1. Do We Understand Interactions of Hard Probes With Dense Matter ? Joint EIC & Hot QCD Workshop on Future Prospects of QCD at High Energy BNL - 20 July 2006 Berndt Mueller (YITP Kyoto & Duke University)

2. It’s all about “Matter” What’s the Matter? Probing the Matter Understanding the Matter

3. General comments A young field: ~10 years of serious theory, 5 years of data! We are still in the conceptual phase. A rich field – for theorists and experimentalists alike: Full of well defined questions and challenges. An exciting field – new, unanticipated phenomena are discovered at a rapid pace in theory and experiment.

4. Part I What’s the Matter?

5. QCD phase diagram Saturation Baryon density Hadronic matter Critical end point ? Nuclei Chiral symmetry restored Color SC Neutron stars Entropy density Coexistence region QGP RHIC Color charge density EIC Chiral symmetry broken CEBAF CGC

6. Past and future of QCD The first 30 years of QCD were concerned (at the perturbative scale Q 2 ) with single parton distributions: PDF’s, FF’s, GPD’s. The future - exploration of multi-parton (N  2) correlations. These are generally:  Higher-twist effects (suppressed by powers of Q 2 ).  Substantial effects in perturbative Q 2 range require high parton densities: A  1, x  0, dN/dy large.

7. Parton correlations J/  x1x1’x1x1’ x2x2

8. Part II Probing the matter

9. Theoretical tools: Factorization QCD factorization: pp   0 central N coll = 975  94 AuAu   0 Medium modifies the fragmentation function D(z) “Higher twist”

10. High-energy parton loses energy by rescattering in dense, hot medium. q q “Jet quenching” = parton energy loss Described in QCD as medium effect on parton fragmentation: Medium modifies perturbative fragmentation before final hadronization in vacuo. Roughly equivalent to an effective shift in z: Important for controlled theoretical treatment in pQCD: Medium effect on fragmentation process must be in perturbative q 2 domain.

11. Mechanisms High energy limit: energy loss by gluon radiation. Two limits: (a) Thin medium: virtuality q 2 controlled by initial hard scattering (LQS, GLV) (b) Thick medium: virtuality q 2 controlled by rescattering in medium (BDMPS) Trigger on leading hadron (e.g. in R AA ) favors case (a). Low to medium jet energies: Collisional energy loss is competitive! Especially when the parent parton is a heavy quark (c or b). q q L qq g L

12. q q Radiative energy loss: Radiative energy loss Scattering centers = color charges qq g L Density of scattering centers Range of color force Scattering power of the QCD medium:

13. Higher twist formalism

14. Eikonal formalism quark   xx x-x- Gluon radiation: + x  = 0 xx Kovner Wiedemann Radiation probablility ~ correlation function C along forward light cone Gluonic energy density  correlation length Nonperturbative definition of q-hat

15. q-hat in AdS/CFT horizon (3+1)-D world Liu, Rajagopal, Wiedemann, hep-ph/0605178

16. Dynamic medium Thin medium: opacity expansion (GLV) works well for leading hadron assumes perturbative scattering and simplified evolution of the medium

17. Modeling sensitivity Surface emission of leading hadrons I. Vitev, hep-ph/0603010 Renk & Ruppert Details of modeling of the medium and probability distribution P(  E) of energy loss are very important. Average interaction length  L  is not appropriate. Value of q-hat is very sensitive to modeling details.

18. Energy loss at RHIC Data suggest large energy loss parameter: RHIC Eskola et al. p T = 4.5–10 GeV Dainese, Loizides, Paic Present calculations use simplified geometry and evolution models.

19. q-hat at RHIC Pion gas QGP Cold nuclear matter sQGP? ? ? RHIC data Caveat: Details of medium evolution are important for quantitative extraction of q-hat from data! A. Majumder – HT formalism with realistic evolution 

20. The QGP is a “windy” place Longitudinally and transversely flowing medium distorts jet cone Along axisOff axis T. Renk, J. Ruppert, PRC 72 (2005) 044901

21. Flat or rising R AA ? Vitev et al (GLV) LHC Armesto et al (ASW) Extrapolations to LHC energy vary widely due to modeling differences:

22. Charm energy loss q_hat = 14 GeV 2 /fm q_hat = 4 GeV 2 /fm q_hat = 0 GeV 2 /fm dN g /dy = 1000 Very surprising, b/c radiative energy loss of heavy quarks should be suppressed  Reconsider collisional energy loss mechanism (Mustafa & Thoma) From “non-photonic” electrons: S. Wicks et al nucl-th/0512076

23. Reaction plane correlations Quenching effect in non-central collisions depends on direction of jet relative to the collision plane: Allows for limited (!) test of L dependence! 

