1. Tcc and double charm production
arXiv: [hep-ph]
Shigehiro Yasui (KEK, IPNS)
Hyodo Tetsuo (Tokyo Tech.)
Yan-Rui Liu (Tokyo Tech./Shandong U.)
Makoto Oka (Tokyo Tech.)
Kazutaka Sudoh (Nishogakusha U.)
International Workshop on using Heavy Flavors to Probe
New Hadron Spectroscopies/Dynamics
@Haeundae Grand Hotel, Busan, Nov. 2012

2. Contents
1. What’s doubly charmed exotic meson Tcc? – Mass spectroscopy
2. Tcc production in e+e- collisions
3. Summary & perspectives

3. 1. Doubly charmed mesons (Tcc)
Tetraquark Tcc1
Flavor Exotic
Lee, SY, Liu and Ko (2008)
Lee and SY (2009)
✓ no annihilation
Tcc1
Important for study of
quark-quark correlation
color confinement c d u
I(JP)=0(1+)
strong ud
attraction
Gluon exchange force induces color-spin interaction
ud pair
1/mC0
dominant attraction (3c, I=0, 1S0)
cu pair
1/mC1
suppressed
cc pair
1/mC2
more suppressed

4. 1. Doubly charmed mesons (Tcc)
Tetraquark Tcc1
Flavor Exotic
Lee, SY, Liu and Ko (2008)
Lee and SY (2009)
✓ no annihilation
Tcc1 c d u
Tcc is double charm |C|=2.
cf. X(3872) is |C|=0.
I(JP)=0(1+)
strong ud
attraction
Gluon exchange force induces color-spin interaction
ud pair
1/mC0
dominant attraction (3c, I=0, 1S0)
cu pair
1/mC1
suppressed
cc pair
1/mC2
more suppressed

5. 1. Doubly charmed mesons (Tcc)
Doubly charmed compact tetraquark I(JP)=0(1+)
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D(*)D(*) molecules with I(JP)=0(0-), 0(1+), 0(1-), 0(2+), 0(2-), 1(0-)
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Lattice QCD (bottom) with I(JP)=0(0+) (?)
・ P. Bicudo, M. Wagner, arXiv: [hep-ph].
・ Z. S. Brown, K. Orginos, arXiv: [hep-lat]. c d u
Tetraquark Tcc1
Flavor Exotic
Lee, SY, Liu and Ko (2008)
Lee and SY (2009)
✓ no annihilation c d u
Tcc1
I(JP)=0(1+)
cc pair
1/mC2
ud pair
1/mC0
cu pair
1/mC1
Gluon exchange force induces color-spin interaction
more suppressed
dominant attraction (3c, I=0, 1S0)
suppressed
strong ud
attraction
D*- D0
≈ 75 MeV (Binding energy)
D* threshold (3880 MeV) D
Stable bound state (weak decay only; D*Kπ) u c d +

6. 1. Doubly charmed mesons (Tcc)
Λc,Σc,Σc*(cqq)
Tcc(ccqq)
q=u,d,s cc qq
flavor SU(3) qq
flavor SU(3)
Σc 1/2+ Σc* 3/2+
3c(3S1) ×
3c(3S1)
3c(3S1)
“bad” diquark
D*D* threshold
color-spin interaction
（fine mass-splitting）
200 MeV
DD* threshold
75 MeV
“good” diquark
Tcc1
Λc 1/2+ 1+ ×
3c(1S0)
3c(3S1)
3c(1S0)

7. 1. Doubly charmed mesons (Tcc)
Λc,Σc,Σc*(cqq)
Tcc(ccqq)
q=u,d,s cc qq
flavor SU(3) × qq
new!!
6c(1S0)
6c(1S0)
flavor SU(3) 0+
Σc 1/2+ Σc* 3/2+
3c(3S1) ×
3c(3S1)
3c(3S1)
“bad” diquark
D*D* threshold × 1+
new!!
6c(1S0)
6c(3S1)
color-spin interaction
（fine mass-splitting）
200 MeV
DD* threshold
75 MeV
“good” diquark
Tcc1
Λc 1/2+ 1+ ×
3c(1S0)
3c(3S1)
3c(1S0)

8. 1. Doubly charmed mesons (Tcc)
Λc,Σc,Σc*(cqq)
Tcc(ccqq)
q=u,d,s cc
3c(1S0)
6c(3S1)
3c(3S1)
6c(1S0)
125 MeV
75 MeV
25 MeV 1+ 0+ qq
flavor SU(3) × qq
new!!
6c(1S0)
flavor SU(3)
Σc 1/2+ Σc* 3/2+
3c(3S1) ×
3c(3S1)
“bad” diquark
D*D* threshold ×
new!!
6c(1S0)
color-spin interaction
（fine mass-splitting）
200 MeV
DD* threshold
75 MeV
“good” diquark
Tcc1
Λc 1/2+ ×
3c(1S0)
3c(3S1)

