1. Double charmonium production from B factories
new states
large cross section
P. Pakhlov (ITEP, Moscow) for the Belle Collaboration
Charm October 2010, Beijing

2. Charmonium in a variety of processes
Since 1974 numerous processes in which different charmonia produced.
hadron production with fixed target (pN, πN) and collider (√s ~ 10 GeV – 2 TeV)
e+e– → Vector charmonia and pp → many different QN charmonia resonant production (√s ~ 3 – 5 GeV)
γγ production resonant or not (B-factories, LEP, LEPII)
B-decays
photo-, lepto- production at HERA
quark-gluon plasma?
Is it possible to describe all this variety at once?
Charmonium is a cc-bound state. Can we calculate the production of ingredients?
Do we have a recipe how to cook charmonium from the ingredients?
CHARM2010, Beijing, 21 October, 2010
P. Pakhlov (ITEP)

3. NRQCD: brilliance & ...
Last 30 years NRQCD serves to calculate charmonium production:
factorization perturbative (cc-pair production) and non-perturbative (cc hadronization into charmonium)
 = n(cc) Oncc
n(cc) can be calculated using perturbative QCD: c-quark is heavy enough? αs(q2 = mc) ~ 0.25
It is pity, but we do not know how to calculate Oncc. We only believe that they are universal (do not depend on the process)!
Further simplification: color singlet model. Do we need to take into account all possible Oncc? Let’s consider only colorless (cc)0, corresponding to final charmonium quantum numbers. Then the single Oncc is known from dielectron (γγ) width.
OK for gg → ηc(χc), gg → J/g, B → J/X etc... but huge disagreement was found for high pT production of J/ and ’ at Tevatron (Tevatron ’ surplus problem (1994)).
CHARM2010, Beijing, 21 October, 2010
P. Pakhlov (ITEP)

4. NRQCD: brilliance & poverty
Color Octet Model was believed helps to solve the Tevatron problem (Braaten, Fleming, 1995)
Some of ignored terms has smaller αs suppression; Compare:
color-singlet: (ggg)0 → (cc)0 → ’
color octet: g8 (gg)8 → (cc)8 → ’
while Oncc for CO terms are small, n(cc)
is large and can compensate the disagreement?
Purely phenomenological approach:
free parameters, Oncc, to be
determined from the data
Using matrix elements tuned from the pt spectra, lead to problem to describe polarization. CDF-II data disagree with NRQCD.
CHARM2010, Beijing, 21 October, 2010
P. Pakhlov (ITEP)

5. Does Color-octet solve the problem?pN
lepto-
production
photo-
production
In pN, πN interactions CO seems help to describe the data better (not so obvious for ’ (no cascade))
In photoproduction CS leading order is too small, however CS NLO already describes the data well
In leptoproduction CS is too small, but CS+CO is too large
In γγ (LEPII) CS is too small, CS+CO describes the data well
... no unambiguous conclusion
CHARM2010, Beijing, 21 October, 2010
P. Pakhlov (ITEP)

6. Charmonium production (non-resonant) in e+e– annihilation
Not expected by theory, but occasionally
observed experimentally
1990 CLEO:  4.6 J/ events in
(4S) data (seen also by ARGUS)
e+e → J/ X exists:
not from B-decays (p>2.0 GeV/c)
not from radiative return (Nch>4)
(e+e → J/ X ) ~ 2 pb
For more than 10 years only available information to guess how charmonia can be produced in e+e annihilation was based on ~15 events
L~1fb-1
Is this sufficient to identify the production mechanism?
CHARM2010, Beijing, 21 October, 2010
P. Pakhlov (ITEP)

7. Production in e+e–: which monsters give birth to charmonium?
Color-Singlet e+e– → J/ cc was estimated to be very small 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  ~ 1 pb Cho-Leibovich (1996)
CHARM2010, Beijing, 21 October, 2010
P. Pakhlov (ITEP)

8. New era come in XXI
Asymmetric e+e– colliders PEPII & KEKB Ecm = GeV.
The highest luminosity! In × 1034 /sm2/sec has been reached at KEKB!
Continuous injection: constant high luminosity during run time!
Accumulated luminosity
КЕКВ >1000/fb
PEPII ~ 530/fb
≈ 100 * CLEO
≈ 3000 * ARGUS
Universal detectors BaBar & Belle: 4π spectrometers with precise vertex and momentum measurement, nice particle identification, good energy resolution for neutrals, etc.
CHARM2010, Beijing, 21 October, 2010
P. Pakhlov (ITEP)

9. Double charmonium production
CHARM2010, Beijing, 21 October, 2010
P. Pakhlov (ITEP)

10. Belle’s first result c’ c c0
Idea is to study the recoil mass against reconstructed J/ using two body kinematics (with 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’
No theoretical predictions for these processes, except for the common sense idea that they should be too small to be observed.
c’
L~45fb-1 c
c0
K.Abe et al. (Belle Collaboration)
Phys.Rev.Lett., 89, (2002)
CHARM2010, Beijing, 21 October, 2010
P. Pakhlov (ITEP)

11. Using more data
c’
Belle 2004: Full analysis of double charmonium production
Reconstructed charmonium:
J/
(2S) → J/ππ
Recoil charmonium:
All known charmonium states below DD threshold in the fitting functions
Only (pseudo)scalars are seen
L~155fb-1 c
c0
c’
c0 c
K.Abe et al. (Belle Collaboration) Phys.Rev., D70, (2004)
CHARM2010, Beijing, 21 October, 2010
P. Pakhlov (ITEP)

12. Cross-sections Born cross-sections [fb]:
(theorists proved to see no difference between the total and Born cross-sections and compared their predicted Born x-section with experimentally measured total x-secion in the first paper total. For experimentalists it is more simple to calculate Born value, than to explain the difference...)
≈ 70% of the total
Born cross-sections [fb]:
 * BR (recoil charmonium → >2charged)
~ 2/3 according to MC generators
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:
Only 0+– and 0–– states are seen recoiling against reconstructed 1–– charmonium!
Orbital excitations are not suppressed!
CHARM2010, Beijing, 21 October, 2010
P. Pakhlov (ITEP)

13. BaBar’s confirmation 2005, BaBar also see double charmonium events
e+e– → J/ c
e+e– → J/ c0
e+e– → J/ c’
Both Belle and BaBar used requirement on charged multiplicity (>4 charged tracks) to suppress QED background. It is not corrected for in the measured x-sections!
B. Aubert et al. (BaBar Collaboration) Phys.Rev., D72, (2005)
CHARM2010, Beijing, 21 October, 2010
P. Pakhlov (ITEP)

14. NRQCD calculations
The first calculations based on NRQCD at LO in αs and υ gave an order of magnitude smaller x-sections:
σ(e+e– →J/c)=(3.8 ± 1.3) fb Braaten, Lee (2003)
σ(e+e– →J/c)=5.3 fb Liu, He, Chao (2003) (using different mc, αs)
Braaten, Lee (2003) showed that υ2 corrections can be large (factor of 2+3–1)! The large uncertainties in determination of q2J/, c (due to large uncertainty in mc) called the reliability of non-relativistic expansion in question.
Zhang, Gao, Chao (2006) NLO QCD corrections can be also large: ratio of NLO/LO ~2
More reliable relativistic corrections + NLO
σ(e+e– → J/ c) = (17.5 ± 5.7) fb Bodwin, Kang, Kim, Lee, Yu (2006) determined binding energy in chramonium from potential models and calculated q2J/= (0.50 ± 0.09 ± 0.15) GeV2. This allows significantly reduce the uncertainty of matrix elements; use ZGC NLO calculations.
σ(e+e– → J/ c) = 20 fb Liu, He, Fan, Chao (2007) calculated q2 from dielectron, γγ, hadronic widths of J/ & c. This gives quite different q2 from BKKLY, though the final x-section is close.
CHARM2010, Beijing, 21 October, 2010
P. Pakhlov (ITEP)

