1. 1 Open Questions in Jet Quenching Theory Ivan Vitev QCD Workshop, Brookhaven National Laboratory July 17-21, 2006, Upton, NY

2. 2 Outline of the Talk  Final state interactions in the QGP:  Radiative energy loss  Recursive solutions for multiple parton scattering  Energy, system size dependence and QGP properties  Heavy versus light quarks in p+p and p+A:  Heavy quark correlations  Cold nuclear matter effects for heavy versus light quarks  Initial state energy loss:  Evidence for energy loss in cold nuclei in p+A  Differential distributions for medium-induced initial state gluon bremsstrahlung  Phenomenological implications I.V., Phys.Lett.B 639 (2006), I.V. in preparation Based on: I.V., T.Goldman, M.B.Johnson, J.W.Qiu, hep-ph/0605200  Conclusions:

3. 3 In-Medium Modification of the PQCD Cross Sections The way to understand medium effects on hadron cross sections in the framework of PQCD is to follow the history of a parton from the IS nucleon wave function (PDF) to the FS hadron wave function (FF) Range of the interaction in matter QGP: Cold nuclear matter: Calculated in the Born approximation Scattering in the medium

4. 4 Understanding the LPM Effect Bremsstrahlung is the most efficient way to lose energy since it carries a fraction of the energy Acceleration: radiation Formation time: coherence effects Onset of coherence Full coherence LPM = Landau- Pomeranchuk-Migdal

5. 5 Building up Multiple Scattering Approximations that allow to treat many scatterings: Single Born scattering Double Born scattering

6. 6 Medium-Induced Radiation in the Final State Includes interference with the radiation from hard scattering Coherence phases (LPM effect) Color current propagators Number of scatterings Momentum transfers + + M.Gyulassy,P.Levai,I.V., Nucl.Phys.B 594 (2001)

7. 7 Analytic Approximations and Numerical Results J.D.Bjorken, Phys.Rev.D 27 (1983) mean number of scatterings Landau-Pomeranchuk -Migdal (LPM) effect 0-10%, 20-30% and 60-80% Au+Au, Cu+Cu and central Pb+Pb

8. 8 Jets and Hadrons from PQCD P’P’ xbP’xbP’ P xaPxaP PcPc PdPd P c / z c P d / z d X X Can also incorporate Cronin effect: Kinematic modifications Nuclear medium

9. 9 System Size Dependence of Jet Quenching I.V., Phys.Lett.B 639 (2006) Absolute scale comparisons can and should be done at large p T Similar p T dependence (flat) in Au+Au and Cu+Cu In classes with the same we find numerically the same suppression (For example central Cu+Cu and mid central Au+Au) Reduction of the hard scattering cross section Probability density -

10. 10 Tomographic Summary SPS 2-3.5 0.8210-2401.5-2.51.4-2200-350 RHIC 7-10 0.6380-40014-206-7800-1200 LHC 17-28 0.2710-850190-40018-232000-3500 SPSRHIC LHC F.Karsch, Nucl.Phys.A698 (2002) D. d’Enterria, Eur.Phys.J C (2005)

11. 11 Transport Coefficients in Thermalized QGP Experimental: Bjorken expansion Theoretical: Gluon dominated plasma Energy density Transport coefficients (not a good measure for expanding medium) Define the average for Bjorken

12. 12 Initial state energy loss + HTS High twist shadowing only Implementation of initial state E-loss S.S.Adler et al., nucl-ex/0603017 New Directions for Energy Loss Calculations One possible discussion A new direction: energy loss in cold nuclear matter, initial state Provide simulations including the geometry, combination of elastic and radiative E-loss, jet topologies … It is a challenging theoretical problem that has not been solved (you will see the solution) Of immediate relevance to pQCD effects in cold nuclear matter p+A

13. 13 High Twist Shadowing in DIS J.W.Qiu, I.V., Phys.Rev.Lett. 93 (2004) x = energy = mass Dynamical parton mass (QED analogy): Final state coherent scattering

14. 14 Shadowing parameterizations: (not) Dynamical calculations of high twist shadowing: (not) Energy loss: in combination with HTS (yes) T.Alber et al., E.Phys.J.C 2 (1998) Cold Nuclear Matter Energy Loss Circular arguments should be avoided Nigh statistics 200 GeV p+A measurements will certainly reduce error bars, however … Most useful measurement – low energy p+A run (only at RHIC II)

