1. Production of exotic hadrons in photo and electroproduction
Institute of High Energy Physics
Production of exotic hadrons in photo and electroproduction
Qiang Zhao
Institute of High Energy Physics, CAS
and Theoretical Physics Center for Science Facilities (TPCSF), CAS
The spectroscopy program at EIC and future accelerators, ECT*, Trento, Dec , 2018

2. Outline
Heavy pentaquark production at LHCb and some essential issues about the underlying dynamics
Searching for the heavy pentaquarks in photo- and electro-production
Production mechanism
Quark counting rule
Spin observables
Brief summary

3. 1. Heavy pentaquark (Pc(4380) and Pc(4450)) production at LHCb and some essential issues about the underlying dynamics

4. Exp. evidence for heavy pentaquarks with hidden charm
M[Pc(4380)] = (4380829) MeV, = (2051886) MeV
M[Pc(4450)] = (4449.81.72.5) MeV, =(39519) MeV
JP = (3/2, 5/2) or (3/2, 5/2)

5. Immediate theoretical studies:
1) Molecular states:
R. Chen, X. Liu, X.-Q. Li, S.-L. Zhu, PRL(2015); arXiv: [hep-ph]
L. Roca, J. Nieves and E. Oset, arXiv: [hep-ph].
A. Feijoo, V. K. Magas, A. Ramos and E. Oset, arXiv: [hep-ph]
J. He, arXiv: [hep-ph]
U.-G. Meissner, J.A. Oller, arXiv: v1 [hep-ph]
2) Multiquark state as an overall color singlet
L. Maiani, A.D. Polosa, and V. Riquer, arXiv: [hep-ph]
R.L. Lebed, arXiv: [hep-ph]
V.V. Anisovich et al., arXiv: [hep-ph]
G.-N. Li, X.-G. He, M. He, arXiv: [hep-ph]
3) Soliton model
N.N. Scoccolaa, D.O. Riska, Mannque Rho, arXiv: [hep-ph]
4) Sum rules study
H. X. Chen, W. Chen, X. Liu, T.G. Steele and S. L. Zhu, PRL(2015); arXiv:
Z.-G. Wang, arXiv:
Many more …
Some early studies:
J. J. Wu, R. Molina, E. Oset and B. S. Zou, PRL105, (2010) [arXiv: [nucl-th]].
J. J. Wu, R. Molina, E. Oset and B. S. Zou, PRC84, (2011) [arXiv: [nucl-th]].
J. J. Wu, T.-S. H. Lee and B. S. Zou, PRC85, (2012) [arXiv: [nucl-th]].
Z. C. Yang, Z. F. Sun, J. He, X. Liu and S. L. Zhu, Chin. Phys. C 36, 6 (2012).

6. Questions and concerns:
Why only a very small number of signals for the pentaquarks seen in experiment?
How essential to introduce the diquarks in multiquark system?
What is the role played by the open-threshold dynamics in the understanding of hadron spectroscopy and how they manifest themselves in experimental observables?
Are there possible alternative explanations for the observed signals?
What could be criteria for distinguishing these different scenarios? ……

7. “Exotics” of Type-III:
Peak structures caused by kinematic effects, in particular, by triangle singularity.
The TS occurs when all the three internal particles can approach their on-shell condition simultaneously:
for all j=1,2,3.
L. D. Landau, Nucl. Phys. 13, 181 (1959);
J.J. Wu, X.-H. Liu, Q. Zhao, B.-S. Zou, Phys. Rev. Lett. 108, (2012);
Q. Wang, C. Hanhart, Q. Zhao, Phys. Rev. Lett. 111, (2013); Phys. Lett. B 725, 106 (2013)
X.-H. Liu, M. Oka and Q. Zhao, PLB753, 297(2016);
F.-K. Guo, C. Hanhart, U.-G. Meissner, Q. Wang, Q. Zhao, B.-S. Zou, arXiv: [hep-ph], Rev. Mod. Phys. 90, (2018)

8. Production mechanism in b decay
Leading production of c*D(*) instead of c*D(*) !
Conerns:
Most theoretical calculations show that c*D(*) interaction is more attractive than that for c*D(*).
Possible solution (1):
Important coupled-channel between the c*D(*) and c*D(*) channels are needed.

