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

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

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

Jet Quenching phenomena at RHIC Pedestal&flow subtracted STAR Preliminary

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

DGLAP Evolution q p k1 k2 Splitting function

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

Different cut-diagrams + …..

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

LPM Interference Formation time Quark-gluon Compton scattering

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

Quadratic Nuclear Size Dependence

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

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

Collinear Expansion Collinear expansion:

Collinear Expansion Collinear expansion: Ward identities

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

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

TMD (unintegrated) quark distribution y Longitudinal gauge link Belitsky, Ji & Yuan’97 Transverse gauge link

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

Maximal Two-gluon Correlation

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

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

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

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

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

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