1. Institute of High Energy Physics, CAS
Review of theoretical prescriptions for the charged heavy quarkonium states
Qiang Zhao
Institute of High Energy Physics, CAS
and Theoretical Physics Center for Science Facilities (TPCSF), CAS
The Seventh International Symposium on Chiral Symmetry in Hadrons and Nuclei, Beihang University, Oct , 2013

2. Outline Experimental evidence for exotic candidates
Understanding the nature of Zc(3900) and relevance
3. Some remarks

3. 1. Experimental evidence for exotic candidates

4. Quantum Chromo-Dynamics:
a highly successful theory for Strong Interactions
Conventional hadrons
Meson
Confinement
Baryon
Asymp. freedom

5. Multi-faces of QCD: Exotic hadrons
Hybrid
Glueball
Tetraquark
Pentaquark
Proton
Hadronic molecule u d u  d
Neutron d u
Deuteron: p-n molecule
The study of hadron structures and hadron spectroscopy should deepen our insights into the Nature of strong QCD.

6. Close to DD* threshold
QWG, [hep-ph]
X(3872)
X(3900)
Close to DD* threshold
Y(4260)
Y(4360)

7. Charged heavy quarkonium states observed in exp.
Panel discussion in Charm 2013, Aug. 31-Sept. 4, 2013, Manchester

8. It could be an opportunity for understanding the mysterious Y(4260).
Y(4260)  e Zc
J/
The mass of the charged charmonium-like structure Zc(3900) is about GeV, close to DD* threshold!
It could be an opportunity for understanding the mysterious Y(4260).
BESIII, PRL110, (2013) [arXiv: [hep-ex]]

9. Belle, PRL110, 252002 (2013) [arXiv:1304.0121v1 [hep-ex]]
Xiao et al., arXiv: v1 [hep-ex]

10. BESIII Collaboration, arXiv:1308.2760 [hep-ex]

11. Zc(4020)
Zc(3900)?
Y(4260)
m(Zc(4020)) =
(Zc(4020)) =
Both Zc(4025) and Zc(4020) are close to the D*D* threshold. Are they the same state?
BESIII Collaboration, arXiv: [hep-ex]

12. JP = 1 Direct determination of the spin-parity! Zc(3900)? JP = 1
BESIII Collaboration, arXiv: [hep-ex]

13. BESIII, PRL110, 252001 (2013) [arXiv:1303.5949 [hep-ex]]
Cited 81 times within half a year!
Theoretical interpretations:
Hadro-quarkonium (M. Voloshin et al.)
Tetraquark (L. Maiani et al.)
Born-Oppenheimer tetraquark (E. Braaten)
Hadron loops (X. Liu et al.)
Hadronic molecule produced in a singularity condition
Would Zc(3900) and Zc’(4020/4025) be an analogue of the Zb and Zb’ in the charm sector?
How those states are formed? Are there always “thresholds” correlated?
What is the dominant decay channel of Zc and Zc’ ?
What can we learn about the production mechanism for Zc and Zc’ from the lineshape measurement of J/psi pipi and hcpipi ?
How to distinguish various proposed scenarios?
… …

14. 2. Understanding the nature of Zc(3900) and relevance

15. Hadro-quarkonium Dubynskiy & Voloshin, PLB2008;
Voloshin, [hep-ph]
Hadro-quarkonium
The QQ pair forms a tightly bound system whose wave function is close to that of one of the heavy quarkonium states. The heavy quark pair is embedded in a spatially large excited state of light mesonic matter and interacts with it by a QCD analog of Van der Waals force.

16. Expectations:
The simplest configuration for Zc(3900) is 1(cc) + 0(qq) .
In the hadro-quarkonium picture, since cc is in a spin-1 state, the Zc(3900) decays into hc  and c  will be suppressed.
The Zc(3900) decays into  will be further suppressed than into J/ due to the distortion effects from the light quark environment in comparison with the tetraquark picture.
Similar to the tetraquark scenario, the decays of Zc(3900) into open charm states, e.g. DD* and D*D*, will be suppressed by the heavy quark spin symmetry in comparison with molecule picture.
Existenc of JP=0 state Wc?