15. 15 Medium-Induced Radiation in the Initial State Bertsch-Gunion case with interference Realistic initial state medium induced radiation Asymptotic Large Q 2 I.V. in preparation

16. 16 Energy Loss to First Order in Opacity Bertsch-Gunion Energy Loss Initial-State Energy Loss Final-State Energy Loss Qualitatively New Old

17. 17 Numerical Results For Quark Energy Loss Fractional energy loss At any order in opacity we require Energetic quark jets can easily lose 20-30% of their energy, gluon jets x Coherence effects lead to cancellation of the medium-induced radiation Radiation intensity Initial state E-loss is much smaller than the incoherent Bertsch-Gunion limit Initial state E-loss is much larger than final state energy loss in cold nuclei M.Djordgevic, M.Gyulassy, Nucl.Phys.A (2004)

18. 18 Path Length Dependence of E-Loss Bertsch-Gunion – linear dependence on L by definition Final state E-loss – approaches quadratic dependence on L, important for the centrality dependence and elliptic flow Initial state E-loss – approaches linear dependence on L, important for the centrality dependence in p+A reactions

19. 19 pQCD Calculations of Heavy Quarks The contribution of logarithms is small in measurable p T ranges Schematic NLO and NNL LO, NLO, NNLO expansion LL, NLL, NNLL expansion m/p T, (m/p T ) 2 power corrections Will return to power corrections The quarks are treated as “heavy” – in the fixed order calculation. Implies that NLO generates the PDF for charm and bottom (mostly) The new scale, mass, implies large logarithms, but … M.Cacciari, P.Nason, JHEP 9805 (1998)

20. 20 Phenomenological Results Description of open charm at the Tevatron is within uncertainties but not perfect M.Cacciari, P.Nason, JHEP 0309 (2003) Scales: Comparison to the Tevatron data Comparison to the RHIC data R.Vogt et al., Phys.Rev.Lett.95 (2005) At RHIC perturbative calculations under predict the data by factor of 2 – 4. Whether it is experimental systematic, incomplete theory or both – open question Residual large scale uncertainties – should be careful with consistent choices

21. 21 Numerical Results and Partonic Sub-Processes Meaningful K-factors (otherwise K>4) Anti-correlation between K and the hardness of fragmentation r If (LO,c-PDF) ~(NLO,no c-PDF) what are the corrections from (NLO,c-PDF)? PDFs: CTEQ 6.1 LO, J.Pumplin et al., JHEP 207 (2002) FFs: Braaten et al., Phys.Rev.D51 (1995) Partonic sub-processes

22. 22 Hadron Composition of C (B) Triggered Jets Can constrain the hardness of D and B meson fragmentation Possibility for new measurements of heavy flavor production at RHIC D (B) meson “Few” hadrons “Many” soft hadrons D (B) meson Can clarify the underlying hard scattering processes and open charm production mechanisms Robust

23. 23 HTS for Light Hadrons and Open Charm Very similar dynamical shadowing for light hadrons and heavy quarks Insufficient to explain the forward rapidity data Single and double inclusive cross sections are similarly suppressed Single inclusive particles Away-side correlations J.W.Qiu, I.V., Phys.Lett.B632 (2006) I.V., T.Goldman, M.B.Johnson, J.W.Qiu, hep-ph/0605200

24. 24 Energy Loss and High Twist Shadowing Main difference is much more p T independent suppression as compared to high twist shadowing Single inclusive particles Double inclusive yields (away-side) Same Very similar e-loss effects for light hadron and heavy quark spectra Single and double inclusive cross sections are similarly suppressed I.V., T.Goldman, M.B.Johnson, J.W.Qiu, hep-ph/0605200

25. 25 Cancellation of collinear radiation – large angle soft gluons and correspondingly soft hadrons Beyond the cancellation region - well defined power dependence The importance – hard scattering has the same power dependence I.V., Phys.Lett.B630 (2005) Effects of Medium-Induced Radiation

26. 26 Phenomenological Implications Suppression at forward rapidity – from energy loss of the incoming partons Enhancement at backward rapidity – comes from the redistribution of the lost energy Consistent pQCD code is still to be developed Correlated! PHENIX Collaboration, Phys.Rev.Lett. (2005)