24. Back-to-back leading hadrons are quadratically suppressed! Di-jet correlations 8 < p T (trig) < 15 GeV/c Away-side jet T. Renk J. Ruppert trigger

25. Photon tagged jets “Golden” channel: q + g  q + . Photon tags p T (and flavor - u/d quark!) of scattered parton. Can be used to perform jet tomography (R AA does not work) Important baseline and calibration for (opposite side) di-hadron tomography. T. Renk, hep-ph/0607166 R AA does not discriminate ?  -jet discriminates models

26. Medium-p T photons Turbide, Rapp, Gale PRC 69 014903 (2004)  0 = 0.33 fm/c, T = 370 MeV Hard Probes 2006, June 15, 2006 – G. David, BNL R.J. Fries, BM, D.K. Srivastava, PRL 90 (2003) 132301 g  q Jet induced contribution

27. Part III Understanding the Matter

28. Where does the “lost” energy go? p+pAu+Au Lost energy of away-side jet is redistributed to rather large angles! Trigger jetAway-side jet

29. Angular correlations STAR Preliminary PHENIX 2.5 < p T,trigger < 4.0 GeV 1.0 < p T,assoc < 2.5 GeV Backward peak of correlated hadrons shifts sideways when p T window of associated hadrons is lowered! Deflection of primary backward parton – or extended shower of secondary particles associated with quenched backward parton?

30. Conical Flow vs Deflected Jets Medium away near deflected jets away near Medium mach cone J. Ulery, Hard Probes 2006 STAR Data Cent=0-5%

31. Theorists’ concepts (Colorless or colorful) sonic shockwave: H. Stöcker, Nucl. Phys. A 750:121-147 (2005), J. Casalderrey-Solana & E. Shuryak, hep-ph/0411315, J. Ruppert & B.M., Phys. Lett. B 618:123-130 (2005), T. Renk & J. Ruppert, hep-ph/0509036 Localized heating of medium: A. Chaudhouri, U. Heinz, nucl-th/0503028 Large Angle Gluon Emission: Ivan Vitev, Phys.Lett.B630:78-84,2005 Cherenkov (-like) radiation: A. Majumder & X. N. Wang, nucl-th/0507062, V. Koch et. al., nuclt-th/0507063, I. Dremin, hep-ph/0507167 Trigger jet

32. Collective QGP modes Transverse modes Signal: Cherenkov rings “Colored” sound ? Longitudinal (sound) modes Normal sound Signal: Mach cones

33. Mach cone phenomenology Trigger jet Away side jet Heating Sound wave Fraction f of isentropic energy deposition into sound mode Fraction (1-f) of dissipative energy deposition into heat – requires viscous, turbulent flow behind leading parton. Thermal spectrum Spectrum of sonic matter Casalderrey et al., hep-ph/0602183

34. Dihadron correlations Two-point velocity correlations among 1-2 GeV/c hadrons             away-side same-side Parton correlations naturally translate into hadron correlations. Parton correlations likely to exist in the quasithermal regime, created as the result of jet-medium interactions. An explanation for compatibility dihadron correclations with recombination? Fries, Bass, BM PRL 94, 122301 (2005)

35. Mach cone phenomenology II Dijet rapidity correlation Trigger vertex distribution Rapidity cut effectsFlow effects on correlation Renk - Ruppert, hep-ph/0605330 Renk, nucl- th/0607035

36. Wakes in the QGP Mach cone requires collective mode with  (k) < k. Question: Is there a colored mode in this kinematic regime? Or – can color field couple “superefficiently” to sound mode? J. Ruppert and B. Müller, PLB 618 (2005) 123 Angular distribution depends on energy fraction in collective mode and propagation velocity

37. Mach cone in AdS/CFT J.J. Friess et al. hep-th/0607022 N = 4 SYM Mach angle

38. The AdS 5 /CFT wake Subsonic Supersonic Angular distributions for v = 0.95 and different k.

39. Summary Jets are rich and discriminative probes of the medium:  Strong energy loss agrees semi-quantitatively with theory;  Probes of a well defined transport coefficient: q-hat;  Quantitative determination of q-hat requires sophisticated and realistic description of medium evolution (transport);  Rigorous, nonperturbative calculation of q-hat in QCD ?  Relative weight of radiative and collisional energy loss ?  Dependence on primary parton flavor ?  Interaction of radiated energy with medium probes dissipation mechanisms and collective QGP modes. Jet studies at the LHC will complement and greatly extend the RHIC measurements, but a lot remains to be explored at RHIC (heavy quarks, photon-jet correl’s, di- and multi-hadron correl’s with particle ID, etc.)