17. Tetra-quark state
The pairs Qq and Qq form relatively tightly bound diquark and antidiquark, which interact by the gluonic color force.
Maiani et al.,
The tetraquark mass spectrum can be evaluated in the constitutent QM.
See also:
Hogaasen, Kou, Richard, and Sorba,

18. But nothing for Zc’ can be compared with the theory-expected Zc(3760)!

19. Born-Oppenheimer approximation
E. Braaten, [hep-ph]
Born-Oppenheimer approximation
The heavy quark and antiquark, i.e. c and c, move adiabatically in Born-Oppenheimer potentials defined by energies of gluons and light quarks with isospin 1. Zc(3900) is an analog of the charmonium hybrid with the excitation of the gluon field replaced by an isospin-1 excitation of the light-quark fields.
Assuming the lowest-energy light-quark excitation in a neutral quarkonium tetraquark is also 1, one expect that the neutral Zc has JPC= 1 !
This scenario has been ruled out by the recent BESIII measurement of the quantum number. q Q Q q

20. “ISPE model” Total amplitudes: Parameters: Direct contributions
The production of Zb, Zb’, and Zc are due to interferences of several transition processes. One key point is that the “direct contribution” can emit the energetic pions via four-point contact interactions at a given c.m. energy W.
Chen, Liu, et al., ;
Direct contributions
Dipion resonances
ISPE mechanism with D*D and D*D*
Total amplitudes:
Parameters:

21. Questions:
The pion emission via local four-point interactions would break down when the pion momentum is much larger than QCD. In such a case, the non-local interaction should be more important.
Some of the relative phases are not well understood.
No implementation of heavy quark spin symmetry.
Parameterized BW for sigma and f0(980).

22. Hadronic molecule produced in a singularity condition -- The nature of Zc(3900) and Y(4260)

23. Hadronic molecule – an analogue to Deuteron
Heavy-light quark-antiquark pairs form heavy mesons, and the meson-antimeson pair moves at distances longer than the typical size of the meson. The mesons are interacting through exchange of light quarks and gluons, similar to nuclear force.
Proton u d u  d
Neutron d u
Deuteron: p-n molecule

24. Weinberg’s Compositeness Theorem
Weinberg (1963); Morgan et al. (1992); Baru, Hanhart et al. (2003); G.-Y. Chen, W.-S. Huo, Q. Zhao (2013) ...
 Probability to find the hadronic molecule component in the physical state A
The effective coupling geff encodes the structure information and can be extracted model-independently from experiment.

25. i) Vector charmonium production in ee annihilations
1, (cc)/(bb) … q
Charmed meson pair production, i.e. D(0)D(0), D*(1)D*(1),
D*D +DD*… e+ * q e c
Belle, BaBar, and BESIII
Direct production of vector charmonium (JPC=1) states.
Dynamics for vector charmonium interactions with final states.
Signals for vector exotics, e.g. Y(4260)? Or exotics produced in vector charmonium decays, e.g. X(3872) and Zc(3900)? ……

26. Observation of Y(4260) in J/  spectrum
PRD77, (2008)
Belle

27. Cross section lineshape in e+e- annihilations into DD pair
X(3900) ?
(4040), 3S
e+e-  DD
(4160)
(4415)
What is X(3900)? (see Wang et al., PRD84, (2011))
X(3900) has not been inlcuded in PDG2010 and PDG2012.
Not in charmonium spectrum
Why Y(4260) is not seen in open charm decays?
… …
Y(4260)
Belle PRD77, (2008).

28. Opportunities for a better understanding the nature of Y(4260)
Theoretical prescriptions:
Hybrid
Tetraquark
Glueball
Hadronic molecules
Calculations done by various approaches:
Quark model
Hadron interaction with effective potentials
QCD sum rules
Lattice QCD
Cited 485 times!
See [hep-ph] for a recent review.