27. 27 Conclusions  In-medim interactions can be understood following the history of a jet in a hard scatter:  Coherent final state interactions:  Shadowing is dynamically generated and arises from the final state  Shadowing for D mesons and light pions is similar  Initial state interactions:  Transverse momentum diffusion and Cronin effect  Energy loss and rapidity asymmetry in p+A – new theoretical results  Radiative energy loss in the QGP:  Predicted supession for Cu+Cu versus centrality and p T  QGP suppression is consistent with perturbative interaction of jets in the medium  Modification of di-jets:  Gluon feedback is important for di-hadrons at large angle  Flow leads to deflection of the jet+gluons, so be exp. determined

28. 28 Initial State Elastic Scatterings Reaction Operator = all possible on-shell cuts through a new Double Born interaction with the propagating system + + The approximate solution is that of a 2D diffusion (Neglect and ) Unitarization of multiple scattering = = Initial condition Solution Mean number of scatterings Elastic scattering cross section Implemented in the PQCD approach as broadening of the initial state partons a) Initial state elastic scattering

29. 29 Cronin Effect Default Good description at mid rapidity Wrong sign at forward rapidity Data I.V., Phys.Lett.B526 (2003) Cronin effect: enhancement of cross sections at intermediate transverse momenta relative to the binary scaled p+p A.Accardi, CERN yellow report, references therein

30. 30 Heavy Quarks in p+p and p+A Anti-correlation between K and the hardness of fragmentation r Non-trivial hadron composition of c and b triggered jets PDFs: CTEQ 6.1 LO, J.Pumplin et al., JHEP 207 (2002) FFs: Braaten et al., Phys.Rev.D51 (1995) Robust New possibility: hadron composition of heavy quark triggered jets

31. 31 In-Medium Modification of the PQCD Cross Sections The way to understand medium effects on hadron cross sections in the framework of PQCD is to follow the history of a parton from the IS nucleon wave function (PDF) to the FS hadron wave function (FF) Jet interactions in the medium result in kinematic modifications to the hard scattering cross section that are process dependent d) Final state interactions in the QGP Jet quenching e) Final state interactions in the QGP Large angle correlations, Di-Jet suppression, Deflection of jets by flow a) Initial state interactions Elastic scattering and Cronin effect c) Final state interactions Dynamical shadowing, Generalization to heavy quarks Cold nuclear matter effects are present at times b) Initial state interactions Energy loss and forward Y suppression

32. 32 Process Dependence of Power Corrections Power corrections are process dependent and not separable in PDFs and FFs The function F(x b ) contains the small x b dependence Enhancement ( ) Suppression ( ) (For example DY) (For example forward rapidity) Similar process dependence in single spin asymmetries S.Brodsky et al, Phys.Rev.D65 (2002) S.Brodsky et al, Phys.Lett.B530 (2002) Shadowing is dynamically generated in the hadronic collision

33. 33 Universal Features of Jet Quenching Baseline: Fractional energy loss: I.V., Phys.Lett.B in press, hep-ph/0603010 Prediction: Natural variables Scalings: Suppression: Approximately universal behavior

34. 34 Numerical Results for Jet E-Loss Small probability not to radiate Small fractional energy loss at large E T 0-10%, 20-30% and 60-80% Au+Au, Cu+Cu and central Pb+Pb … … M.Gyulassy, P.Levai, I.V., Phys.Lett.B (2002) Scales in the QGP Initial parameters

35. 35 System Size Dependence of Jet Quenching I.V., Phys.Lett.B in press, hep-ph/0603010 Absolute scale comparisons can and should be done at large p T Similar p T dependence (flat) in Au+Au and Cu+Cu In classes with the same we find numerically the same suppression For example central Cu+Cu and mid central Au+Au Future tests of high energy nuclear physics at the LHC

36. 36 Energy Loss and Di-Jets One way of incorporating energy loss: Satisfies the momentum sum rule A+A “Standard” quenching of leading hadrons Redistribution of the lost energy in “soft” hadrons RHIC LHC Away-side yields Single inclusive particles I.V., Phys.Lett.B630 (2005) e) QGP effects on di-jet production

