QCD sum rule studies of heavy quarkonium-like states

In 2003 the Belle collaboration announced the discovery of the X(3872) particle. This was confirmed shortly thereafter by the CDF, D0 and BaBar collaborations, and later by the LHCb collaboration. Based on the decay modes that have been observed to date, it is clear that this particle is a hadron, that is, a composite particle that experiences the strong nuclear force. The X(3872) was found within a family of well understood hadrons called charmonia. Interestingly, it is quite difficult to interpret the X(3872) as a charmonium state. For this reason it has been widely speculated that the X(3872) cannot be understood in terms of the quark model, unlike the vast majority of hadrons observed to date. Such hitherto unobserved particles are called exotic hadrons. Since the discovery of the X(3872), many similarly anomalous charmonium-like particles have been discovered. As would be expected, some unanticipated hadrons have also been found in the closely related bottomonium spectrum. These particles are collectively referred to as heavy quarkonium-like. Evidence is growing that at least some of these particles are exotic hadrons. If confirmed, this would have dramatic implications for our understanding of the strong nuclear force. A major experimental and theoretical effort is now underway in the field of hadron spectroscopy to determine the identities of the heavy quarkonium-like states. In order to investigate the possibility that some of these states could be exotic hadrons, theoretical calculations are needed to firmly establish their properties. One of the main arguments for the existence of exotic hadrons is that they are predicted by the fundamental theory of the strong interaction, Quantum Chromodynamics (QCD). Therefore it is desirable to predict the properties of exotic hadrons using a theoretical approach that is firmly based in QCD. One such method is QCD sum rules (QSR). The research presented here uses the QSR technique to study exotic hadrons. There are several themes in this work. First is the use of QSR to predict the masses of exotic hadrons that may exist among the heavy quarkonium-like states. The second theme is the application of sophisticated loop integration methods in order to obtain more complete theoretical results. These in turn can be extended to higher orders in the perturbative expansion in order to predict the properties of exotic hadrons more accurately. The third theme involves developing a renormalization methodology for these higher order calculations. This research has implications for the Y(3940), X(3872), Zc(3895), Yb(10890), Zb(10610) and Zb(10650) particles, thereby contributing to the ongoing effort to understand these and other heavy quarkonium-like states

QCD Sum Rule Analysis of Heavy Quarkonium Hybrids

We have studied the charmonium and bottomonium hybrid states with various $J^{PC}$ quantum numbers in QCD sum rules. At leading order in $\alpha_s$, the two-point correlation functions have been calculated up to dimension six including the tri-gluon condensate and four-quark condensate. After performing the QCD sum rule analysis, we have confirmed that the dimension six condensates can stabilize the hybrid sum rules and allow the reliable mass predictions. We have updated the mass spectra of the charmonium and bottomonium hybrid states and identified that the negative-parity states with $J^{PC}=(0, 1, 2)^{-+}, 1^{--}$ form the lightest hybrid supermultiplet while the positive-parity states with $J^{PC}=(0, 1)^{+-}, (0, 1, 2)^{++}$ belong to a heavier hybrid supermultiplet.Comment: 7 pages, 1 figures. Some minor edits have been made. Presentation at the DPF 2013 Meeting of the American Physical Society Division of Particles and Fields, Santa Cruz, California, August 13-17, 201

Exploring the Spectrum of Heavy Quarkonium Hybrids with QCD Sum Rules

QCD Laplace sum rules are used to calculate heavy quarkonium (charmonium and bottomonium) hybrid masses in several distinct $J^{PC}$ channels. Previous studies of heavy quarkonium hybrids did not include the effects of dimension-six condensates, leading to unstable sum rules and unreliable mass predictions in some channels. We have updated these sum rules to include dimension-six condensates, providing new mass predictions for the spectra of heavy quarkonium hybrids. We confirm the finding of other approaches that the negative-parity $J^{PC}=(0,1,2)^{-+},\,1^{--}$ states form the lightest hybrid supermultiplet and the positive-parity $J^{PC}=(0,1)^{+-},\,(0,1,2)^{++}$ states are members of a heavier supermultiplet. Our results disfavor a pure charmonium hybrid interpretation of the $X(3872)$, in agreement with previous work.Comment: Presented by RTK at the Theory Canada 9 Conference, held at Wilfrid Laurier University in June 2014. Submitted for the conference proceedings to be published in the Canadian Journal of Physics. 5 pages, 1 figure. Version 2: reference added, typo correcte

Mass Predictions for Pseudoscalar JPC=0−+J^{PC}=0^{-+} Charmonium and Bottomonium Hybrids in QCD Sum-Rules

Masses of the pseudoscalar $(J^{PC}=0^{-+})$ charmonium and bottomonium hybrids are determined using QCD Laplace sum-rules. The effects of the dimension-six gluon condensate are included in our analysis and result in a stable sum-rule analysis, whereas previous studies of these states were unable to optimize mass predictions. The pseudoscalar charmonium hybrid is predicted to have a mass of approximately 3.8 GeV and the corresponding bottomonium prediction is 10.6 GeV. Calculating the full correlation function, rather than only the imaginary part, is shown to be necessary for accurate formulation of the sum-rules. The charmonium hybrid mass prediction is discussed within the context of the X Y Z resonances.Comment: 10 pages, 7 embedded figures. Analysis extended and refined in v