29. Hybrid state, F. E. Close and P. R. Page, PLB28(2005)215; S. L
Hybrid state, F.E.Close and P.R.Page, PLB28(2005)215; S.L.Zhu, PLB625(2005)212; E. Kou and O. Pene, PLB631(2005)164
Radial excitation of a diquark-antidiquark state analogous to X(3872), L.Maiani, F.Piccinini, A.D. Polosa and V. Riquer, PRD71(2005)014028
D1 D molecular state, G.J.Ding, PRD79(2009)014001; F. Close and C. Downum, PRL102(2009)242003; A.A.Filin, A. Romanov, C. Hanhart, Yu.S. Kalashnikova, U.G. Meissner and A.V. Nefediev, PRL105(2010)019101
Strongly couple to Χc0ω, M. Shi, D. L. Yao and H.Q. Zheng, hep-ph/
Hadro-quarkonium, M. Voloshin ……

30. Y(4260) could be a hadronic molecule made of DD1(2420)
D (cq), JP=0;
D*(cq), JP=1;
D1 (cq), JP=1.
Y(4260)
DD*
DD1(2420)
W= 4020 MeV
W= 4289 MeV
“threshold state”
D1(2420) D1 D*
Y(4260), 1
Y(4260) 
D(1868) D
D0
Q. Wang, C. Hanhart, QZ, PRL111, (2013); PLB(2013)

31. The signature of Y(4260) could be revealed by the associated Zc near the DD* threshold via “triangle singularity”!
[J.-J. Wu, X.-H. Liu, B.-S. Zou, and Q. Zhao, PRL108, (2012)]
Zc(3900), I,JP= 1, 1 D*
J/  D 
M(Zc)  M(D) + M(D*) = GeV
A systematic study of the singularity regions in e+e-  J/psi pipi, hc pipi and DD*pi is necessary.

32. Lagrangians in the NREFT
Y(4260)D1D coupling:
Zc(3900)DD* coupling:
D1D*pi coupling:
Q. Wang, C. Hanhart, QZ, PRL111, (2013); PLB(2013)

33. The implementation of Weinberg theorem is possible
S-wave dominates in the production of Zc(3900)
S-wave dominates in DD* scattering to J/psi pi
The Zc(3900) decays into hc pi is not necessarily suppressed by the NREFT power counting
Non-local pion radiation via triangle singularity kinematics: D1  D* D 
J/ (hc)

34. Singularity kinematics in ee J/D1  D*  D   Zc
J/
J/
(D1(2420) = 27 MeV
(D*0) = 190 keV
Wang, Hanhart and Zhao, PLB2013; arXiv: [hep-ph]

35. “prediction” from a molecular Y(4260) in J/ decay
BESIII, [hep-ex]
Q. Wang, C. Hanhart, QZ, PRL111, (2013); PLB(2013)

36. Prediction for Y(4260)  hc  with  final state interactions
Q. Wang, C. Hanhart, and Q. Zhao, PRL111, (2013).

37. Singularity kinematics in Y(4170)  J/psi 
CLEO results
Q. Wang, C. Hanhart, and Q. Zhao, PLB725, 106 (2013).

38. Further test of the Y(4260) and Zc(3900) properties in the cross section line shape measurement
Belle
BESIII
D1D
D1D
M. Cleven, Q. Wang, C. Hanhart, U.-G. Meissner, and Q. Zhao,

39. Prediction for the anomalous cross section line shape
D1D
Data from Belle

40. Invariant mass spectra for D, D*, and DD*
Signature for D1(2420) via the tree diagram.
The Zc(3900) could have a pole below the DD* threshold.

41. The puzzling Y(4260) may have a prominent D1D molecular component.
Given the existence of a pole structure for Zc(3900), its production will be driven by the low-momentum DD* scattering via “triangle singularity”.
The threshold phenomena explains the significant heavy quark spin symmetry breaking.
Experimental observations of those “threshold states” , e.g. Z(4430), Zb’s, and Zc’s, have significantly enriched the hadron spectroscopy which are beyond the simple qq picture. The study of the production mechanisms for those states will provide novel insights into the underlying dynamics.
… …

42. 3. Some remarks We are far from knowing the detailed properties of the strong QCD in hadron structure and hadron interactions. The observation of those “threshold states” expose another face of the strong QCD apart from the nuclear interaction.

