Study of charmonium distribution amplitudes
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Study of charmonium distribution amplitudes. V.V. Braguta Institute for High Energy Physics Protvino, Russia. Content:. Introduction Study of 1S and 2S charmonium distribution amplitudes ( Potential models, NRQCD, QCD sum rules approaches ) Properties of distribution amplitudes

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Study of charmonium distribution amplitudes

Study of charmonium distribution amplitudes.

V.V. Braguta

Institute for High Energy Physics

Protvino, Russia


Content

Content:

  • Introduction

  • Study of 1S and 2S charmonium distribution amplitudes ( Potential models, NRQCD, QCD sum rules approaches)

  • Properties of distribution amplitudes

  • Application: double charmonium production at B-factories


The results were obtained in papers

The results were obtained in papers:

  • “The study of leading twist light cone wave functions of eta_c meson”

    V.V. Braguta, A.K. Likhoded, A.V. LuchinskyPhys.Lett.B646:80-90,2007

  • “The study of leading twist light cone wave functions of J/Psi meson”

    V.V. BragutaPhys.Rev.D75:094016,2007

  • “The study of leading twist light cone wave functions of 2S state charmonium mesons”

    V.V. Braguta, to be published in Phys. Rev. D


Introduction

Introduction


Light cone formalism

Light cone formalism

The amplitude is divided into two parts:

Hadronization can be describedby distribution amplitudes


Definitions of leading twist da

Definitions of leading twist DA


Evolution of da

Evolution of DA

  • DA can be parameterized through the coefficients of conformal expansion an :

  • Alternative parameterization through the moments:


Da of nonrelativistic system

DA of nonrelativistic system


Study of charmonium distribution amplitudes1

Study of charmonium distribution amplitudes


Different approaches to the study of da

Different approaches to the study of DA

1. Functional approach

- Bethe-Salpeter equation

2. Operator approach

- NRQCD

- QCD sum rules


Potential models

Potential models

Brodsky-Huang-Lepage procedure:

  • Solve Schrodinger equation

  • Get wave function in momentum space:

  • Make the substitution in the wave function:

  • Integrate over transverse momentum:


Property of da

Property of DA

DA of nS state has 2n+1 extremums


Model for da within nrqcd

Model for DA within NRQCD

At leading order approximation is the only parameter


Model for da within qcd sum rules

Model for DA within QCD sum rules

Advantage:

The results are free from the uncertainty due to the relativistic corrections

Disadvantage:

The results are sensitive to the uncertainties in QCD sum rules parameters:

QCD sum rules is the most accurate approach


The results of the calculation

The results of the calculation

The results for 1S states

The results for 2S states


Models of das

Models of DAs

1S states

2S states


Properties of distribution amplitudes

Properties of distribution amplitudes


Relativistic tail

Relativistic tail

  • At DA is suppressed in the region

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

  • Fine tuning is broken at due to evolution


Improvement of the model for da

Improvement of the model for DA

The evolution of the second moment

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


Application double charmonium production at b factories

Application: Double charmonium production at B-factories


Results of the calculation

Results of the calculation

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

Why LO NRQCD is much smaller than the experimental results?

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


Study of charmonium distribution amplitudes

Thank You.


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