Изучение процессов двойного рождения

чармониев на B-фабриках и волновые функции

чармониев В.В. Брагута

Институт Физики Высоких Энергий

Content:Content:

Introduction Charmonia Distribution Amplitudes Properties of Charmonia Distribution

Amplitudes Double Charmonium Production at B-

factories Conclusion

Introduction

FactorizationFactorization

effects) bative(nonpertur 0|| :oncontributi distance Large 2.

QCD) ive(perturbat C :oncontributi distanceShort 1.

n

:onsContributiDifferent

nOM

0|)0(| C T

:formulaion Factorizat

n arg

.

n

Dist.eL

n

DistShort

OM

Nonperturbative effectsNonperturbative effects

q...DD q q,D q q, q

...; qDDD q q,DD q q,D q q, q

...; qDDD q q,DD q q,D q q, q

0

211

321211

321211

555

5555

production tocontribute that Operators

GGG

On

... :section cross The 22

110 nnn sss

At given order approximation in 1/s expansion some operators can be omitted

The leading twist distribution The leading twist distribution amplitudeamplitude

Distribution amplitudes Resume infinite series of operators Resume leading logarithmic radiative corrections

1

1 n

1n 1 n 2

5 1 2

1

Operators that contribute at the leading order approximation:

M(p)|q D ...D q|0 z z ...z ~ (pz) ( ), z 0,

Distribution amplitude ( ) can be c

n d x x

onsidered as a meson wave function.

hard

1

1

E~ ), ,( ),H(

dT

Distribution Amplitudes are the key ingredient

of Light Cone Formalism

Charmonia Distribution Amplitudes

The models of leading twist The models of leading twist DAsDAs

4.0~1

~v velocity sticcharacteri

,5.2 ,03.0

-1-Exp )( )1(~)~,(

2

2.30.8-

32.003.0

222

cm

1S states 2S states

25.0~1

~v velocity sticcharacteri

,7.08.3

-1-Exp )1(~)~,(

2

22

cm

V. Braguta, et.al., Phys.Lett.B646:80-90,2007

V. Braguta, Phys.Rev.D75:094016,2007

V. Braguta, arXiv:0709.3885 [hep-ph]

The twist-3 distribution amplitudesIf one ignores the contribution of the higher Fockstates, EOM unambiguously fix twist-3 distributionamplitudes

P.Ball, et.al., Nucl.Phys. B529

P. Ball, JHEP 9901:010

Properties of distribution amplitudes

Relativistic tailRelativistic tail

75.0||

n

2/32 )( )(a )1(~ ),( nn G

cm~

cm

At DA is suppressed in the region

Fine tuning is broken at due to evolution

This suppression can be achieved if there is fine tuning of an

Improvement of the model for Improvement of the model for DADA The evolution of the second moment

3512 )(a

51

22

The accuracy of the model for DA becomes better at larger scales

increases as decreases in error The

increases as decreases )(a tscoefficien The

2

2

19.0 18.0

state 2

005.0123.0 007.0070.0

state 1

3.04.0GeV 10

25.07.0~

2

GeV 102

~2

c

c

m

m

S

S

Pion distribution amplitudePion distribution amplitude

Distinction from pion distribution amplitude

Much better knowledge of DAs (even for higher twist and excited states) Improvement of the accuracy of models

Rather accurate predictions for exclusive charmonia production

Double charmonium production at B-factories

The processes:

'' ,' ,' / , / cccc JJee

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

This formula was first derived in Bondar, Chernyak, Phys. Lett. B612, 215 (2005)

The results of the calculationThe results of the calculation

Why LO NRQCD predictions are much smaller than the experimental results?

[1] E. Braaten, J. Lee[2] K.Y. Liu, Z.G. He, K.T. Chao[21] D. Ebert, R.N.Faustov, V.O.Galkin, A.P. Martynenko[26] Z.G. He, Y.Fan, K.T. Chao[27] G.T. Bodwin, J. Lee, C.Yu [ ] A.E. Bondar, V.L. Chernyak

1. Relativistic corrections K~3-142. Leading logarithmic radiative corrections K~1.3-2.3

NRQCD resultsNRQCD results

D75 Rev. Phys. al.,et He 20 )/(

D77 Rev. Phys. al.,et Bodwin 6.17)/( 7.103.8

fbJee

fbJee

c

c

NRQCD results are overestimated

ConclusionConclusion Light cone formalism is natural approach to

hard exclusive processes Within the accuracy of the calculation one can

reach the agreement between the experimental results and light cone predictions for the double charmonium production

In hard exclusive processes (e+e- annihilation, bottomonium decays) relativistic and leading logarithmic radiative corrections are very important

Спасибо Спасибо

за вниманиеза внимание