The masses of 1 −− charmonium and bottomonium hybrids are evaluated in terms of QCD sum rules. We find that the ground state hybrid in charm sector lies in m Hc = 4.12 ∼ 4.79 GeV, while in bottom sector the hybrid may situated in m H b = 10.24 ∼ 11.15 GeV. Since the numerical result on charmonium hybrid mass is not compatible with the charmonium spectra, including structures newly observed in experiment, we tempt to conclude that such a hybrid does not purely exist, but rather as an admixture with other states, like glueball and regular quarkonium, in experimental observation. However, our result on bottomonium hybrid coincide with the "exotic structure" recently observed at BELLE.

The generalized Chen's conjecture on biharmonic submanifolds asserts that any biharmonic submanifold of a non-positively curved manifold is minimal.In this paper, we prove that this conjecture is false by constructing a foliation of proper biharmonic hyperplanes in a 5-dimensional conformally flat space with negative sectional curvature. Many examples of proper biharmonic submanifolds of non-positively curved spaces are also given.Date: 01/18/2011. 1991 Mathematics Subject Classification. 58E20, 53C12, 53C42.

By using QCD Sum Rules, we found that the charged hidden charm tetraquark [cu][cd] states with J P = 1 − and 2 + , which are possible quantum numbers of the newly observed charmonium-like resonance Z c (4025), have masses of m c 1 − = (4.54 ± 0.20) GeV and m c 2 + = (4.04 ± 0.19) GeV. The contributions up to dimension eight in the operator product expansion were taken into account in the calculation. The tetraquark mass of J P = 2 + state was consistent with the experimental data of Z c (4025), suggesting the Z c (4025) state to possess the quantum number of J P = 2 +. Extending to the b-quark sector, the corresponding tetraquark masses m b 1 − = (10.97 ± 0.25) GeV and m b 2 + = (10.35 ± 0.25) GeV were obtained, which values are testable in future B-factories.

With appropriate interpolating currents the mass spectrum of 0 −− oddball is obtained in the framework of QCD Sum Rules (QCDSR). We find there are two stable oddballs with masses of 3.81±0.12 GeV and 4.33±0.13 GeV, and analyze their possible production and decay modes in experiments. Noticing that these 0 −− oddballs with unconventional quantum number are attainable in BESIII, BELLEII, PANDA, Super-B and LHCb experiments, we believe the long search elusive glueball could be measured shortly. PACS numbers: 11.55.Hx, 12.39.Mk, 13.20.Gd Quantum Chromodynamics (QCD) is the underlying theory of hadronic interaction. In the high energy regime, it has been tested up to 1% level due to the asymptotic freedom [1]. However, the nonperturbative aspect related to the hadron spectrum is difficult to be calculated from the first principle because of the confinement [2]. A unique attempt in understanding the nonperturbative aspect of QCD is to study the glueball (gg, ggg, · · · ), where the gauge field plays a more important dynamical role than in ordinary hadrons. This has intrigued much interest in theory and experiment for quite long time.In the literature, many theoretical investigations on glueball were made through various techniques, including lattice QCD [2-4], flux tube model [5], MIT bag model [6,7], Coulomb Gauge model [8] and QCD Sum Rules (QCDSR) [9][10][11][12][13][14][15][16][17]. Of these techniques, the model independent QCDSR, developed more than thirty years ago by Shifman, Vainshtein and Zakharov (SVZ) [9], has some peculiar advantages in the study of hadron phenomenology. Its starting point in evaluating the properties of the ground-state hadron is to construct the current, which possesses the foremost information about the concerned hadron, like quantum numbers and constituent quark or gluon. By using of the current, one can then construct the two-point correlation function, which has two representations: the QCD representation and the phenomenological representation. Equating these two representations, the QCDSR will be formally established.In the framework of QCDSR, the two-gluon glueballs with quantum numbers of 0 ++ [11-13] and 0 −+ [13,14] have been studied extensively in the literature. Note that these glueballs were also constructed and investigated through tri-gluons [15][16][17], which is enlightening for the research in this work.Although glueball has been searched for many years in experiment, so far there has been no definite conclusion about it, mainly due to the following three reasons: the mixing effect between glueballs and quark states, the lack of the glueball production mechanism, and the lack of the necessary knowledge about glueball decay properties. Of these difficulties, from the experimental point of view, the most outstanding obstacle is how to isolate glueball from the mixed quarko- * Electronic address: qiaocf@ucas.ac.cn † Electronic address: tangl@ucas.ac.cn nium states ( qq). Fortunately, there is a class of glueballs, the unconventional glueballs, which with quantum number...

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