37. 37 Radiation Distribution and Flow Effects Gluon number distribution without or with q 0 = 1 GeV Mechanical analogy, Theoretical derivation We cannot confirm the prescription q0q0 N.Armesto et al., Phys.Rev.C (2005) Result: same energy loss and shifted reference frame Problem Solution: expand about Show that vanishes Important for deflected jets, to be seen in experiment

38. 38

39. 39 Cancellation of collinear radiation

40. 40

41. 41

42. 42 Energy Loss to First Order in Opacity Bertsch-Gunion Energy Loss Initial-State Energy Loss Final-State Energy Loss Qualitatively

43. 43 Non-Perturbative Scales Chiral perturbation theory (Generalized) vector dominance model Implementation J.W.Qiu, I.V., Phys.Rev.Lett. 93 (2004) Coherent high twist shadowing Bertsch-Gunion QCD evolution of FFs and PDFs

44. 44 Numerical Results For Quark Energy Loss Fractional energy loss At any order in opacity we require Energetic quark jets can easily lose 20-30% of their energy, gluon jets x Coherence effects lead to cancellation of the medium-induced radiation Radiation intensity Initial state E-loss is much smaller than the incoherent Bertsch-Gunion limit Initial state E-loss is much larger than final state energy loss in cold nuclei

45. II. Coherent Power Corrections Data from: NMC Shadowing Ivan Vitev, LANL Longitudinal size: Transverse size: If then If then exceed the parton size Deviation from A-scaling: What remains for theory: power corrections in DIS - suppression FSI are always present: S.Brodsky et al.

46. 46 Medium-Induced Bremsstrahlung 2 Vacuum DGLAP type + + + ++ + + + +... + + Calculate everything else p p Example of hard scattering Calculating the multiple scatterings in the plasma Potential M.Gyulassy, P.Levai, I.V., Nucl.Phys.B594 (2001) Reaction operator: (Cross section level ) Medium Advantage: applicable for elastic, inelastic and coherent scattering controlled approach to coherent radiation (LPM)

47. 47 Comparison to Other Models How do you build from T = 400 MeV LHC: from T = 1 GeV B.Cole, QM 2005 proceedings Strong coupling used as a parameter Find T = 370 MeV (OK) S.Turbide et al., Phs.Rev.C. (2005) I.V., M.Gyulassy, Phys.Rev.Lett. (2002) I.V. Phys.Lett.B in press Find dN g /dy = 1200 (OK) G.Paic et al., Euro Phys.J C (2005) K.Eskola et al., Phys.Rev.D (2005) Find (NOT OK) These are not equivalent descriptions – the medium properties differ by more than an order of magnitude (sometimes close to two)

48. 48 The Source of the Problem Typical gluon energy Note that the region of P T at RHIC is 10-20 GeV and at the LHC 100-200 GeV Energy momentum violation Problem Negative gluon number and jet enhancement from energy loss Negative probability density C.A.Salgado, U.Wiedeman, Phys.Rev.D (2003) GLV Symptomatic of problems in the underlying model of energy loss A useful table Realistic

49. 49 Analytic Limits of Delta E - transport coefficient - effective gluon rapidity density M.Gyulassy, I.V., X.N.Wang, Phys.Rev.Lett.86 (2001) Controlled approach to coherence GLV Includes the fluctuations of the gluon momentum and energy Average implementations in the large number of scatterings limit BDMPS, AMY Calculate differential spectra in Calculate the energy loss Static: BJ expansion: BJ+2D Different dynamics REQUIRES different solutions

50. 50 Energy Loss and High Twist Shadowing Main difference is much more p T independent suppression as compared to high twist shadowing Single inclusive particles Double inclusive yields (away-side) Same Very similar e-loss effects for light hadron and heavy quark spectra Single and double inclusive cross sections are similarly suppressed I.V., T.Goldman, M.B.Johnson, J.W.Qiu, hep-ph/0605200

51. 51 Future Directions of Jet Interaction Studies Self consistency of the description of interactions in cold nuclear matter I.V., in preparation Regimes of initial state energy loss Is there a full Reaction Operator (GLV-like) expression via a formal solution to recurrence relations? Cronin effect What is the energy loss for such momentum transfer from the medium?

52. 52 Energy Loss to First Order in Opacity Bertsch-Gunion Energy Loss Initial-State Energy Loss Final-State Energy Loss Qualitatively New Meaning of the expansion in “n”