9. 1. Doubly charmed mesons (Tcc)
Λc,Σc,Σc*(cqq)
Tcc(ccqq)
q=u,d,s cc
3c(1S0)
6c(3S1)
3c(3S1)
6c(1S0)
125 MeV
75 MeV
25 MeV 1+ 0+ qq
flavor SU(3) × qq
new!!
6c(1S0)
flavor SU(3)
Σc 1/2+ Σc* 3/2+
3c(3S1) ×
3c(3S1)
“bad” diquark
D*D* threshold ×
new!!
6c(1S0)
color-spin interaction
（fine mass-splitting）
200 MeV
DD* threshold
State mixing is suppressed
by O(1/mc) in color-spin int.
75 MeV
“good” diquark
Tcc1
Λc 1/2+ ×
3c(1S0)
3c(3S1)

10. 1. Doubly charmed mesons (Tcc)
Λc,Σc,Σc*(cqq)
Tcc(ccqq)
q=u,d,s cc
3c(1S0)
6c(3S1)
3c(3S1)
6c(1S0)
125 MeV
75 MeV
25 MeV 1+ 0+ qq
flavor SU(3) × qq
new!!
6c(1S0)
flavor SU(3)
Σc 1/2+ Σc* 3/2+
3c(3S1) ×
3c(3S1)
“bad” diquark
D*D* threshold ×
new!!
6c(1S0)
color-spin interaction
（fine mass-splitting）
200 MeV
Tcc1 [6c]
DD* threshold
State mixing is suppressed
by O(1/mc) in color-spin int.
75 MeV
“good” diquark
Tcc1 [3cbar]
Tcc1
Λc 1/2+ ×
3c(1S0)
3c(3S1)

12. Question to be addressed
What is the production of Tcc1 [3cbar] and Tcc1 [6c] from e+e- collisions in Belle?
Tcc1 [3cbar] ???
Tcc1 [6c] ??? cc e+ e- X
(unobserved for cbarcbar)
Cf. double charm production (cccbarcbar) in e+e- collisions
(Belle, Phys. Rev. Lett. 89, (2002))

13. 2. Tcc production in e+e- collisions
L.O.
p/2
inclusive process c
Tcc1 [3cbar] or Tcc1 [6c]
Tcc e- c g γ* c
p/2
+ (p3 ←→ p4) √ s p4 e+
cbar p3
(unobserved)
cbar
Factorization (Ansatz)
short distance
long distance
h3 for [cc]3cbar(3S1) in Tcc1 [3cbar] h6 for [cc]6c(1S0) in Tcc1 [6c]
unknown parameter:
based on NRQCD formalism
Cf. Bodwin, Braaten Lepage, PRD51, 1125 (1995)

14. + 2. Tcc production in e+e- collisions p p/2 c Tcc e- γ* c p/2 g
L.O.
p/2
inclusive process c
Tcc1 [3cbar] or Tcc1 [6c]
Tcc e- γ* c +
p/2 g
+ (p3 ←→ p4) √ s p4
cbar e+
cbar p3
(unobserved)
cbar
Factorization (Ansatz)
short distance
long distance
h3 for [cc]3cbar(3S1) in Tcc1 [3cbar] h6 for [cc]6c(1S0) in Tcc1 [6c]
unknown parameter:
based on NRQCD formalism
Cf. Bodwin, Braaten Lepage, PRD51, 1125 (1995)

15. 2. Tcc production in e+e- collisions p uk(p/2) p/2
Tcc1 [3cbar] or Tcc1 [6c] c
Tcc e-
Projection for Tcc1 [3cbar](3S1) c g
uj(p/2) γ* c
p/2
anti-symmetric √ s p4
Projection for Tcc1 [6c](1S0)
cbar e+
symmetric p3
(unobserved)
cbar

16. 2. Tcc production in e+e- collisions
Tcc1 [3cbar] or Tcc1 [6c] Θ p
√s=10.6 GeV (Belle)
mc=1.5 GeV
αs=0.26
Numerical Results
Tcc1 [3cbar]
[1/GeV]
Tcc1 [6c]
Remark : independent of h3(6) value.

17. 2. Tcc production in e+e- collisions
Tcc1 [3cbar] or Tcc1 [6c] Θ p
√s=10.6 GeV (Belle)
mc=1.5 GeV
αs=0.26
Numerical Results
Tcc1 [3cbar]
Different behavior for Tcc1 [3cbar] and Tcc1 [6c]
・ Peak position and height
・ Θ-dependence
・ Threshold behavior
[1/GeV]
Tcc1 [6c]
Remark : independent of h3(6) value.

18. 2. Tcc production in e+e- collisions
Numerical Results
Absolute value of the cross section σ ?
→ How to fix h3 for Tcc1 [3cbar] and h6 for Tcc1 [6c] ?

