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Workshop on Structure of hadrons and nuclei at an Electron Ion Collider, Trento, July 13-18, 2008

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. e -. Jet quenching. e -. k T broadneing.

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Workshop on Structure of hadrons and nuclei at an Electron Ion Collider, Trento, July 13-18, 2008

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  1. 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 e- Jet quenching e- kT broadneing

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

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

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

  6. DGLAP Evolution q q k1 k2 p p Splitting function

  7. Induced gluon emission in twist expansion q q xp xp x1p+kT Ap Ap 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 Modified splitting functions Two-parton correlation: Guo & XNW’00

  12. Quadratic Nuclear Size Dependence

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

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

  15. Collinear Expansion Collinear expansion:

  16. Collinear Expansion Ward identities Collinear expansion:

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

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

  19. TMD (unintegrated) quark distribution y 0 Longitudinal gauge link Transverse gauge link Belitsky, Ji & Yuan’97

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

  21. Maximal Two-gluon Correlation

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

  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 Gluon saturation Casalderrey-Salana, & XNW’07 Multi-gluon correlation: Kochegov & Mueller’98 McLerran & Venugapolan’95

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

  26. Measuring qhat q q xp xp x1p+kT Ap Ap Measuring parton energy loss or modified fragmentation function 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 Direct measurement:

  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

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