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Register a new userQCD Sum Rule Studies of Heavy Quarkonium-like States
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Robin Kleiv
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The research presented here uses QCD sum rules (QSR) 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 $Y(3940)$, $X(3872)$, $Z_c^pmleft(3895right)$, $Y_bleft(10890right)$, $Z_b^{pm}(10610)$ and $Z_b^{pm}(10650)$ particles, thereby contributing to the ongoing effort to understand these and other heavy quarkonium-like states.
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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.
The in-medium masses of the bottomonium ground states [$1S$ ($Upsilon (1S), eta_b$) and $1P$ ($chi_{b0},chi_{b1}$)] are investigated in the magnetized vacuum (nuclear medium), using the QCD sum rule framework. In QCD sum rule approach, the mass modifications are calculated in terms of the medium modifications of the scalar and twist-2 gluon condensates, which are obtained in the nuclear medium, from the medium change of a scalar dilaton field, $chi$ within a chiral effective model. The in-medium masses of the bottomonium ground states are observed to decrease with increasing density. P-wave states are observed to have more appreciable mass-shifts than the S-wave states. In the present investigation, the effects of spin-mixing between 1S bottomonium states, $Upsilon(1S)$ and $eta_b$ are taking into account in presence of an external magnetic field. The contribution of magnetic fields are seen to be dominant via spin-magnetic field interaction effects, which leads to an appreciable rise and drop in the in-medium masses of the longitudinal component of vector $1S$ state ($Upsilon$) and pseudoscalar state ($eta_b$) respectively. For zero magnetic field, the effects of baryon density on the bottomonium ground states in isospin asymmetric nuclear medium are observed to be quite appreciable. These should have observable consequences for the production of the open and hidden bottom meson states resulting from high energy asymmetric nuclear collisions in facilities which probe high density baryonic matter. There is observed to be large contributions to the masses of the longitudinal component of the vector bottomonium state, $Upsilon (1S)$ and pesudoscalar state $eta_b$ in strong magnetic fields.
We use QCD Laplace sum-rules to explore mixing between conventional mesons and hybrids in the heavy quarkonium vector $J^{PC}!=!1^{--}$ channel. Our cross-correlator includes perturbation theory and contributions proportional to the four-dimensional and six-dimensional gluon condensates. We input experimentally determined charmonium and bottomonium hadron masses into both single and multi-resonance models in order to test them for conventional meson and hybrid components. In the charmonium sector we find evidence for meson-hybrid mixing in the $J/psi$ and a $approx4.3$ GeV resonance. In the bottomonium sector, we find that the $Upsilon(1S)$, $Upsilon(2S)$, $Upsilon(3S)$, and $Upsilon(4S)$ all exhibit mixing.
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.
We use QCD Laplace sum-rules to study meson-hybrid mixing in vector ($1^{--}$) heavy quarkonium. We compute the QCD cross-correlator between a heavy meson current and a heavy hybrid current within the operator product expansion. In addition to leading-order perturbation theory, we include four- and six-dimensional gluon condensate contributions as well as a six-dimensional quark condensate contribution. We construct several single and multi-resonance models that take known hadron masses as inputs. We investigate which resonances couple to both currents and so exhibit meson-hybrid mixing. Compared to single resonance models that include only the ground state, we find that models that also include excited states lead to significantly improved agreement between QCD and experiment. In the charmonium sector, we find that meson-hybrid mixing is consistent with a two-resonance model consisting of the $J/psi$ and a 4.3~GeV resonance. In the bottomonium sector, we find evidence for meson-hybrid mixing in the $Upsilon(1S)$, $Upsilon(2S)$, $Upsilon(3S)$, and $Upsilon(4S)$.
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