15. Light cone approximation
After the importance of relativistic corrections become clear, alternative method of calculation has been suggested.
Ma, Si (2004) pointed out that light cone approximation can help (but no idea how to fix the wave function). The calculated cross section varied from 7 to 30 fb.
Bondar, Chernyak (2005) used charmonium wave function parametrized by average charm-quark velocity in charmonium (the same parametrization gave correct result for light meson production)
σ(e+e–→ J/ c) = 33 fb
Braguta (2008) used different twist-2 and twist-3 amplitudes
σ(e+e– → J/ c) = (14+11–10) fb
light mesons
charmonium
bottomonium
CHARM2010, Beijing, 21 October, 2010
P. Pakhlov (ITEP)

16. Is the discrepancy resolved?
compare with
exp: 20fb /Br
Yes! There is no more order of magnitude disagreement
Adding more and more corrections allows to increase the calculated cross sections, which are now marginally consistent with the data.
However, it is unclear how the next corrections change the result.
Even the known uncertainties in calculations are still large.
Two competing approaches: NRQCD people believe that the main effect is NLO corrections, while LC adherent think that NLO corrections are overestimated and the effect is dominated by relativistic corrections.
The experimental values include Br(cc → >2 charged) that can increase the cross section by 1.5
CHARM2010, Beijing, 21 October, 2010
P. Pakhlov (ITEP)

17. Angular analysis e+ e– θprod J/ θhel ℓ+ ℓ– c , c0, c’
prod=hel (assume single photon annihilation)
prod
hel
prod=hel
NRQCD c
+1.4
+0.5
+0.93
+1.0
c0
–1.7  0.5
–0.5
–1.01
+0.25
c’
+1.9
+0.3
+0.87
–0.8
+1.1
–1.2
+2.0
+0.7
–0.5
+1.0
–0.7
+0.87
–0.47
+0.86
–0.63
+0.38
–0.33
Important for efficiency corrections
Interesting to compare with predictions:
for c, c’ good agreement with NRQCD (and naive expectation of the dominance of the lowest L=1 wave amplitude)
for c0 in contradiction with NRQCD, expecting comparable L=0, 2 amplitudes for P-wave charmonium production
CHARM2010, Beijing, 21 October, 2010
P. Pakhlov (ITEP)

18. New states
CHARM2010, Beijing, 21 October, 2010
P. Pakhlov (ITEP)

19. New peak in inclusive J/ recoil mass spectra
Add more data and extend searching region above DD threshold
New peak at M ~ 3.9 GeV, temporary called X(3940)
Two peaks are not excluded, but the second is not significant with this statistics
Significance 5.0 
=3926 90%C.L.)
Seen also in exclusive decay X(3940) → DD*
M = (3943 ± 6 ± 6) MeV/c 2
  Br(X(3940) → >2 charged) =
(10.6 ± 2.5 ± 2.4) fb
357fb-1

20. observe e+e− → J/ D(*)D(*)
wait for another portion of data and
observe e+e− → J/ D(*)D(*)
DD*
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) DD
693fb-1
D*D*
DD*
All signals are > 5
to search new X → D(*)D(*)
Phys. Rev. Lett. 98, (2007)
CHARM2010, Beijing, 21 October, 2010
P. Pakhlov (ITEP)

21. New states in e+e− → J/ D(*)D(*)
M = ±6 MeV
tot = ±12 MeV D +7 −6
+26
−15
X(3940) → DD* D*
M= 15 MeV
tot = 21 MeV
+25
−20 D
+111
−61
X(4160) → D*D*
X(?) → DD
Broad bump at MDD not consistent with non resonant DD production (3.8  only); large fitting systematic error in the parameters of this enhancement.
X(3940)DD* confirmed with new data (6.0 )
New state, X(4160), is observed in D*D*.
CHARM2010, Beijing, 21 October, 2010
P. Pakhlov (ITEP)

