Double charm production in e+e--annihilation

Anatoly Likhoded, IHEP, Protvino

•The conflict between Theory and Experiment in double charmonium production

• Beyond the -approximation

•Light-cone results

•Quark-hadron duality for cccc-sector

Bound states are similar to QED positronium

Simple strong-interactive system

Non-relativistic for

less for

small component velocity

and small

are the expansion parameters in NRQCD

The properties of these bound states, their decay and production

channels are a good laboratory for QCD both in perturbative and

non- perturbative modes

The simplest system clarifying the transitions particles

_QQ

_bb

_cc

v

sa

_QQ ® ( / , , )J y c g

Introduction

One of the most challenging open problems in heavy quarkonium is:

the large discrepancy of the double charmonium production cross sections measured in e+e- annihilation at B factories and the theoretical calculations from NRQCD.

Double charmonium production

K. Hagiwara, E. Kou and C.-F.Qiao,

A. Berezhnoy, A. Likhoded:

E. Braaten, J. Lee:

K.-Y. Liu, Z.-G. He and K.-T Chao:

The calculated exclusive cross sections are about an order of magnitude smaller than exp. results!

The calculated inclusive cross section of J/ is about a factor of 5 smaller than exp. results!

NRQCD factorization formalism CS dominantfb 5.5 ) /(

cJee

fb 3.2 ) /( cJee

Theoretical calculations (LO):

PLB557 (2003) 45

PLB570 (2003) 39

e+

e-

* .)correction icrelativist (inclu. fb 5.5

fb )09.1(2.31 ) /(10.63.5-

cJee (PRD 67 (2003) 054007)

one of 4 diagrams

exclusive double charmonium production via e+e- annihilation to a *. two charmonium states with opposite C parities

( / ) 2.6 fbce e Js y h+ - ® =

Experiment

Belle

BaBar

Trends

The Belle cross section has moved down from

BaBar cross section is even lower

NLO in give an enhancement factor 1.8 (Zhang et al)

Discrepancy still remains

( / )* ( 2) 25.6 2.8 3.4fbce e J Br n

( / )* ( 2) 17.6 2.8 2.1fbce e J Br n

7633 9fb

s

NRQCD predictions for double charmonium production

Papers where NRQCD was applied for double charmonium production:

E.Braaten, J.Lee, Phys. Rev. D67, 054007 (2003)

K. Liu, Z. He, K. Chao, Phys.Lett.B557 (2003)

G. T. Bodwin, J. Lee, E. Braaten, Phys.Rev.Lett.90, 162001 (2003)

G. T. Bodwin, J. Lee, E. Braaten, Phys.Rev.D67, 054023 (2003)

Y. Zhang, Y. Gao, K. Chao, Phys.Rev.Lett.96, 092001 (2006)

q

e+

e-

*

g

x1

x2

-approximation (Bethe-Heitler)

gluon virtuality 2 2

1 2q Q x x=

In -approximation

2 21 2

1, 1/ 2

4q Q x x= =;

for massless quarks

In frame the c-quark distribution over the momentum fraction x is

py ® ¥

2

( ) (1 )gc x x xy ya a- -= -

/ trajectory intercept

2.2 3

0.488

0.023

c

g

J

x

x

y

y

a y

a

-

= - ¸ -

=

=

V.G. Kartverishvili, A.K. Likhoded

Nucl. Phys. B148 (1979), 400

J/ structure function

is the same in fragmentation function ( )c DD z

-approximationd

3

2

A proposed solution

• Bondar and Chernyal have proposed to calculate the cross section in the

framework of light-cone formalism.

• BC result

if light-cone distributions (z-1/2) are taken, the cross section reduces to ~3 fb

( / ) 33fbce e J

J.P. Ma, Z.G. Si // Phys.ReV. D70 (2004) 074007

A.E. Bondar, V.L. Chernyak // Phys.Lett. B612 (2005) 215

V. Braguta, A. Luchinsky, A. Likhoded // Phys.Rev.D72 (2005) 094018

processes' ', ,c c ce e yh y h yh+ - ®

( )32

22 p6 VPe e VP F

spa

s + - ® =

where is defined fromVPF

1 2 1 2( , ), ( ) | | 0 VPV p P p J p p Fba nm mnabl e e=

Leading asymptotic behavior

( ) 1 2 1

1 1 1 2 2 21

( , ) ( , ) | | 0M p M p Js

l l

ml l- +

:

1 1 1 1 1( , ) ( , )M p V pl l= 2 2 2 2 2( , ) ( ) 0M p P pl l= Þ =

1 1 21

( , ) ( ) | | 0V p P p Jsml :

Light-cone formalism

_( , ) ( , ) | ( ) ( ) | 0V p V p Q zQ zabl l= -

_( ) ( ) | ( ) ( ) | 0P p P p Q zQ zab= -

Light-cone wave functions, that are expressed as the expansion over poorly known wave functions. For example, from the asymptotical Regge behavior

1 21 2 (1 )x x x xy ya a d- - - -

e+

e-

* x1

y1

1 1 1 11 1

( , )d x y x yy xd dæ öæ ö÷ ÷ç ç= + +÷ ÷ç ç÷ ÷ç çè øè ø

1 11 1

( )(1 )

QZ Ms x x

y y ss= +-

1 11 1

( )(1 )

QZ Ms y y

x x ss= +-

( )2_

( )m QZ k M

sd=

In -approximation we haved 114s

Light-cone wave functions

, ; , , ,A P T AP P V V V K

are unknown.

Can be estimated from the wave-functions obtained in the framework of potential models.

Light cone wave functions.

