1. 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

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

3. 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, (2006)

4. 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

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

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

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

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

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

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

11. 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/ )
With the vector current insertion , these
Matrix elements can be calculated through the three point
function,

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

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

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

16. 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.

17. 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.

18. 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

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

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

21. These are known functions

22. 6. The control of systematic uncertainties
The continuum extrapolation

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

24. 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

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

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

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

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

29. 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.

30. 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.

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

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

33. 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.

34. IV. Future work

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

36. 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-+

37. 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.

41. Foldy-Wouthuysen-Tani transformation:

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

48. Discussion

49. 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)

50. Bottomium system
Charmonium system

51. 1P bottomium center : M(1P) = 9900 MeV

52. Thank You!