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

Charmonium production in e+e– annihilation

L~1fb-

1

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

Is this suffucuent to identify the production mechanism?

Charmonium production at hadron machinesLast 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

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)

Double charmonium production

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

Using more data

Belle 2004: Full analysis of double charmonium production

Reconstructed charmonium:J/(2S)

Recoil charmonium:All known charmonium states below DD threshold

L~155fb-1

Cross-sections

Interesting: Orbital excitations are not suppressed!

Only 0+– and 0–– states are seen recoiling against reconstructed 1–– charmonium!

c J/ c0 c1+c2 c(2S) (2S)

J/(2S)

25.62.83.4 16.34.63.9

<9.1

<16.9

6.41.71.0 12.53.83.1

<5.3

<8.6

16.51.70.4

16.35.13.8

<13.3

<5.2

Born cross-sections:

* BR (recoil charmonium >2charged)

Recon

stru

cte

d R e c o i l

≈70%

All signals are > 5

693fb-1

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)

Phys. Rev. Lett. 98, 082001 (2007)

D*D*

D*D*DD*

DD

DD*

Observation of e+e− J/ D(*)D(*)

BaBar’s confirmation

2005, BaBar also see double charmonium events

e+e– J/ c

e+e– J/ c0

e+e– J/ c‘

NRQCD & light cone approximationThe 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

M = 3942 ±6 MeV

tot =37 ±12 MeV

+7-6

+26 - 15

D*

D*πD*

D

D

New states in e+e− J/ D(*)D(*)

M= 4156 15 MeV

tot = 139 21 MeV

+25−20

+111 −61

Two new states observed, both decay at open charm final states like “normal” charmonium.

X(3940) → DD*

X(4160) → D*D*

Possible assignments are c(3S) and c(4S). But in both cases the masses predicted by the potential models are ~100-150 MeV higher than observed.Theory probably needs more elaborated model to take into account interaction of charmonium with open charm.

J/ production with charmed hadrons

с с

сс

Based on LUND predictions for cD(*)

Perturbative QCD: Berezhnoy-Likhoded (2003)

Looking for D0 and D*+ in J/ events

to remove D from B-decays

3.5

5.3

─────────── ~ 0.1(e+e–J/cc)(e+e–J/gg)

─────────── =0.590.140.12(e+e–J/cc)(e+e–J/X)

Hc=D0 Hc=D+s

Hc=D+

Hc=D0 Hc=D+s

Hc=Λc+

Hc sb8.2σ

3.6σ

2.2σ

12.4σ

All double charmonium final states below open charm threshold

New measurement of e+e–→J/ψ cc cross section

preliminary

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′

ηcχc0

ηc′

hc

J/ hc

Mrecoil(J/) Mrecoil(χc1)

Mrecoil((2S))

J/

Mrecoil(χc2)

ηc

χc0

ηc′

ηcχc0

ηc′

hc

J/ hc

All (except for Ξc/Ωc) ground state charmed hadrons

+½

σ(e+e–→J/ cc),pb 0.74±0.08+0.09–0.08

σ(e+e–→J/ non-cc), pb 0.43±0.09±0.09

e+e–→J/ψ cc and non-cc cross sections

Model independent full cross sections

e+e– → J/ ccdominant!!!

e+e–→J/ non-cc

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J/ helicity

J/ production

e+e– → J/ X

½ e+e– → J/ Hc Xc

─────────── ~ 0.1(e+e–J/cc)

(e+e–J/gg)

preliminary

Perturbative QCD: Berezhnoy-Likhoded (2003)

Perturbative QCD (no relativisitc corrections):

Kiselev et al. (1995)

(e+e–J/cc) ~ 0.05pb

No correction on for Nch requirement!J/ from cascade decays included!

SummaryCharmonium 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)