Institute of High Energy Physics, Chinese Academy of Sciences, China Glueballs in J/psi Radiative Decays Ying Chen Institute of High Energy Physics, Chinese Academy of Sciences, China 2011. 03. 19

Outline Motivation The widths of J/psi radiatively decaying to glueballs III. Numerical details IV. Summary and concluding remarks

I. Introduction QCD predicts the existence of glueballs Quenched LQCD predicts glueball spectrum Lowest-lying glueballs have masses in the range 1~3GeV Experimentally, f0(1370), f0(1500), f0(1710), etc., are glueball candidates, but decisive conclusion cannot be drawn. Due to its abundance of gluons, J/psi radiative decay can be the best hunting ground. BESIII in Beijing is producing J/psi events Y. Chen et al, Phys. Rev. D 73, 014516 (2006)

II. The widths of J/psi radiatively decaying to glueballs (We focus on the scalar glueball in this talk) Method 1: Effect theory and dispersion relation (V.A. Novikov et al. , Nucl. Phys. B 165 (1980) 67. ) By the use of dispersion relation, we have, Glueball Matrix Element

Glueball Matrix Element Calculate the amplitude Apply the dispersion relation Assume the charmonium dominance Glueball Matrix Element

Method 2: Tree-level perturbative QCD J/psi BS wave func. Glueball BS wave func. Can be calculated explicitly

J/psi BS wave func. Glueball BS wave func.

Assume c-cbar annihilate at a point Can be calculated explicitly

Glueball-to-vacuum matrix elements Lattice QCD results (quenched): Y. Chen et al, (Phys. Rev. D 73, 014516 (2006) ) H.B. Meyer (arXiv:08083151 [hep-lat]) Other phenomenological results: QCD sum rules with non-perturbative topology effects: (H. Forkel, hep-ph/0608071) Instanton liquid model: T. Schaafer and E.V. Shuryak, PRL75(1995)1707

Predictions of J/psi radiatively decaying to glueballs Method 1: two-photon-two-gluon induced H.B. Meyer, (arXiv:08083151 [hep-lat]) Method 2: Tree-level perturbative QCD results with GME by QLQCD (Y. Chen, G. Li, and Y.J. Zhang )

Method 3: Direct calculation in LQCD The decay width of J/psi radiatively decaying to the scalar glueball can be derived from the formular where E1(0) is the on-shell form factor, which appears in the matrix elements (J.J. Dudek,hep-lat/0601137) With the vector current insertion , these Matrix elements can be calculated through the three point function,

After the intermediate state insertion, the three-point function can be written as Two-point function of vector meson

III. Numerical details 1. Actions bare speed of light, should be tuned to give the correct dispersion relation

Self consistent check of the speed of light for J/psi

5000 gauge configurations, separated by 100 HB sweeps 3. Configurations and quark propagators In order to get fair signals of the three point functions, a large enough statistics is required. 5000 gauge configurations, separated by 100 HB sweeps Charm quark mass is set by the physical mass of J/psi On each configuration, 96 charm quark propagators are calculated with point sources on all the 96 time slices. The periodic boundary conditions are used both for the spatial and temporal directions.

4. The glueball operators Building prototypes (various Wilson loops) Smearing: Single link scheme (APE) and double link scheme (fuzzying) The essence of the VM is to find a set of combinational coefficients such that the operator couples mostly to a specific state.

The horizontal line is the theoretical prediction with . It is seen that the deviations are less than 5% The energies of 27 momentum modes of scalar glueballs are calculated. Plotted are the plateaus using the optimized operators

5. Three point functions Temporarily, we only analyze the following cases:

The plots for the ratios Exponential fit by taking the glueball energies as known parameters

These are known functions

6. The control of systematic uncertainties The continuum extrapolation

The lattice vector current has not been renormalized. The uncertainty owing to the quenched approximation. ( Cannot be resolved in the near future.)

2.4 1.36 0.049(7) 2.8 1.54 8. The form factor and the decay width Polynomial fit: The branch ratio is Branch ratio 2.4 1.36 0.049(7) 2.8 1.54

Experimental results for J/psi radiatively decaying to scalars C. Amsler et al., Phy. Lett. B667, 1 (2008)

E. Klempt, A. Zaitsev, Phys. Rept. 454 (2007).

Partial decay widths of scalar mesons Flavor-blindeness of glueball decays

Glueballs couplings to two photons Since gluons are electrically neutral, glueball production in two-photon collisions and glueball Decays into two photons are suppressed.

Stickness (Chanowitz): f0(1500) and f0(1710) have large stickness, in particular for the f0(1710). The f0(1500) is not directly observed in J/psi hadronic decays in BES. Searching for the f0(1500) in more decay modes and studying its spin-parity will be crucial for clarifying its nature.

Chiral suppression (Carlson, Chanowitz): Due to the fact that in pQCD the amplitude is propoportional to the current quark mass in the final state, J=0 glueballs should have larger couplings to e.g. KKbar than to pion-pion.

Glueball-qqbar meson mixing pattern Close&Kirk Maiani et al Tetraquark picture Fariborz Nonlinear Chiral model

f0(1370) f0(1500) f0(1710) √ √ √ √ ? Flavor blandness Stickiness Two photon couplings Chiral suppression Mixing pattern √ √ √ Radiative production as a scalar glueball ?

IV. Summary and concluding remarks For the first time, the form factors relevant to the J/psi radiatively decaying to glueballs are calculated in the quenched lattice QCD. With these form factors, the decay widths can be predicted more reliably. We obtain a raw estimation of the branch ratio We are also working on other channels, such as tensor and pseudoscalar. This work is in the quenched approximation The mixing of glueballs and conventional mesons should be considered.

IV. Future work

Charmonium and Hybrid Charmonium Ying Chen, Longcheng Gui, Yi-Bo Yang

I. Motivation X(3872) Experimental facts: Belle, CDFII, and D0 have found a charmonium-like narrow resonance Its productions and decays suggest that its quantumnumber is mostly likely 1++. Recently, the angular distribution analysis of BaBar favors its quantum number 2-+

Theoretical study of its status: If 1++ conventional charmonium, its mass is almost 100 MeV lower than the precdiction of “successful” non-relativistic potential model and 200 MeV lower than previous quenched lattice QCD study. Its width is so small. These facts motivate the speculation that it do not be a conventional charmoium state. Many theorist interpret it as an exotic state, such as molecule state, hybrid, tetraquark state, etc.

Foldy-Wouthuysen-Tani transformation:

~4.3-4.5GeV Note that 1-+ hybrid chanonium is estimated to have a mass of 4.3 GeV or so.

Discussion

3.410(18) 3.477(14) 3.488(13) 3.410(18) 3.477(14) 3.488(13) 3.825(88) 3.852(57) 3.858(70) 3.825(88) 3.852(57) 3.858(70)

Bottomium system Charmonium system

1P bottomium center : M(1P) = 9900 MeV

Thank You!