Modified Fragmentation Function in Strong Interaction Matter Enke Wang (Institute of Particle Physics, Huazhong Normal University) Jet Quenching in QCD-based Model Jet Quenching in High-Twist pQCD Jet Tomography of Hot and Cold Strong Interaction Matter Modification of Dihadron Frag. Function

Fragmentation Function: Jet Quenching: hadrons q leading particle leading particle p-p collision Leading particle suppressed particle suppressed A-A collision Fragmentation Function: DGLAP Equation p

I. Jet Quenching in QCD-based Model G-W (M. Gyulassy, X. –N. Wang) Model: Static Color-Screened Yukawa Potential

Feynman Rule: q p p-q p+k k k-q,a k,c q,b

Opacity Expansion Formulism (GLV) GLV, Phys. Rev. Lett. 85 (2000) 5535; Nucl. Phys. B594 (2001) 371 Elastic Scattering Double Born Scattering

Assumption The distance between the source and the scattering center are large compaired to the interaction range: The packet j(p) varies slowly over the range of the momentum transfer supplied by the potential: The targets are distributed with the density: Opacity: Mean number of the collision in the medium

First Order in opacity Correction

First Order in opacity Correction Induced gluon number distribution: Non-Abelian LPM Effect Medium-induced radiation intensity distribution: Induced radiative energy loss: QCD: QED:

Higher order in Opacity Reaction Operator Approach: (GLV) Induced gluon number distribution: Non-Abelian LPM Effect

Radiated Energy Loss vs. Opacity First order in opacity correction is dominant!

Detailed Balance Formulism (WW) E. Wang & X.-N. Wang, Phys. Rev. Lett.87 (2001) 142301 Stimulated Emission Thermal Absorption B-E Enhancement Factor 1+N(k) Thermal Distribution Func. N(k)

Final-state Radiation Energy loss induced by thermal medium: = Net contribution: Energy gain Stimulated emission increase E loss Thermal absorption decrease E loss

First Order in Opacity Correction Single direct rescattering: Double Born virtual interaction: Key Point: Non-Abelian LPM Effect—destructive Interference!

Energy Loss in First Order of Opacity Energy loss induced by rescattering in thermal medium: Take limit: Zero Temperature Part: L 2 GLV Result Temperature-dependent Part: Energy gain

Numerical Result for Energy Loss Intemediate large E, absorption is important Energy dependence becomes strong Very high energy E, net energy gain can be neglected

Parameterization of Jet Quenching with Detailed Balance Effect Average parton energy loss in medium at formation time: Energy loss parameter proportional to the initial gluon density Modified Fragmentation Function (FF) (X. -N. Wang , PRC70(2004)031901)

Comparison with PHENIX Data Nucl. Phys. A757 (2005) 184

DGLAP Equation at Finite Temperature J. A. Osborne, E. Wang, X.-N. Wang, Phys. Rev. D67 (2003) 094022

DGLAP Equation at Finite Temperature Splitting function at finite temperature:

Quark Energy Loss from Splitting Function The minus sign indicates that the absorptive processes in the plasma overcome the emissive processes. The net Contribution is energy loss!

II. Jet Quenching in High-Twist pQCD Frag. Func.

Modified Fragmentation Function Cold nuclear matter or hot QGP medium lead to the modification of fragmentation function

Jet Quenching in e-A DIS X.-N. Wang, X. Guo, NPA696 (2001); PRL85 (2000) 3591 e-

Modified Frag. Function in Cold Nuclear Matter Modified splitting functions Two-parton correlation: LPM

Modified Frag. Function in Cold Nuclear Matter hadrons ph parton E are measured, and its QCD evolution tested in e+e-, ep and pp collisions Suppression of leading particles Fragmentation function without medium effect: Fragmentation function with medium effect:

Heavy Quark Energy Loss in Nuclear Medium B. Zhang, E. Wang, X.-N. Wang, PRL93 (2004) 072301; NPA757 (2005) 493 Mass effects: 1) Formation time of gluon radiation time become shorter LPM effect is significantly reduced for heavy quark 2) Induced gluon spectra from heavy quark is suppressed by “dead cone” effect Dead cone Suppresses gluon radiation amplitude at

Heavy Quark Energy Loss in Nuclear Medium LPM Effect 1) Larg or small : 2) Larg or small :

Heavy Quark Energy Loss in Nuclear Medium The dependence of the ratio between charm quark and light quark energy loss in a large nucleus

III. Jet Tomography of Hot and Cold Strong Interaction Matter E. Wang, X.-N. Wang, Phys. Rev. Lett. 89 (2002) 162301 Cold Nuclear Matter: Quark energy loss = energy carried by radiated gluon Energy loss

Comparison with HERMES Data , , HERMES Data: Eur. Phys. J. C20 (2001) 479

Expanding Hot Quark Gluon Medium R. Baier et al

Initial Parton Density and Energy Loss jet1 jet2 Initial energy loss in a static medium with density 15 2 A R t » t = 0.1 fm GeV/fm Initial parton density (Energy loss ) is 15~30 times that in cold Au nuclei !

Comparison with STAR data STAR, Phys. Rev. Lett. 91 (2003) 172302

d-Au Result 理论预言 实验结果 E. Wang, X.-N. Wang, Phys. Rev. Lett. 89 (2002) 162301 STAR, Phys. Rev. Lett. 91(2003) 072304

IV. Modification of Dihadron Frag. Function A. Majumder, Enke Wang, X. –N. Wang, Phys. Rev. Lett. 99 (2007) 152301 Dihadron fragmentation: h1 h2 h1 h2 jet

DGLAP for Dihadron Fragmentation

Evolution of Dihadron Frag. Function

Evolution of Dihadron Frag. Function

Medium Modi. of Dihadron Frag. Function

Nuclear Modification of Dihadron Frag. Func. e-A DIS

Hot Medium Modification

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