9. 1/mQ << 1/mq Possible solution (2):
Color-suppressed transitions may not be so suppressed!
Favored by the molecular picture although color suppressed.
However, compact light diquark should be ruled out.
1/mQ << 1/mq

10. Rescattering via triangle diagrams are possible
Thresholds for cJ p
X.-H. Liu, Q. Wang, and Q. Zhao, arXiv: [hep-ph]

12. Invariant mass distribution of J/ p with different K−p momentum cuts

13. The ATS can mimic a resonance behavior in certain cases
F.-K. Guo, U.-G. Meissner, W. Wang, and Z. Yang, arXiv: [hep-ph]

14. 2. Searching for the heavy pentaquarks in photo- and electro-production

15. J/ photoproduction near threshold:
Diffractive dominant at forward angle: Pomeron exchange model
Q. Wang, X.-H. Liu, and Q. Zhao, PRD(2015); arXiv: [hep-ph]

16. Kinematic features of the production mechanism
Forward angle peaking is predominant due to the diffractive process, i.e. Pomeron exchanges.
S-channel resonance excitations contribute to the cross sections at middle and backward angles.
U-channel contributes to backward angles.
d/d
t-channel:
Pomeron exchange
s-channel
u-channel
Interferences from different transition mechanisms 90
180
Scattering angle

17. s and u-channel pentaquark production
Coupling vertices for NPc:
S. H. Kim, S. i. Nam, Y. Oh and H. C. Kim, PRD 84, (2011)
Q. Wang, X.-H. Liu, and Q. Zhao, arXiv: [hep-ph]

18. Coupling vertices for J/NPc:
Leading transition matrix elements:
Rarita-Schwinger spin projections:
with

19. Vector meson dominance 
J/
J/
eh1 g1
J/ Pc Pc p p p p e+
J/ e
By assuming that the J/ p saturate the decay widths of the Pc states, we have
A form factor is included:

20. Total cross sections predicted:
Full width prediction
Prediction with 5% of b.r. to J/ p:
Challenge:
J/psi p CANNOT be the dominant decay channel of these pentaquark candidates!

21. Predicted differential cross sections at different energies:
W= 4.15 GeV
W= 4.38 GeV
W= 4.45 GeV
W= 4.50 GeV

22. Predicted differential cross sections at different energies:
W= 4.15 GeV
W= 4.38 GeV
W= 4.45 GeV
W= 4.50 GeV
What are the effective D.O.F. if hidden charm pentaquarks do exit?

23. Quark-hadron duality Bloom-Gilman Duality
The electroprod. of N* at low energies and momentum transfers empirically averages smoothly around the scaling curve for nucleon structure function F2(W2,Q2) measured at large momentum transfers for both proton and neutron targets.
Low-energy reso. phenomena
 High-energy scaling behaviour
Degrees-of-freedom duality
Hadronic degrees of freedom
 Quark-gluon degrees of freedom
Nachtmann scaling variable:
=2x/[1+(1+4M2 x2 /Q2 )1/2],
where x=Q2/2M2
Bloom and Gilman, PRD4, 2901 (1971); Close, Gilman and Karliner, PRD6, 2533 (1972); I. Niculescu et al, Phys. Rev. Lett. 85, 1182 (2000); 85, 1186 (2000).

24. Photoproduction from threshold to the region beyond resonances M
N*,*
Strong EM N N
g + p -> p + p- + p+
g + p -> p + p0 + p0
g + p -> p + p0
g + p -> K+ + L
g + p -> p + h

25. Quark counting rules (QCR)
At high energy and large transverse momentum, the differential cross section for a two-body reaction A + B  C + D scales as:
t =(pA–pC) =(pB–pD)2
A,
C, M
s =(pA+pB) =(pC+pD)2
B, N
D, N   p n
Brodsky and Farrar, PRL31, 1153 (1973); PRD11, 1309 (1975).
Matveev, Muradian and Tavkhelidze, Nuovo Cim. Lett. 7, 719 (1973).
Lepage and Brodsky, PRD22, 2157 (1980).

