Some Issues in Charmonium PhSome Issues in Charmonium Ph

ysicsysics

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 –in B meson decay–S-D Mixing

3. Search for hC in B exclusive decays and infrared divergences

Puzzles in Double Charm Production Puzzles in Double Charm Production in ein e++ee Annihilation 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 ePuzzles in Double Charm Production in e++ee AnnihilationAnnihilation

EXCLUSIVE PROCESS

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 charge

d) (PRL89, 142001)

Puzzles in Double Charm Production in ePuzzles in Double Charm Production in e++ee AnnihilationAnnihilation

Theory: via TWO photons Enhanced by photon fragm

entation (small photon virtuality 4mc

2s ) Suppressed by QED over Q

CD couplings Exclusive J/ +J/ enhan

ced (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 ePuzzles in Double Charm Production in e++ee AnnihilationAnnihilation

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 D-wave Charmonium production in ein e++ee Annihilation and B decay 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 la

rge, 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 char

monium production in B meson decay and in e+e Anni

hilation

S-D mixing betweenS-D mixing between ’= ’= (2S) &(2S) & ’’=’’= (3770)(3770)

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

DDetailed calculations (including tensor forcetailed calculations (including tensor force and coupled channel effects) indicating e and coupled channel effects) indicating

absolutely value smaller than absolutely value smaller than 10º 10º (Eichten et al, Kuang-Yan, Moxhay-Rosner,…)(Eichten et al, Kuang-Yan, Moxhay-Rosner,…)

Including D-wave contribution to leptonic Including D-wave contribution to leptonic

widths widths –– 10º 10º or or +30º +30º

+30º disfavored because it would give E1 transit+30º disfavored because it would give E1 transition width 5 times larger than the observed value of ion width 5 times larger than the observed value of

(2S)(2S)coco (Ding-Qin-Chao, PRD44(1991)(Ding-Qin-Chao, PRD44(1991)

Measurement of Measurement of (3770)(3770)cJ cJ at CLEOc & BESIII will at CLEOc & BESIII will

be another helpful check for the S-D mixingbe another helpful check for the S-D mixing

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

D-wave heavy quarkonium production D-wave heavy quarkonium production may be a crucial test of NRQCD color-may be a crucial test of NRQCD color-

octet mechanism.octet mechanism.In certain processes (e.g. gluon fragmentation, B In certain processes (e.g. gluon fragmentation, B meson decay,…) the D-wave charmonium signal meson decay,…) the D-wave charmonium signal

could be as strong as could be as strong as (2S)(2S) (Qiao-Yuan-Chao, PRD55(1997)4001)(Qiao-Yuan-Chao, PRD55(1997)4001) ( (Yuan-Qiao-Chao, PRD56(1997)329)Yuan-Qiao-Chao, PRD56(1997)329)

Color-Octet (CO) mechanism may play important rColor-Octet (CO) mechanism may play important role for D-wave charmonium production in B decay ole for D-wave charmonium production in B decay due to large Wilson coefficient for CO effective V-due to large Wilson coefficient for CO effective V-A Hamiltonian and the NRQCD Fock state ExpansiA Hamiltonian and the NRQCD Fock state Expansi

on.on.

CO coefficient >> CS coefficientCO coefficient >> CS coefficient

The inclusive decay branching ratio was predictedThe inclusive decay branching ratio was predictedBR(BBR(B(3770)X)=0.28% (3770)X)=0.28%

(Yuan-Qiao-Chao,1997)(Yuan-Qiao-Chao,1997), , [c.f. BR(B[c.f. BR(B++(2S)X)=(0.35(2S)X)=(0.35±0.05)%]±0.05)%]

[see also Ko-Lee-Song(1997)][see also Ko-Lee-Song(1997)]

NRQCD velocity scaling rules (with NRQCD velocity scaling rules (with some uncertainties)some uncertainties)

0018.0)()()(

71

38

51

38

31

38

111

CCC M

DO

M

PO

M

SOccc

D-wave charmonium production in eD-wave charmonium production in e++ee Annihilati Annihilationon

Color-Octet insignificant for double charm Color-Octet insignificant for double charm Color-singlet contributes 2-4 fb to e+

e (3770)cc\bar (Hao-Liu-Chao, PLB5

46(2002)216)

Color-octet suppressed by color fa

ctor of 3/32, no significant contrib

ution

S-D mixing will much help, since t

he 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 eD-wave Charmonium production in e++ee Annihilation and B meson decayAnnihilation and B meson decay

Observed large rate of B+(3770)K+ could be

a strong support to either the Color-Octet mec

hanism 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 an

other helpful check for the S-D mixing.

Infrared Divergences in BInfrared Divergences in B CJ CJ K and BK and B

hhCCK Decays in QCD FactorizationK Decays in QCD Factorization(Song, Chao, Phys.Lett. B568 (2003)127)(Song, Chao, Phys.Lett. B568 (2003)127)

(Song, Meng, Gao, Chao, hep-ph/0309105)(Song, Meng, Gao, Chao, hep-ph/0309105)

BBNS (Beneke et al.) QCD factorization:

Good for Bpi pi, BD pi.

OK (infrared safe) for BJ/ K (Chay-Kim, Chen

g-Yang) B C K (Song-Meng-Chao); Color transpa

rency, small cc-bar size, viewed as color dipole.

Infrared divergences for B CJ K and B hCK Decays in QCD factorization and NRQCD

Z= MZ= M22/M/MBB2 2 4m 4mc c

22 /m /mbb22

is the gluon mass for infrared is the gluon mass for infrared regularizationregularization

If using the infrared divergence term to esIf using the infrared divergence term to es

timate the decay widthstimate the decay widths as in the case of hadronic widths:as in the case of hadronic widths:

(hc ggg)=5/6 (c1qqg)

Very large branching ratio obtained for BhcK obtained!

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