22. Looking for assignments
Two new states observed to decay in open charm final states like “normal” charmonium.
In e+e− → double charmonim ηc and c0
(and likely their radial excitations) likes to be produced with J/.
c0(2P) is allowed to decay to DD (should be the dominant decay mode) and c0(2P) should be wide! Seen as a bump in e+e− → J/ DD?
Possible assignments
X(3940) = ηc(3S) and
X(4160) = ηc(4S).
X(3940) is MeV lighter than predicted ηc(3S) (mass splitting 31S0-33S0 ~100MeV to be compared with ~40MeV for 21S0-23S0 )
X(4160) is much more problematic! 200 MeV shifted to the predicted ηc(4S)
(mass splitting 41S0-43S0 >200MeV if assignment of (4S)= (4415) correct)
CHARM2010, Beijing, 21 October, 2010
P. Pakhlov (ITEP)

23. Large e+e– → J/ cc cross sectionс
CHARM2010, Beijing, 21 October, 2010
P. Pakhlov (ITEP)

24. J/ production with charmed hadrons
Looking for D0 and D*+ in J/ events
to remove B-decays
5.3
M = 10.1
+3.6
−3.0
Based on LUND predictions for c  D(*)
using
(e+e–→ J/X) = 1.5 pb (Belle)
= 2.2 pb (BaBar)
obtain  (e+e–→J/cc) ~ 1 pb
compare with theory
 ~ 0.05 pb; Kiselev et al. (1994)
───────── = 0.59  0.14  0.12
(e+e–→J/cc)
(e+e–→J/X)
3.5
M = 14.8
+5.4
−4.8
Phys.Rev.Lett., 89, (2002)
CHARM2010, Beijing, 21 October, 2010
P. Pakhlov (ITEP)

25. +½ New measurement of e+e– → J/ψ cc cross section
Belle, 2009
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
CHARM2010, Beijing, 21 October, 2010
P. Pakhlov (ITEP)

26. e+e–→J/ψ cc and non-cc cross sections
e+e– → J/ X
673fb–1
½ e+e– → J/ Hc Xc
J/ helicity
e+e– → J/ cc
dominant!
J/ production
e+e– → J/ non-cc
Model independent full cross sections
No correction on for Nch requirement for σ(e+e– → J/ non-cc)!
J/ from cascade decays included!
σ(e+e– → J/ cc), pb
0.74± –0.08
σ(e+e– → J/ non-cc), pb
0.43±0.09±0.09
CHARM2010, Beijing, 21 October, 2010
P. Pakhlov (ITEP)

27. NRQCD vs pQCD calculations
The hadronization uncertainties mostly cancel in the ratio, calculated with pQCD:
Berezhnoy, Likhoded (2003)
Even more simple... estimate e+e– → cc cc ignoring hadronization.
σ(e+e– → cccc) ~ 0.37pb Berezhnoy, Likhoded (2007) using the most optimistic mc, αs
─────────── ~ 0.1
σ(e+e– → J/ cc)
σ(e+e– → J/ gg)
NRQCD + NLO
Zhang, Chao (2007) NLO for e+e– → J/ cc + J/ from cascade decays
Ma, Zhang, Chao (2009) NLO for e+e– → J/ gg
Gong, Wang (2009) NLO for e+e– → J/ cc and gg
CHARM2010, Beijing, 21 October, 2010
P. Pakhlov (ITEP)

28. Summary Charmonium production in e+e– annihilation:
Double charmonium production problem seems to be solved by taking into account relativistic & QCD corrections. The order of magnitude discrepancy has been removed, but the factor of 2 uncertainty is still present.
The similar situation with e+e– → J/ cc production in NRQCD. pQCD has no “soft” uncertainties and predicts e+e– → cccc ~ ½ of measured e+e– → J/ cc (NLO corrections? ISR?).
The new experimental result (including angular and momentum study) is now available. e+e– → J/ non-cc is also observed: the kinematic 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.
If these assignments will be confirmed, this could be important input to resolve the puzzles of Vector states.
CHARM2010, Beijing, 21 October, 2010
P. Pakhlov (ITEP)

29. New Tevatron measurements and NLO corrections
Hopefully the experimental data on charmonium production in e+e– annihilation was extremely helpfull to constrain theoretical models.
New Tevatron measurements and NLO corrections
Many efforts from experimentalist and theorists still required to have calculable theory
THANK YOU
CHARM2010, Beijing, 21 October, 2010
P. Pakhlov (ITEP)