Enke Wang

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Modified Fragmentation Function from Quark
Recombination

• Enke Wang
• (Institute of Particle Physics, Huazhong
  Normal University)
• with A. Majumder, X.-N. Wang
• I. Introduction
• Quark Recombination and Parton Fragmentation at
  zero temperature
• Quark Recombination and Parton Fragmentation in a
  Thermal Medium
• Conclusion
• Nucl-th/0506040

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I. Introduction
Fragmentation Function in Vacuum
are measured, and its QCD evolution
tested in ee-, ep and pp collisions
Modification of Fragmentation Function in
Medium
Jet Quenching
Suppression of leading particles
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Energy Loss in Cold Nuclear Matter from e-A DIS
E. Wang, X.-N. Wang, Phys. Rev. Lett. 89 (2002)
162301
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Energy Loss in Hot Medium from Au-Au Collision
Energy loss (initial parton density) 30 times
larger than that in cold Au nuclei !
PHENIX, Nucl. Phys. A757 (2005) 184
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Quark Recombination in intermediate Pt Region
Baryon
Meson
Intermediate Pt Quark Recombination R.
C. Hwa, C. B. Yang, PRC67 (2003) 034902
V. Greco, C. M. Ko, P. Levai, PRL90 (2003)
202302 R. J. Fries, B. Muller, C. Nonaka,
S. A. Bass, PRL90 (2003) 202303
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Motivation of the Work
How to deal with the quark recombination
from the quantum field theory? Is it
possible to deal with the jet quenching and the
recombination in a unified framework?
This Work Establish the theoretical
framework of the quark recombination from the
modification of fragmentation function in thermal
medium.
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II. Quark Recombination and Parton Fragmentation
at zero Temperature
Single hadron fragmentation function
DGLAP
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Constitutent Quark Model
Meson state
Baryon state
Insert them into
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Meson Production from Recombination (T0)
Recombination Probability
Constituent Diquark Distribution Function
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Evolution of Double Constituent Quark
Distribution Function
Radiative correction to diquark distribution
function
DGLAP Equation of diquark distribution function
They have the same form as the single hadron
fragmentation function !
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Sum Rule for Constituent Quark Distribution
Function
Single Constituent Quark Distribution Function
Diquark Distribution Function
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III. Quark Recombination and Parton Fragmentation
in a Thermal Medium
J.Osborne, E.Wang, X.N.Wang PRD67 (2003) 094022
Thermal Average
Single hadron fragmentation at finite T
Difference with that at zero temperature
Depend on initial energy of parton and
Temperature T Parton hadronize all together
with the medium
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Shower-Shower Shower-Thermal
Modified fragmentation function with energy loss
in thermal medium
Shower-Shower Contribution
Shower-Thermal Contribution
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Thermal-Thermal Contribution
R. Fries, B. Muller, C. Nonaka, S. Bass, PRC68
(2003) 044902
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Baryon Production from Quark Recombination
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Fragmentation at extreme high Pt
Extreme high transverse momentum
Fragmentation is dominant
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VI. Conclusion

• The hadron fragmentation function can be
  expressed as the convolution of the recombination
  probability and the constituent quark
  distribution function.
• The DGLAP equation of the constituent quark
  distribution function is derived. The relation
  among triquark, diquark and single quark
  distribution function is obtained through sum
  rule.
• Both thermal-shower recombination and parton
  energy loss lead to medium modification of parton
  fragmentation functions
• A unified framework for parton energy loss and
  quark recombination

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Thank You
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Thermal Average of Matrix Element
Shower-Shower
Shower-Thermal
Thermal-Thermal
represents the modified fragmentation function
with energy loss and detailed balance in hot
medium
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Meson Production from Thermal Quark Recombination
Meson fragmentation function at finite T