Some Issues in Charmonium Physics

1. Some Issues in Charmonium Physics K-T Chao Peking University

2. 1. Puzzles in Double Charm Production in e+e Annihilation • Inclusive J/ cc{\bar} production • Exclusive J/ C (C0, C(2S),…) production 2. D-wave Charmonium production • in e+e Annihilation • in B meson decay • S-D Mixing 3. Search for hC in B exclusive decays and infrared divergences

3. Puzzles in Double Charm Production in e+e Annihilation INCLUSIVE PRODUCTION : e+e J/cc 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 0.10-0.15pb • Belle data  0.9pb,PRL89(2002)142001 • larger than theory by almost one order of magnitude. Higher order corrections expected not large enough.

4. Puzzles in Double Charm Production in e+e Annihilation EXCLUSIVEPROCESS e+e J/ C (C0, C(2S),…) Theory: via ONE virtual photon (Braaten-Lee (2003) PRD67, 054007) (Liu-He-Chao (2003) PLB557, 45) (Hagiwara-Kou-Qiao (2003) PLB570, 39) pQCD prediction smaller again by an order of magnitude than Belle cross section  0.033 pb for e+eJ/C(decaying to  4 charged)(PRL89, 142001)

5. Puzzles in Double Charm Production in e+e Annihilation • Theory: via TWO photons • Enhanced by photon fragmentation (small photon virtuality 4mc2s ) • Suppressed by QED over QCD couplings • Exclusive J/ +J/ enhanced (Bodwin-Braaten-Lee, PRL90, 162001), the same order as for J/+ C(but ruled out later by data) • Inclusive J/ cc\bar via two photons prevail over via one photon when s  20GeV (Liu-He-Chao, PRD68, R031501)

6. Puzzles in Double Charm Production in e+e Annihilation • Annihilation into 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 contributions are negligible • pQCD factorization fails(?) • C=+ glueballs misidentified as C (?) (Brodsky et al.) Search for C=+ glueballs near 3 GeV from (2S) decay @ CLEOc & BESIII

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/0307061) • 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? • 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   – 10ºor   +30º

10.   +30º disfavored because it would give E1 transition width 5 times larger than the observed value of (2S)co (Ding-Qin-Chao, PRD44(1991)Measurement of (3770)cJ  at CLEOc & BESIII will be another helpful check for the S-D mixing

11. tan2 =0.11, if   ± 19º tan2 =0.03, if   -- 10º Small S-D mixing can hardly explain the Belle data if only the Color-Singlet (CS) S-wave component contributes (via CS V-A currents) 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) (Yuan-Qiao-Chao, PRD56(1997)329)

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 predictedBR(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 AnnihilationColor-Octet insignificant for double charm Color-singlet contributes 2-4 fb to e+e (3770)cc\bar (Hao-Liu-Chao, PLB546(2002)216) • Color-octet suppressed by color factor of 3/32, no significant contribution • S-D mixing will much help, since the observed rate of e+e(1S)cc\bar  0.9pb, (2S)cc\bar expected to be about a half of (1S)cc\bar.

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 either the Color-Octet mechanism or the large S-D mixing. • e+e (3770)cc\bar could be another test of S-D mixing (no Color-Octet contamination). • (3770)cJ  at CLEOc & BESIII will be another helpful check for the S-D mixing.

18. Infrared Divergences in B CJ K and B hCK Decays in QCD Factorization(Song, Chao, Phys.Lett. B568 (2003)127)(Song, Meng, Gao, Chao, hep-ph/0309105) • BBNS (Beneke et al.) QCD factorization: • Good for Bpi pi, BD pi. • OK (infrared safe) for BJ/ K (Chay-Kim, Cheng-Yang)B C K (Song-Meng-Chao); Color transparency, small cc-bar size, viewed as color dipole. • Infrared divergences for B CJ K and B hCK Decaysin QCD factorization and NRQCD

36. Z=M2/MB2  4mc 2 /mb2  is the gluon mass for infrared regularization

43. If using the infrared divergence term to estimate the decay widthsas in the case of hadronic widths: (hc ggg)=5/6  (c1qqg)

45. Very large branching ratio obtained for BhcK obtained! But new method based on NRQCD still expected to remove infrared divergences!