26. Exclusive photoproduction reactions at fixed scattering angles
Other channels are also measured
Anderson et al., PRD14, 679 (1976)

27. Scaled? Oscillating?   p    n
Oscillatory deviations from the scaling behavior of dimensional quark-counting rules above the nucleon resonance region.
  p    n
Scaled?
Oscillating?
L. Y. Zhu et al., Phys. Rev. Lett. 91, (2003); L.Y. Zhu et al., PRC71, (2005)

28. Soft contribution dominant
Dashed curves: Soft contributions
Solid curves: Leading asymptotic contributions
Dot-dashed: Bound on the leading asymptotic contributions
Isgur and Llewellyn Smiths, PRL52, 1080 (1984)

29. Bloom-Gilman duality realized in the quark model
How does the square of sum become the sum of squares? Close and Isgur 
F1n / F1p =2/3
F1p,n ~1/2 + 3/2
hadrons
g1 p / F1p =5/9
g1 p,n ~ 1/2  3/2
p,n
g1n / F1n =0
For F1p,n and g1p , duality is recognized with the sum over both 56 and 70 states and negative parity ones.
For g1n , the duality could be localized to 56 states alone.
Close, Gilman, and Karliner, PRD6, 2533 (1972); Close and Isgur, PLB 509, 81 (2001)

30. Manifestation of duality in exclusive reaction and restricted locality of quark-hadron duality  Pi y z Pf Pi Pf
Sum over intermediate states: r
q1, e1
q2, e2 R r1 r2
Close and Zhao, PRD 66, (2002)

31. Forward scattering (Close and Isgur’s duality) :   0
where the coherent term (~e1e2) is suppressed due to destructive interferences.
The square of sum of charges becomes the sum of squared charges

32. Large angle scattering:  = 90
i) At high energies, i.e. in the state degeneracy limit with s >> mN*, all terms of N > 0 (L=0, …, N) vanish due to destructive cancellation: (–C22+C20) 0; (3C44–10C42+7C40) 0; …
R(t) : QCR-predicted scaling factor.
Close and Zhao, PRD 66, (2002); PLB 553, 211(2003);
Zhao and Close, PRL 91, (2003)

33. s1/2 Large angle scattering:  = 90
At intermediate high energies, i.e. state degeneracy is broken, terms of N > 0 (L=0, …, N) will not vanish: (–C22+C20)  0; (3C44–10C42+7C40)  0; …
Deviations from QCR due to higher excited states are expected !
The presence of hidden charm pentaquarks will lead to deviations from QCR at =90.
The differential cross section measurement should be a direct probe for pentaquarks with hidden heavy flavors!
s7d/dt (=90)
s1/2
Close and Zhao, PRD 66, (2002); PLB 553, 211(2003);
Zhao and Close, PRL 91, (2003)

34. Spin observables sensitive to pentaquarks
Helicity amplitudes: x z
V, q, V y x
, k,
cm z
N, Pi , 1 y
N, Pf , 2
General form for spin observable :
Where A, AN, BV and BN denote the Hermitian spin matrices for the initial and final state hadrons.
M. Pichowsky, C. Savklı, and F. Tabakin, PRC53, 593 (1996);
Q. Zhao, J. Al-Khalili, P. Cole, PRC71, (2005)

35. With the density matrix for the incident photon polarization:
The general form of the angular distribution for the vector meson decays into final states can be expressed as:
The angular distribution can be written in terms of the vector meson density matrices elements (DMEs) vv:
The vector meson DMEs can be related to the photon polarizations:

36. The polarized beam asymmetry:x
The polarized beam asymmetry: z
V, q, V y x
, k,
cm z
N, Pi , 1 y
N, Pf , 2  
Interference between the background terms and resonance amplitude is anticipated.
Advantage: S-channel resonances can interfere with the Pomeron exchange term and produce drastic change of asymmetries at large angles.

37. Photoproduction of Zc(4430) observed in psi’ pipi:
Vector meson dominance
X.H. Liu, Q. Zhao and F. Close, PRD 77, (2008).

38. Different assignment of quantum numbers:
JPC=1+
Different assignment of quantum numbers:
JPC=1-
JPC=0-

39. Dalitz plot analysis:

40. Summary
The triangle singularity (TS) is strongly correlated with threshold phenomena and can produce observable effects when the condition is fulfilled in the physical regime.
The photo- or electro-production process can disentangle the TS mechanism from a genuine pole.
If pentaquarks with hidden heavy flavors do exist, it will cause deviations from the QCR.

41. Thanks for your attention!
Institute of High Energy Physics
Thanks for your attention!

42. Institute of High Energy Physics
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