philosophy / Atoms, the stuff of everyday matter, consist of a number of electrons bound to a compact nucleus. This nucleus, in turn, contains one or more protons and neutrons, which are themselves made up of constituent particles called quarks that interact with one another by exchanging particles called gluons. Although great strides were made during the last century to further our understanding of the fundamental structure of matter, a comprehensive description of nuclear structure, at the quark level, eludes us. What we do know is that the force responsible for binding the large number of positively charged protons within the narrowly confined nucleus of, say, a gold atom is incredibly strong---in reality, more than 137 times as strong as the electromagnetic (EM) interaction, which is responsible for binding electrons around the nucleus in atoms. Unlike the EM force, which has one charge that can be either positive or negative, the strong interaction has three. This leads to a manifestly more complicated phenomena whose mathematical descriptions are computationally intractable. To study the strong interaction, we seek out the simplest of strongly bound states---called the meson---which consist of a quark and its anti-particle counterpart. The meson made up of a bottom quark/anti-quark pair, called bottomonium, provides an ideal laboratory for our investigations. In bottomonium, the quarks are very heavy (about 4.5 times the mass of a proton) and move relatively slowly compared to the quarks within a proton. This allows for some simplifications in the mathematical description of the bottomonium system, making it possible to compute predictions that can be tested in the lab. In this low energy regime, the strong interaction gives rise to a family of excited bottomonium states that have a structure similar to the excited states of an atom. Just as scientists learned about the EM interaction by studying the decays of excited atomic states, so too do we study the strong force by measuring the decays of bottomonium states. We call this study heavy quarkonium spectroscopy. When excited bottomonium states transition to lower-energy states, they may emit photons (as excited atoms do) or gluons. These emitted gluons, in turn, produce other particles. Measurements of the decay rates of bottomonium states may be predicted from the mathematical description of the strong interaction, providing direct experimental tests of the theoretical models. This dissertation presents a study of the decays of several bottomonium states, which are produced at the Belle experiment at the KEKB electron--positron collider. The decay rates, called the branching fractions, of these transitions are measured and used to test the prediction from theory, which we calculate. This work is leveraged to search for several previously unobserved decays, which are expected to be exceptionally rare.

We investigate charmonium production in the hot medium created by heavy-ion collisions by setting up a framework in which in-medium charmonium properties are constrained by thermal lattice QCD (lQCD) and subsequently implemented into kinetic approaches. A Boltzmann transport equation is employed to describe the time evolution of the charmonium phase space distribution with the loss and gain term accounting for charmonium dissociation and regeneration (from charm quarks), respectively. The momentum dependence of the charmonium dissociation rate is worked out. The dominant process for in-medium charmonium regeneration is found to be a 3-to-2 process. Its corresponding regeneration rates from different input charmquark momentum spectra are evaluated. Experimental data on J/[psi] production at CERN-SPS and BNL-RHIC are compared with our numerical results in terms of both rapidity-dependent inclusive yields and transverse momentum (pt) spectra. Within current uncertainties from (interpreting) lQCD data and from input charm-quark spectra the centrality dependence of J/[psi] production at SPS and RHIC (for both mid-and forward rapidity) is reasonably well reproduced. The J/[psi] pt data are shown to have a discriminating power for in-medium charmonium properties as inferred from different interpretations of lQCD results.