1. Lawrence Berkeley National Laboratory
Workshop on Structure of hadrons and nuclei at an Electron Ion Collider, Trento, July 13-18, 2008
Jet transport and gluon saturation in medium
Xin-Nian Wang
Lawrence Berkeley National Laboratory

2. Hard Probes & Structure of Dense Matter
Jet quenching
kT broadneing
Measure the current-current correlator of the medium. Depending on the resolution of the virtual photon, giant dipole resonance

3. Quark Propagation: Jet Quenching & Broadening
Dh/a(z)=dN/dz (z=ph/E)
hadrons ph
parton E
Fragmentation Function
dN/d2kT
Angular distribution
<Dk2T>  jet broadening
dE/dx  modified frag. functions
Suppression of leading particles

4. Jet Quenching phenomena at RHIC
Pedestal&flow subtracted
STAR Preliminary

5. Loosely bound nucleus (p+, q- >> binding energy)
DIS off a large nucleus e-
Loosely bound nucleus (p+, q- >> binding energy)

6. DGLAP Evolution q p k1 k2
Splitting function

7. Induced gluon emission in twist expansionq Ap xp
x1p+kT
Collinear expansion:
Eikonal contribution to vacuum brems.
Double scattering

8. Different cut-diagrams
+ …..

9. Eikonal contribution
central-cut = right-cut = left-cut in the collinear limit

10. LPM Interference
Formation time
Quark-gluon Compton scattering

11. Modified Fragmentation
Guo & XNW’00
Modified splitting functions
Two-parton correlation:

12. Quadratic Nuclear Size Dependence

13. Validity of collinear expansion
One has to re-sum higher-twist terms
Or model the behavior of small lT behavior
Need to include all:

14. Gauge Invariance p k Expansion in kT One should also consider
Final matrix elements
should contain:
TMD factorization

15. Collinear Expansion
Collinear
expansion:

16. Collinear Expansion
Collinear
expansion:
Ward identities

17. Collinear Expansion (cont’d)q xp
‘Twist-2’ unintegrated quark distribution
Liang & XNW’06
‘Twist-3’ unintegrated quark distribution
x1p q xp

18. TMD (unintegrated) quark distribution
Contribute to azimuthal and single spin asymmetry
Twist-two integrated quark distribution

19. TMD (unintegrated) quark distributiony
Longitudinal gauge link
Belitsky, Ji & Yuan’97
Transverse gauge link

20. All info in terms of collinear quark-gluon matrix elements
Transport Operator
Taylor expansion
Transport operator
Color Lorentz force:
All info in terms of collinear quark-gluon matrix elements
Liang, XNW & Zhou’08

21. Maximal Two-gluon Correlation

22. Jet transport parameter
Nuclear Broadening
Liang, XNW & Zhou’08
Majumder & Muller’07
Kovner & Wiedemann’01
Jet transport parameter
Solution of diffusion eq.

23. Extended maximal two-gluon correlation
Scale dependent qhat
Non-Gaussian distr. contains information about multi-gluon correlation in N

24. Jet transport parameter & Saturation
Multi-gluon correlation:
Kochegov & Mueller’98
McLerran & Venugapolan’95
Gluon saturation
For unpolarized nuclei,
Equivalent to short distance approximation of dipole cross section
Though it is not clear how this two is related.
Casalderrey-Salana, &
XNW’07

25. Conformal or not Gluon distr. from HTL at finite-T (gluon gas)
Casalderrey-Salana, XNW’07
Gluon distr. from HTL at finite-T (gluon gas)
DGLAP
DGLAP evolution in linearized regime
DGLAP with
fixed as:
Under double log approximation
Strong coupling SYM:
Hatta, Iancu & Mueller’08
Gubser 07,
Casaderrey-Salana & Teaney’07

26. Measuring qhat xp Direct measurement: Measuring parton energy loss
or modified fragmentation function
Measuring parton energy loss
GW:Gyulassy & XNW’04
BDMPS’96
LCPI:Zakharov’96
GLV: Gyulassy, Levai & Vitev’01
ASW: Wiedemann’00
HT: Guo & XNW’00
AMY: Arnold, Moore & Yaffe’03 q Ap xp
x1p+kT

27. Summary
Jet transverse momentum broadening provides a lot of information about the medium: gluon density, gluon correlations, etc, all characterized by jet transport parameter qhat
Jet quenching provided an indirect measurement of qhat
Jet quenching phenomenology has advanced to more quantitative analysis
More exclusive studies such as gamma-jet and medium excitation are necessary