Exclusive%20charmonium%20production%20within%20Light%20Cone%20Formalism.

1
Exclusive charmonium productionwithin Light
Cone Formalism.

• V.V. Braguta
• Institute for High Energy Physics
• Protvino, Russia

2
Outline

• Introduction
• Charmonium Distribution Amplitudes (DA)
• Exclusive charmonium production within
• light cone formalism
• Conclusion

3
Introduction
4
Light Cone Formalism
Light cone formalism is designed to study hard
exclusive processes
The amplitude is divided into two parts
Hadronization
Twist-2 2-distribution amplitudesTwist-3
4-distribution amplitudes

5
Comparison of LCF and NRQCD

• The cross section is double series

LCF Power corrections
NRQCD Relativisitic corrections
Radiative corrections
6
Relativistic corrections
LCF
NRQCD
DA resums relativististic corrections to the
amplitude.
7
Leading logarithmic radiative corrections
Inclusive quarkonium production
Exclusive quarkonium production
DA resums leading logarithmic radiative
corrections.
8
Distribution Amplitudes are the key ingredient
of Light Cone Formalism
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Charmonium Distribution Amplitudes
10
The models of leading twist DAs
1S states
2S states

• V.V. Braguta, A.K. Likhoded, A.V. Luchinsky,
  Phys.Lett.B64680-90,2007
• V.V. Braguta, Phys.Rev.D75094016,2007
• V.V. Braguta, arXiv0709.3885 hep-ph

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The model of DAs within NRQCD
At leading order approximation is the only
parameter
12
The violation of NRQCD scaling rules

• At larger scales the fine tuning of
• the coefficients an is broken
• and
• NRQCD scaling rules are violated

NRQCD velocity scaling rules are violated in hard
processes
13
Improvement of the model for DA

• The evolution of the second moment

The accuracy of the model for DA is better at
larger scales
14
Exclusive charmonium production within light
cone formalism
15
The processes
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The diagrams
Fragmentation diagrams
Nonfragmentation diagrams
17
The cross section at NLO
18
Relativistic and leading logarithmic radiative
corrections
Interference of fragmentation and
nonfragmentation diagrams
The role of corrections
19
The results of the calculation
a Bodwin, Braaten, Lee, Phys. Rev. D74
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The processes
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ee- gV(3S1) P(1S0)
This formula was first derived in Bondar,
Chernyak, Phys. Lett. B612, 215 (2005)
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Twist-3 distribution amplitudes
ProblemThe scale dependences of some twist-3
DAs are unknown
23
First modification of BC formula

• Propagators

24
Second modification of BC formula
Problems1. Violation of
velocity scaling rules at larger scales2. v2
correction can be large for 1S and 2S states
25
The constants needed in the calculation
The values of the constants(preliminary results)
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The results of the calculation
a E. Braaten, J. Leeb K.Y. Liu, Z.G. He,
K.T. Chao
Why LO NRQCD predictions are much smaller than
the experimental results?
1. Relativistic corrections K2.5-62. Leading
logarithmic radiative corrections K1.5-2.5
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Conclusion

• The processes considered in the report
• Within the error of the calculation the results
  are in agreement with the experiments
• In hard exclusive processes (ee- annihilation,
  bottomonium decays) relativistic and leading
  logarithmic radiative corrections are very
  important