Excited Charmonium

in e+e- annihilation and B decay

K-T ChaoPeking University

QWG Workshop, Beijing, Oct. 12-15, 2004

1. Double Charm Production in e+e AnnihilationInclusive J/ cc{\bar} productionExclusive J/ C (C0(1P), C(2S),…) production

Search for excited C0(2P), C(3S)…

Has C0(2P) or C(3S) been observed at 3.94GeV in e+e- J/ cc{\bar} by Belle?

2. Charmonium in B exclusive decays with QCD factorizationPredicted rates too small (but infrared safe) for

B J/ +K, C+K, C1+K, (3770)+K (with S-D mixing)Infrared divergences in

B C0+K, C2+K , hC +K

The role of NRQCD color-octet in exclusive processes?

Double Charm Production in e+e Annihilation

INCLUSIVE PRODUCTION : e+e J/cc\bar Theory: via ONE virtual pho

ton Cho-Leibovich (1996) Yuan-Qiao-Chao (1997) Baek-Ko-Lee-Song (1998)pQCD predicts: cross sectio

n at s 10.6 GeV 0.10-0.15pb

larger than theory by at least 5 times. Higher order relativistic and QCD radiative corrections?

Belle data 0.9pb, PRL89(2002)142001

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, 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 33 femto-barn for

e+e J/C (decaying to 4 charged) (PRL89, 142001)

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)

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.) excluded!

Search for excited charmonium states in e+e- annihilation

(Liu, He & Chao, hep-ph/0408141)

Predicted relative production rates seem to be compatible with data (Belle: PRL89(2002)142001; hep-ex/0407009)

See also: ICHEP04/Belle, Pakhlov et al.In e+e- → J/(cc)res e+e- → (2S)(cc)res

c, c0, c(2S) seen[c1, c2, J/, (2S) not seen]

Calculate the production cross sections, and Search for excited C0(2P), C(3S)…

•Test the production mechanisms

•Search for new charmonium states

e+e- → J/(cc)res with L=155 fb-1

Yields for J/, c1, c2, (2S) ~ 0 set UL

c, c0, c’ confirmed J/, c1, c2, (2S) not seen

N M [ GeV/c] c

J/c0

c1 +c2

c’(2S)

235 26

-14 20

89 2410 27

164 30

-26 29

2.9720.007

fixed3.407 0.011

fixed3.630 0.008

fixed

10.7--

3.8--

6.0--

Study recoil mass against J/: Mrecoil ((Ecms –EJ/)2 –PJ/

2)½ Include all known charmonium states:

c, J/, c0, c1, c2, c’, (2S)

ICHEP04/Belle, Pakhlov et al.

e+e- → (2S)(cc)res

Similar analysis for reconstructed (2S)J/

Fit to Mrecoil ((2S)) spectrum:N

c

J/c0

c1 +c2

c’(2S)

36.7 10.4

6.9 8.935.4

10.76.6 8.0

36.0 11.4

-8.3 8.5

4.2--

3.5--

3.4--

Similar tendency: c, c0, c’ seen… J/, c1, c2, (2S) not seen

5.3 observation of sum of c, c0, c’

Evidence for new charmonium

The reconstruction and selection procedure is not changed since the first Belle paper

Extend the studied region

No signal of X(3872)Significant peak at M=3.9400.011 GeV/c2

N=14833 (4.5)The width is surprisingly narrow <~ resolution (= 32 MeV)

X(3940) could be C0(2P) or C(3S)…? C0(2P) 0++

mass: consistent with potential model estimate.narrow width: node in wave function may cause suppression for DDbar (see e.g. Eichten et al); but 0++ can not decay to DD*bar.

C(3S) 0-+ mass: lower than potential model expected [close or even heavier than (3S) = (4040)]decay: 0-+ can not decay to DD\bar, and the allowed DD*\bar could be suppressed by the node structure--natural explanation for the observed decay width and modes?

Unkonw 1++ : if it is C1(2P), why C1(1P) not observed? Another 1++?

Is this X(3940) related to the J/ structure at 3940 MeV in B decay? Branching ratio C0(2P) J/ seems too large? Width smaller than 90 MeV.

Infrared Divergences in B CJ K and B

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

(Song, Meng, Gao, Chao, Phys.Rev.D69(2003)054009)(Song, Meng, Chao, Eur.Phys.JC36(2004)365)

BBNS (Beneke et al.) QCD factorization: Good for Bpi pi, BD pi. Problems for Bcharmonium+K

Color transparency, cc-bar small size, viewed as a color (singlet) dipole, factorization might be good?S-wave: BJ/ K (infrared safe) , but smaller than data by ~ 8 times (Chay-Kim, Cheng-Yang) ;

S-wave: B C K (infrared safe) , but smaller th

an data by ~ 8 times (Song-Meng-Chao); P-wave: B CJ K and B hCK , Infrared divergences (due to vertex corrections) in QCD factorization and NRQCD

Z= M2/MB2 4mc

2 /mb2

is the gluon mass for infrared

regularization

If using the infrared divergence term to estimate the B exclusive decay widths as in the case of hadronic decay widths:

(hc ggg)=5/6 (c1qqg)

Too large branching ratio for BhcK !

New method and ingredients based on NRQCD are expected to remove infrared divergences !

Questions about NRQCD color-octet mechanism

Color octet components in charmonium shouldhelp, as in the INCLUSIVE B decays, to enhance the decay rates and remove the infrared divergences, but HOW to do it in EXCLUSIVE decays?

Other approach to solve the problems

Rescattering effects by intermediate charmed mesons, B D+DsXco+K

(Colangelo-DeFazio-Pham,PLB542(2002)71; PRD69(2004),054023)

LCSR: large for BJ/psi+ K, Xc1+K small for Betac+K, Xco+K (Melic, PRD68(2003)034004) (Wang-Li-Huang, hep-ph/0311296)