1. Problems in Charmonium Production in e+e Annihilation and B Decay
Kuang-Ta Chao
Peking University

2. Puzzles in Double Charm Production in e+e Annihilation
Inclusive J/ cc{\bar} production
Exclusive J/ C (C0, C(2S),…) production
D-wave Charmonium production
in e+e Annihilation
in B meson decay
S-D Mixing

3. Puzzles in Double Charm Production in e+e Annihilation
INCLUSIVE PRODUCTION :
e+e J/cc{\bar}
Theory: via ONE virtual photon
Cho-Leibovich (1996)
Yuan-Qiao-Chao (1997)
Baek-Ko-Lee-Song (1998)
pQCD predicts: cross section at s  10.6 GeV  pb
Belle data  0.9pb (2002)
larger than theory by almost one order of magnitude. Higher order corrections expected not large.

4. Puzzles in Double Charm Production in e+e Annihilation
EXCLUSIVE PROCESS
e+e  J/ C (C0, C(2S),…)
theory: via ONE virtual photon
Braaten-Lee (2003) PRD67,
Liu-He-Chao (2003) PLB557, 45
Hagiwara-Kou-Qiao (hep-ph/03)
pQCD prediction smaller again by an order of magnitude than
Belle cross section  pb for
e+e J/C (PRL89, )

5. Puzzles in Double Charm Production in e+e Annihilation
via TWO virtual photons
Enhanced by photon fragmentation (small photon virtuality 4mc2s )
Suppressed by QED over QCD couplings
Exclusive J/ +J/ enhanced (Bodwin-Braaten-Lee, PRL90, ), but not J/+ C
Inclusive J/ cc\bar via two photons prevail over via one photon when s  20GeV (Liu-He-Chao, PRD68, )

6. Puzzles in Double Charm Production in e+e Annihilation
Two photons can NOT solve problems for both inclusive and exclusive double charm production
Both data larger than pQCD predictions by about an order of magnitude
Color octet no help
Non pQCD effects (?)
Other explanations (e.g. Ioffe-Kharzeev)

7. D-wave Charmonium production in e+e Annihilation and B decay
New finding by Belle: D-wave charmonium is observed in B decay for the first time (hep-ex/ )
B+(3770)K+ , BR = (0.48 ±0.11± 0.12) x 10-3, very large, even comparable to
B+(2S)K+, BR=(0.66±0.06) x 10-3
If this implies large 2S-1D mixing? (as suggested in hep-ex/ )
S-D mixing vs. Color-Octet mechanism in D-wave charmonium production in B meson decay and in e+e Annihilation

8. S-D mixing between ’= (2S) & ’’= (3770)
If ignoring D-wave contribution to leptonic widths  mixing angle   ± 19º

9. Detailed calculations (including tensor force and coupled channel effects) indicating  absolutely value smaller than 10º (Eichten et al, Kuang-Yan, Moxhay-Rosner,…) Including D-wave contribution to leptonic widths    -- 10º or   +30º

10.   +30º should be ruled out because it would give E1 transition width 5 times larger than the observed value of (2S)co (Ding-Qin-Chao, PRD44(1991)

11. tan2  =0.11, if   ± 19º tan2  =0.03, if   -- 10º
S-D mixing can NOT explain the Belle dada If only the Color-Singlet (CS) S-wave component contributes (via CS V-A current)
B+(3770)K+ , BR = (0.48 ±0.11± 0.12) x 10-3,
B+(2S)K+, BR=(0.66±0.06) x 10-3

12. D-wave heavy quarkonium production may be a crucial test of NRQCD color-octet mechanism. In certain processes (e.g. gluon fragmentation, B meson decay,…) the D-wave charmonium signal could be as strong as (2S) (Qiao-Yuan-Chao, PRD55(1997)4001)

13. Color-Octet (CO) mechanism may play important role for D-wave charmonium production in B decay due to large Wilson coefficient for CO effective V-A Hamiltonian and the NRQCD Fock state Expansion. CO coefficient >> CS coefficient

14. The inclusive decay branching ratio was predicted BR(B(3770)X)=0
The inclusive decay branching ratio was predicted BR(B(3770)X)=0.28% (Yuan-Qiao-Chao,1997), [c.f. BR(B+(2S)X)=(0.35±0.05)%] [see also Ko-Lee-Song(1997)]

15. NRQCD velocity scaling rules (with some uncertainties)

16. D-wave charmonium production in e+e Annihilation Color-Octet no help in double charm process
CS contributes 2.4fb to e+e  (3770)cc\bar
CO suppressed by color factor of 3/32, so no help
S-D mixing will help, since the observed rate of
e+e(1S)cc\bar  0.9pb,
and (2S)cc\bar could be more than a half of it.

17. D-wave Charmonium production in e+e Annihilation and B meson decay
Observed large rate of B+(3770)K+ could be a strong support to the Color-Octet mechanism.
Measurement of inclusive B+(3770)X needed.
e+e  (3770)cc\bar could be another test of S-D mixing (no Color-Octet contamination).
Further work should be done for the 2^{--} D-wave candidate at 3872MeV observed by Belle.

18. 2^{--} D-wave candidate at 3872MeV
The production rate should be comparable to (3770) in B decay (about 5/3). If so, its decay branching ratio to  would be only 2% based on Belle data. In any reasonable models the E1 transition rates for 2^{--} D wave should be larger than 200 KeV, and larger than into  . But CJ  not seen by Belle.
The 2^{--} decay branching ratio to  was estimated to be 0.12 (for charged pions) [Qiao-Yuan-Chao, PRD55(1997), 4001], based on the multipole expansion theory. But for the corresponding (3770) transition, BES data not agree with CLEO-c, Kuang-Yan model not agree with Voloshin’s. Both experiment and theory need to be clarified.

19. 2^{--} D-wave candidate at 3872MeV
Note the charmonium molecle (4030) suggested by DeRujula-Georgi-Glashow in 1977 has been re-explained as (3S) with the wave function node structure responsible for mainly decaying to D*D*\bar. And its decay to  not be seen.
Measure CJ  decay with higher statistics is still crucial to understand the nature of X(3872).