19. 2. Tcc production in e+e- collisions
Numerical Results
Absolute value of the cross section σ ?
→ How to fix h3 for Tcc1 [3cbar] and h6 for Tcc1 [6c] ?
Estimate by quark model
(crude approximation) c u d
Tcc1 [3cbar]
Tcc1 [6c]
H.O. potential
Cf. Ξcc production based on NRQCD formalism
・ Ma, Si, Physics Letters B568, 135 (2003)
・ Jian, Wu, Liao, Zheng, Fang, arXiv: [hep-ph]

20. 2. Tcc production in e+e- collisions
Numerical Results
Absolute value of the cross section σ ?
→ How to fix h3 for Tcc1 [3cbar] and h6 for Tcc1 [6c] ?
Estimate by quark model
(crude approximation) c u d
Tcc1 [3cbar]
≈ GeV3
Tcc1 [6c]
H.O. potential
Cf. Ξcc production based on NRQCD formalism
・ Ma, Si, Physics Letters B568, 135 (2003)
・ Jian, Wu, Liao, Zheng, Fang, arXiv: [hep-ph]

21. 2. Tcc production in e+e- collisions
Numerical Results
Absolute value of the cross section σ ?
→ How to fix h3 for Tcc1 [3cbar] and h6 for Tcc1 [6c] ?
Estimate by quark model
(crude approximation) c u d
Tcc1 [3cbar]
σ = 129 fb
almost same as Ξcc
≈ GeV3
Tcc1 [6c]
H.O. potential
Cf. Ξcc production based on NRQCD formalism
・ Ma, Si, Physics Letters B568, 135 (2003)
・ Jian, Wu, Liao, Zheng, Fang, arXiv: [hep-ph]

22. 2. Tcc production in e+e- collisions
Numerical Results
Absolute value of the cross section σ ?
→ How to fix h3 for Tcc1 [3cbar] and h6 for Tcc1 [6c] ?
Estimate by quark model
(crude approximation) u c
Tcc1 [3cbar]
σ = 129 fb
almost same as Ξcc d c
≈ GeV3
Tcc1 [6c]
H.O. potential
Cf. Ξcc production based on NRQCD formalism
・ Ma, Si, Physics Letters B568, 135 (2003)
・ Jian, Wu, Liao, Zheng, Fang, arXiv: [hep-ph]

23. 2. Tcc production in e+e- collisions
Numerical Results
Absolute value of the cross section σ ?
→ How to fix h3 for Tcc1 [3cbar] and h6 for Tcc1 [6c] ?
Estimate by quark model
(crude approximation) u c
Tcc1 [3cbar]
σ = 129 fb
almost same as Ξcc d c
≈ GeV3
Tcc1 [6c]
H.O. potential
≈ GeV3
Cf. Ξcc production based on NRQCD formalism
・ Ma, Si, Physics Letters B568, 135 (2003)
・ Jian, Wu, Liao, Zheng, Fang, arXiv: [hep-ph]

24. 2. Tcc production in e+e- collisions
Numerical Results
Absolute value of the cross section σ ?
→ How to fix h3 for Tcc1 [3cbar] and h6 for Tcc1 [6c] ?
Estimate by quark model
(crude approximation) u c
Tcc1 [3cbar]
σ = 129 fb
almost same as Ξcc d c
≈ GeV3
Tcc1 [6c]
σ = 43 fb
H.O. potential
≈ GeV3
Cf. Ξcc production based on NRQCD formalism
・ Ma, Si, Physics Letters B568, 135 (2003)
・ Jian, Wu, Liao, Zheng, Fang, arXiv: [hep-ph]

25. 2. Tcc production in e+e- collisions
Numerical Results
Absolute value of the cross section σ ?
→ How to fix h3 for Tcc1 [3cbar] and h6 for Tcc1 [6c] ?
Estimate by quark model
(crude approximation) u c
Tcc1 [3cbar]
σ = 129 fb
almost same as Ξcc d
Upper limit c
≈ GeV3
Tcc1 [6c]
σ = 43 fb
H.O. potential
≈ GeV3
Cf. Ξcc production based on NRQCD formalism
・ Ma, Si, Physics Letters B568, 135 (2003)
・ Jian, Wu, Liao, Zheng, Fang, arXiv: [hep-ph]

26. 3. Summary and perspectives
・ Tcc1 [3cbar] and Tcc1 [6c] are flavor exotic doubly charmed tetraquarks.
・ We estimate the cross sections of Tcc1 [3cbar] and Tcc1 [6c] produced in e+e- collisions.
・ The cross sections of Tcc1 [3cbar] and Tcc1 [6c] have different momentum- and angle-dependence.
→ Experimental method to identify the color structure (3cbar, 6c) of
a quark pair in exotic hadrons?
・ More studies should be required.
- Rigorous discussion about applicability of NRQCD formalism
- Higher order in velocity-expansion
- Precise estimate of expectation value of long-distance operator
- ...

27. Thank you !!

28. Appendix

29. A. Del Fabbro, D. Janc, M. Rosina, D. Treleani, PRD71, 014008 (2005)

30. JP=1+ JP=1+ Mixing of Tcc1 [3cbar] and Tcc1 [6c] is suppressed !!
Remark
Mixing of Tcc1 [3cbar] and Tcc1 [6c] is suppressed !!
ubar
[ubardbar]6cbar(3S1)
[ubardbar]3c(1S0)
dbar
JP=1+
JP=1+
Tcc1 [6c]
magnetic gluon
Tcc1 [3cbar] c
[cc]6c(1S0)
[cc]3cbar(3S1) c
suppressed by 1/mc
Time
Tcc1 [6c] will decay almost to DD* in s-wave.