Exclusive charmonium productionwithin

Light Cone Formalism.

V.V. BragutaInstitute for High Energy Physics

Protvino, Russia

Outline:Outline:

Introduction Charmonium Distribution Amplitudes

(DA) Exclusive charmonium production within light cone formalism:

Conclusion

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Introduction

Light Cone Formalism

The amplitude is divided into two parts: Hadronization

Twist-2 2-distribution amplitudesTwist-3 4-distribution amplitudes … …

Light cone formalism is designed to study hard exclusive processes

Comparison of LCF and NRQCDThe cross section is double series

1.0~ GeV 6.10s

~

2

2

sM

at

sM

parameterExpansion

LCFPower corrections:

NRQCDRelativisitic corrections:

Radiative corrections:

sonsS state mefor

sonsS state me for

parameterExpansion

2 50.0~v

1 25.0~v

:

2

2

2.0~)( s ss:correctionRadiative

5.0~)( : 2s

Ms

LogsscorrectionRadiativecLogarithmiLeading

Relativistic corrections

21

1

1

xx

),( )H(

dT

LCF NRQCD

DA resums relativististic corrections to the amplitude.

nnCT v

Leading logarithmic radiative corrections

),( ),( ),(

E~ ),,( ),( )(

1

0

ch

1

0

yDz/yPy

dyzD

zDpddzpd

Mji

jiMi

Mii

iM

Exclusive quarkonium production

Inclusive quarkonium production

DA resums leading logarithmic radiative corrections.

),( ),,V( ),(

s~ ),,( ),H(

1

1

1

1

d

dT

Distribution Amplitudes are the key ingredient

of Light Cone Formalism

Charmonium 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.V. Braguta, A.K. Likhoded, A.V. Luchinsky, Phys.Lett.B646:80-90,2007

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

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

The model of DAs within The model of DAs within NRQCDNRQCD

22 v ,1

VELOCITY RELATIVE IN IONAPPROXIMAT ORDERLEADING

n

nn

At leading order approximation is the only parameter

|)|-( 1

)(

The violation of NRQCD scaling The violation of NRQCD scaling rulesrules

At larger scales the fine tuning ofthe coefficients an is broken andNRQCD scaling rules are violated

NRQCD velocity scaling rules are violated in hard processes

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 is better at larger scales

decreases in error The

increases as decreases )(a tscoefficien The n

n

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

Exclusive charmonium production

within light cone formalism

The processes:

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The diagramsThe diagrams

)()()( int sss nonfrfr

Fragmentation diagrams

Nonfragmentation diagrams

The cross section at NLOThe cross section at NLO

...

issection cross theFormalism ConeLight Within

110 nn ss

Relativistic and leading logarithmic radiative Relativistic and leading logarithmic radiative correctionscorrections

3

int1,11,00,11,1

1

is NLOat section cross The

sOfrfrfr

Interference of fragmentation and nonfragmentation Interference of fragmentation and nonfragmentation diagramsdiagrams

The role of correctionsThe role of corrections

The results of the calculationThe results of the calculation

CL) % (90 fb 2.5)'()' /(

CL) % (90 fb 1.9)/()/ /(

:(Belle) results alExperiment

2

2

BrJee

JBrJJee

coson xdistributiAngular

a Bodwin, Braaten, Lee, Phys. Rev. D74

The processes:

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

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

Twist-3 distribution amplitudesTwist-3 distribution amplitudes

)(),( 2.

)O(v)m~,()m~,( .1

:known isWhat

3

2c2c3

asymptotictwist

twisttwist

),()(),(

:amplitudeson distributi of model The

2 twistasymptotic

%50~~ resumation the toduety Uncertain2.

30%-10%~ :parameters of variation the toduety Uncertain1.

:model theofy Uncertaint

2s

M

sLog

Problem:The scale dependences of some twist-3 DAs are are

unknownunknown

First modification of BC formulaFirst modification of BC formulaPropagators:Propagators:

s

MMs PV

PV

22PV

p2pion approximat LOAt

)(p2p BCpaper In

c2V

2c

2c

m Mk m2s

if

k m2s

if

sy

syy

0 if , :asymptotic Unphysical

sm

~ ),)1(

( ),)(( :paper

~T

:amplitude in the divergence , :coneLight

22

2c22

20

22

x,kq

xxysk

xy

yxsqBC

xyxy

dy dx

sykxysq

Second modification of BC formulaSecond modification of BC formula

2

V

v~ where,M

2 BCpaper In

)(0 CC ),(

:currentTensor

cT

T

mf

ppifpV

Problems:Problems:1. Violation of velocity scaling rules at larger scales2. v2 correction can be large for 1S and 2S states

The constants needed in the The constants needed in the calculationcalculation

pifpif

ppifpppifpJ

MfpMfpJ

AcAc

TT

LJL

'5

'5

'

''

/

0 CC 0 CC

)(0 CC ),(' )(0 CC ),(/

0 CC ),(' 0 CC ),(/

(82%) GeV )038.0047.0( (30%) GeV )039.0120.0(

(50%) GeV )038.0076.0()( (24%) GeV )042.0173.0()(

(2.5%) GeV )002.0092.0( %) (2.5 GeV )004.0173.0(

22'22

2/

2'2/

2

22'22

AA

JTJT

LL

ff

MfMf

ff

The values of the constantsThe values of the constants(preliminary results)

The results of the calculationThe results of the calculation

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

a E. Braaten, J. Leeb K.Y. Liu, Z.G. He, K.T. Chao

1. Relativistic corrections K~2.5-62. Leading logarithmic radiative corrections K~1.5-2.5

ConclusionConclusion

The processes considered in the report:

Within the error of the calculation the results are in agreement with the experiments

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

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'' ,'/ ,/ / JJJee