43. Something we don’t know whether we know:
Something we know:
Ground states are well established in the quark model.
Recently a large number of excited states (XYZ) are observed in experiment. Some of them can be accommodated by the conventional quark model while some cannot!
Lattice QCD still cannot provide a full quantitative description of the hadron spectroscopy.
Something we don’t know whether we know:
Do we have efficient and sufficient criteria for identifying exotic hadrons?
Do we have indisputable evidence for exotic hadrons?
Where to look for exotic hadrons?
… …

44. Thanks for your attention!

45. On the Zb(10610) and Zb(10650)

46. Resonant structure Z(4430)
Charged charmonium-like states
S.K. Choi et al., PRL 100, (2008)
Resonant structure Z(4430)
Close to D*D01 threshold
Q = 1, JP= 0,1,2
M= 4433 MeV
= 45 MeV
First direct evidence for an exotic quark configuration, i.e. (cc ud).

47. Observation of charged bottomonium Zb and Zb’
[(5S) (1,2,3S) +–] >> [(4,3,2S) (1S) +–]
(11020, 6S)
11.00
(10860, 5S)
partial width (keV) – +
10.75
260 Zb
(4S)
2M(B)
10.50 2 +
(3S)
Mass, GeV/c2
hb(2P)
10.25
430 1
b(2S)
(2S)
10.00
hb(1P)
290 6
9.75
9.50
(1S)
b(1S)
Belle, Phys. Rev. Lett. 108 (2012)

48. Belle, arXiv:1105.4583[hep-ex]; PRL108, 22001 (2012)
Heavy quark symmetry breaking?

49. (5S)→B*B(*)π: Results
Branching fractions of (10680) decays (including neutral modes):
BBp < 0.60% (90%CL)
BB*p = 4.25 ± 0.44 ± 0.69%
B*B*p = 2.12 ± 0.29 ± 0.36%
Assuming Zb decays are saturated by the already observed (nS)π, hb(mP)π and B(*)B* channels, one can calculate complete table of relative branching fractions:
NEW!
Belle PRELIMINARY
B(*)B* channels dominate Zb decays !
A. Bondar at ICHEP2012

50. Resonant structure of (2S)00
Dalitz plot analysis
with Zbs
without
NEW!
Clear Zbs signals are seen in (2S)π0π0
Significance of Zb(10610) is 5.3σ (4.9σ with systematics)
Zb(10650) is less significant (~2σ)
Fit to the Zb(10610) mass gives M=10609±8±6 MeV
M(Zb )= ±2.0 MeV +
Belle PRELIMINARY
A. Bondar
at ICHEP2012 50 50

51. Including width effects for internal D1 and D*
W=4.43 GeV
(D1(2420) = 27 MeV
(D*0) = 190 keV

52. Singularity kinematics in ee (nS) 
Two singularity regions by the BB* and B*B* thresholds can appear in the same c.m. energy in the (6S) decays. Two peaks are expected!

53. Kinematic singularity at the Upsilon(5S) energy is only visible for its decays into Upsilon(3S)pipi, not for Upsilon(1S, 2S)pipi.

54. Observation of X(3872) dm = 0.35 ± 0.41 MeV
new Belle meas.
<MX>= ± 0.19 MeV
new CDF meas.
MD0 + MD*0
3871.8±0.4 MeV
dm = 0.35 ± 0.41 MeV
The mass of X(3872) does not fit in (cc) 1++ state of quark model
Small mass difference to DD* threshold
Large isospin-violating decay modes
JPC = 1 is confirmed by LHCb

55. X(3872) as an analogue to the deuteronc c
D*0
D0 u u 0 u u D0
D*0 c c
X(3872): D0D*0 with Isospin =0.
How about D0D*0 with Isospin =1? If YES, we will have three states:
D0D*0 +c.c. : [cu uc]
DD*0 +c.c. : [cd uc]
DD*0 +c.c. : [cu dc]
Charged charmonium states!