1. Double charmonium production in e+e– annihilation
Pavel Pakhlov
ITEP, Moscow
International Workshop on Heavy Quarkonia 2008
2-5 December 2008,
Nara Women's University

2. Charmonium production in e+e– annihilation
Not expected by theory, but occasionally observed experimentally
1990 CLEO: e+e–  J/ X exists:
not from B-decays (p>2.0 GeV/c)
not from radiative return (Nch>4)
15.2  4.6 J/ events in (4S) data
(e+e–  J/ X ) ~ 2 pb
For more than 10 years these ~15 events served as the only information available to guess how charmonia can be produced in e+e– annihilation
L~1fb-1
Is this suffucuent to identify the production mechanism?

3. Charmonium production at hadron machines
Last 30 years NRQCD serves to calculate charmonium production:
factorization perturbative (cc production) and non-perturbative (cc hadronization into charmonium)
 = n(cc) Oncc
Color Singlet Model (ignore (cc)8) was ok before Tevatron ’ surplus problem was found (1994)
Color Octet Model was believed can solve the Tevatron problem (Braaten, Fleming)
Purely phenomenological approach: free parameters -- Oncc, to tune to the data
If tune parameters to the observed p((2S)) spectra, still have problem to describe polarization

4. Production in e+e–: which monsters give birth to charmonium?
Color-Singlet e+e–  J/ cc was estimated to be very small by Kiselev et al. (1994)
 ~ 0.05 pb  should be unobservable even at high luminosity B-factories
Color-octet e+e–  (cc)8 g  J/ g (with Oncc fixed to Tevatron and others data) should not be large as well (but can be significant around the end-point of J/ momentum) Braaten-Chen (1996)
Color-Singlet e+e–  J/ gg is the best candidate! Predicted CS ~ 1 pb Cho-Leibovich (1996)

5. Double charmonium production

6. Belle’s first result
Idea is to study the recoil mass against reconstructed J/ using two body kinematics (with a known initial energy)
Mrecoil = (Ecms– EJ/)2 – PJ/ 2 )
2002, Belle found large cross-sections for:
e+e–  J/ c
e+e–  J/ c0
e+e–  J/ c‘
L~45fb-1

7. Using more data
L~155fb-1
Belle 2004: Full analysis of double charmonium production
Reconstructed charmonium:
J/
(2S)
Recoil charmonium:
All known charmonium states below DD threshold

8. Cross-sections Born cross-sections:
 * BR (recoil charmonium  >2charged)
≈70%
R e c o i l c
J/
c0
c1+c2
c(2S)
(2S)
25.62.8 4.63.9
<9.1
<16.9
6.41.7 3.83.1
<5.3
<8.6
16.51.70.4
16.35.13.8
<13.3
<5.2
Reconstructed
Interesting:
Orbital excitations are not suppressed!
Only 0+– and 0–– states are seen recoiling against reconstructed 1–– charmonium!

9. Observation of e+e−  J/ D(*)D(*)
Reconstruct J/ and one of two D (or D*)
Unreconstructed D(*) is seen as a peak Mrecoil (J/ D)
D and D* recoiling against reconstructed J/ D are well separated (~2.5)
D*D* DD
693fb-1
D*D*
DD*
Phys. Rev. Lett. 98, (2007)
All signals are > 5

10. BaBar’s confirmation e+e–  J/ c e+e–  J/ c0 e+e–  J/ c‘
2005, BaBar also see double charmonium events
e+e–  J/ c
e+e–  J/ c0
e+e–  J/ c‘

11. NRQCD & light cone approximation
The first calculations based on NRQCD gave 10 times smaller x-sections
Ma, Si pointed out that light cone approximation can help (but no idea how to fix the wave function)
Bondar, Chernyak used charmonium wave function parametrized by average charm-quark velocity in charmonium (the same parametrization gave correct result for light meson production)
NRQCD with NLO calculation+radiative+ RELATIVISTIC corrections (He, Fan, Chao; Bodwin, Lee,Yu; Gong, Wang) now also fits the data.
light mesons
charmonium
bottomonium

12. New states in e+e− J/ D(*)D(*)
M = ±6 MeV
tot = ±12 MeV +7 -6
+26
- 15 D*
D*π D
X(3940) → DD*
M= 15 MeV
tot = 21 MeV
+25
−20
+111
−61
X(4160) → D*D*
Two new states observed, both decay at open charm final states like “normal” charmonium.
Possible assignments are hc(3S) and hc(4S). But in both cases the masses predicted by the potential models are ~ MeV higher than observed.
Theory probably needs more elaborated model to take into account interaction of charmonium with open charm.

13. J/ production with charmed hadronsс
Looking for D0 and D*+ in J/ events
to remove D from B-decays
5.3
Based on LUND predictions for cD(*)
Perturbative QCD:
Berezhnoy-Likhoded (2003)
─────────── =0.590.140.12
(e+e–J/cc)
(e+e–J/X)
3.5
─────────── ~ 0.1
(e+e–J/cc)
(e+e–J/gg)

14. +½ New measurement of e+e–→J/ψ cc cross section
e+e– → J/ (cc) = e+e– → J/ (cc) res + ½ e+e– → J/ Hc Xc
Mrecoil(J/)
Mrecoil(χc1)
Mrecoil((2S))
J/
Mrecoil(χc2) ηc
χc0
ηc′ hc
Hc=D0
Hc=D0
Hc=D+s
Hc=D+s
12.4σ
3.6σ +½
Hc=D+
Hc=Λc+
8.2σ
Hc sb
2.2σ
All double charmonium final states below open charm threshold
All (except for Ξc/Ωc) ground state charmed hadrons
preliminary

15. e+e–→J/ψ cc and non-cc cross sections
e+e– → J/ X
673fb–1
J/ helicity
½ e+e– → J/ Hc Xc
J/ production
e+e– → J/ cc
dominant!!!
Perturbative QCD (no relativisitc corrections):
Kiselev et al. (1995)
e+e–→J/ non-cc
preliminary
Model independent full cross sections
(e+e–J/cc) ~ 0.05pb
σ(e+e–→J/ cc),pb
0.74± –0.08
σ(e+e–→J/ non-cc), pb
0.43±0.09±0.09
Perturbative QCD:
Berezhnoy-Likhoded (2003)
─────────── ~ 0.1
(e+e–J/cc)
(e+e–J/gg)
No correction on for Nch requirement!
J/ from cascade decays included!

16. Summary Charmonium production in e+e– annihilation:
Double charmonium production problem seems to be solved by taking into account relativistic corrections (charm quark motion in charmonium)
Still no quantative model to calculate e+e– → J/ cc production. The new experimental result (including angular and momentum study) is now available
e+e– → J/ non-cc is also observed: the kinematical features are quite different from e+e– → J/ cc
New charmonium states (and their decays):
Two new states X(3940) and X(4160) have been observed. Possible assignments are ηc(3S) and ηc(4S) in contradiction with mass predictions from potential models
Production of radially excited states is not suppressed: good chance to observe more states and to study the production kinematics and decays of X(3940) and X(4160)