The model for the light cone wave functions:

)21

-(x (x) 0v

The property of the wave functions:• •

A.E. Bondar, V.L. Chernyak, Phys.Lett.B612:215, (2005)

)( (x) 1v as x

e+e- V(3S1) P(1S0)

e+e- V(3S1) S(3P0)

Numerical results.

Conclusion: Formfactor = NRQCD xInternal Motion

WFs of charmonium are wide NRQCD is not applicable

Uncertainties: Poor knowledge of the light cone wave functions Radiative corrections 1/s corrections

V.V. Braguta, A.K. Likhoded, A.V. Luchinsky

Phys.Rev.D72 (2005) 094018

Phys.Lett.B635 (2006) 299

26.7

16.3

26.6

14.5

Observation of X(3940) at Belle.

K.Abe et al., hep-ex/0507019

meson is X(3940) .2

mesons , , of one is X(3940) 1.''

c

'2

'1

'0

ccc

Two possibilities:

Hypothesis: X(3940) is one of , , )P2( 0

3'0c )P2( 1

3'1c

If is dominant decay mode than X(3940) is If is seen than must be seen Decay mode of is

We reject this hypothesis

)P2( 23'

2c

DD

*DD )P2( 13'

1c)P2( 1

3'1c )P2( 0

3'0c

)P2( 03'

0c

Hypothesis:

fb)4.25.26.10()2particles charged)3940(())3940(/( XBrXJee

Our estimation:

fb6.13))3940(/( XJee

Experimental result:

)S3( is X(3940) 01''

c

Let us consider the process

LO - tot(4c) ~ O(s)2 depends on s and mc

for mc=1.25 GeV and s=0.24

tot(4c)=372 fb

_ _e e cccc+ - ®

Quark-hadron duality

OZI-rule forbids transition to and light quark sectors _

c c

It is interesting to compare these results with cccc-final state in hadronic Z-decay, where three experimental values are known (L3, OPAL, ALEPH)

_ _ ( ) 160pbZcccc

m

_ _

_

2

2

2.54 10 ( 0.22)

3.01 10 ( 0.24)scccc

scc

_ _

2 32

~ lnscccc

c

s

s m

A.K. Likhoded, A.I.Onishenko

Phys.Atom.Nucl, 60 (1997) 623

Than at we have10.6GeVs

_ _

_

44 10cccc

cc

2

-2

(3.23 0.2 0.42) 10 (ALPEPH)

(2.45 0.29 0.053) 10 ( 3)L

Inclusive charmonium production

In the peak of Z-boson_ 20

2_ 3

0

(0)( )0.187

( )s

RZ ccR

MZ cc

Numerically at s=0.24 this ratio is

42 10R

Good agreement with L3 result.

E. Braaten and K.Cheung

Phys.Rev.D48 (1993) 4230

A.L., V. Kiselev, M. Shevlyagin

Phys.Lett.B332 (1995) 351

We can compare the sum of the cross sections of inclusive production of J/, c and P-wave sates calculated in the framework of perturbative QCD (LHS), with the cross section of the singlet cc-production in duality interval (RHS)

0 2 cm m 2th DM M M ~ 0.5GeVM

In the duality interval the RHS cross section

S=1 S=0sing sing( ) 204fb ( ) 76fbc c c c

_0 _

_ __ _

sing

,

( ( ) )( ( ( ) ) )

thM

m ccnL Jcc

d e e cc c ce e nL cc J c c dM

dM

The sum is sing( ) 280fbc c

LHS cross section consists of perturbative contributions from J/, c and P-wave states

sing( ) 216fbc c

B.K.L // Phys.Lett.B 323 (1994) 411

Liu et al // PR D69 (2004) 094027

There is a reasonable agreement between these two estimates

If we restrict the mass of pair in the process

by the duality interval, we get

It should be compared with Belle and BaBar results:

_

c c_

/e c ce J

( / charmonium) 40fbJ

55 10fb (Belle)( / charmonium)

44.3 9fb (BaBar)J

We observe a good agreement with the experiment

These cross sections include both/ charmoniume e J

and_

/e e J DD

Substracting the cross section of exclusive pair production we obtain

_

( / ) ~ 240fbJ DD

This value should be compared with the Belle result

_

( / ) ~ 870 26fbJ DD

It should be noticed, that this result is sufficiently larger, than the absolute bound for production cross section

_ _

c c c c_ _

( ) 372fbc c c c

Using final state we can estimate the upper bound on (ccq) baryon production. Let us assume that it is produced through the production of cc-diquark in color-antitriplet state.

Cross section of production in duality interval

Double charmed baryon production_ _

cc c c

3c

2 2 , 0.5GeVc cc Dm m M

_

_ _

33

( ( ) ( ) ) 32fbe e cc c c

The upper limit for the cross sections of the processes like_ _

ccce e D

_ _

( ) 70fbccc D

First attempt to search doubly charmed baryons and was done in BaBar experiment hep-ex/0605075

Events containing candidates were searched for the processes

and

cc cc

c pK

cc cK cc cK

Upper limits

if14.5fb

24fb

, 400 700

2 3%

fb

~Br

rBr

B

This is about an order of magnitude higher, than our predictions

Conclusion1) Light cone partially resolves the discrepancy between theory and experiment

The drawback of a light-cone formalism is a large number of unknown wave functions (for critics see G. Bodwin, D. Kang, J. Lee hep-ph/0603185)

2) NRQCD (-approximation) does not work for exclusive processes.

In inclusive processes, on the contrary, -approximation gives a quite good

accuracy

3) Quark-hadron duality as an independent way to estimate cross section gives good agreement with experiment (20% accuracy) and allows to predict Double Charm Baryon production cross section.

A.P. Martynenko , Phys.ReV. D72 (2005) 074022