Enke Wang (Institute of Particle Physics, Huazhong Normal University)

with A. Majumder, X.-N. Wang

I. Introduction

II. Quark Recombination and Parton Fragmentation at zero temperature

III. Quark Recombination and Parton Fragmentation in a Thermal Medium

IV. Conclusion

Nucl-th/0506040

Modified Fragmentation Function from Quark Recombination

I. Introduction

hadrons

ph

parton

E

),,()(0 EzDzD ahah

)(0 zDah

are measured, and its QCD evolutiontested in e+e-, ep and pp collisions

Suppression of leading particles

Fragmentation Function in Vacuum:

Modification of Fragmentation Function in Medium:

),1

(1

1),( 0

z

zD

zEzD ahah

Jet Quenching

Energy Loss in Cold Nuclear Matter from e-A DIS

0.5 GeV/fmdE

dx

E. Wang, X.-N. Wang, Phys. Rev. Lett. 89 (2002) 162301

Energy Loss in Hot Medium from Au-Au Collision

PHENIX, Nucl. Phys. A757 (2005) 184

fmGeVdx

dE8.13

Energy loss (initial parton density) ~ 30 times larger than that in cold Au nuclei !

Quark Recombination in intermediate Pt Region

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

Baryon

Meson

Baryon

Meson

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.

II. Quark Recombination and Parton Fragmentation at zero Temperature

Single hadron fragmentation function:

DGLAP:

Meson state:

Constitutent Quark Model

Baryon state:

Insert them into:

Meson Production from Recombination (T=0)

Recombination Probability:

Constituent Diquark Distribution Function:

Evolution of Double Constituent Quark Distribution Function

DGLAP Equation of diquark distribution function:

They have the same form as the single hadron fragmentation function !

Radiative correction to diquark distribution function:

Sum Rule for Constituent Quark Distribution Function

Single Constituent Quark Distribution Function:

Diquark Distribution Function:

III. Quark Recombination and Parton Fragmentation in a Thermal Medium

Thermal Average:

Single hadron fragmentation at finite T:

J.Osborne, E.Wang, X.N.Wang

PRD67 (2003) 094022

Difference with that at zero temperature:

Depend on initial energy of parton and Temperature T

Parton hadronize all together with the medium

“Shower-Shower” & “Shower-Thermal”

“Shower-Shower” Contribution:

“Shower-Thermal” Contribution:

Modified fragmentation function with energy loss in thermal medium

“Thermal-Thermal” Contribution

R. Fries, B. Muller, C. Nonaka, S. Bass, PRC68 (2003) 044902

Baryon Production from Quark Recombination

= +

++

Fragmentation at extreme high Pt

Extreme high transverse momentum:

01

1/||

TpTe)|(| TpT

Fragmentation is dominant

Baryon

Meson

VI. Conclusion

1. The hadron fragmentation function can be expressed as the convolution of the recombination probability and the constituent quark distribution function.

2. 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.

3. Both thermal-shower recombination and parton energy loss lead to medium modification of parton fragmentation functions

4. A unified framework for parton energy loss and quark recombination

Thank YouThank You

Thermal Average of Matrix Element

Shower-Shower

Shower-ThermalThermal-Thermal

represents the modified fragmentation function with energy loss and detailed balance in hot medium

Meson Production from Thermal Quark Recombination

Meson fragmentation function at finite T: