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

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some issues in charmonium physics

Some Issues in Charmonium Physics

K-T Chao

Peking University

slide2
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

puzzles in double charm production in e e annihilation
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.
puzzles in double charm production in e e annihilation1
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)

puzzles in double charm production in e e annihilation2
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)
puzzles in double charm production in e e annihilation3
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

d wave charmonium production in e e annihilation and b decay
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
s d mixing between 2s 3770
S-D mixing between’= (2S) &’’=(3770)

If ignoring D-wave contribution to leptonic widths  mixing angle   ± 19º

slide9

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

slide10

  +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

slide11
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

slide12

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)

slide13

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

slide14

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)]

d wave charmonium production in e e annihilation color octet insignificant for double charm
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.

d wave charmonium production in e e annihilation and b meson decay
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.
slide18

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
slide43
If using the infrared divergence term to estimate the decay widthsas in the case of hadronic widths:

(hc ggg)=5/6  (c1qqg)

slide45

Very large branching ratio obtained for BhcK

obtained!

But new method based on NRQCD still expected to remove infrared divergences!