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Problems in Charmonium Production in e + e  Annihilation and B Decay

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

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Problems in Charmonium Production in e + e  Annihilation and B Decay

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  1. Problems in Charmonium Production ine+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  0.10-0.15pb • 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 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 (hep-ph/03) pQCD prediction smaller again by an order of magnitude than Belle cross section  0.033 pb for e+eJ/C (PRL89, 142001)

  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, 162001), butnot J/+ C • Inclusive J/ cc\bar via two photons prevail over via one photon when s  20GeV (Liu-He-Chao, PRD68, 031501)

  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/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? (as suggested in hep-ex/0307061) • 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 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 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 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).

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