Jet Tomography and Particle Correlations in Heavy-Ion Collisions Barbara Betz Thanks to: Miklos Gyulassy, Jorge Noronha, Dirk Rischke, Giorgio Torrieri Phys. Rev. C 79, (2009); Nucl. Phys. A 830, 777c (2009); Phys.Rev. Lett. 105, (2010); arXiv: [nucl-th] arXiv: [nucl-th]

2 HIC Facilities initial state pre-equilibrium expanding fireball hadronization hadronic phase and freeze-out S. Bass, Talk Quark Matter 2001 RHIC FAIR LHC 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz  RHIC, BNL: 2000 – … p+p, d+Au, Cu+Cu, Au+Au  LHC, CERN: 2008/9 - … p+p, Pb+Pb  FAIR, GSI: ~ … accelerates ions from p to U ??

303/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz Tomography and Correlations What can be extracted about medium proper- ties? What do conical correlations tell us? What is the role/impact of fluctuating initial conditions? Test sensitivity of azimuthal dependence of single and dihadron nuclear modification factors 4 < p T trigger < 6 GeV/c 0.15 < p T assoc < 4 GeV/c STAR, Nucl. Phys. A 774, 129 (2006) PHENIX, Phys. Rev. Lett. 105, (2010) The Medium Initial Conditions

4 2 Major RHIC Results 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz

5  Reproducing the elliptic flow v 2 P. Romatschke and U. Romatschke, Phys. Rev. Lett. 99, (2007) Medium behaves like an almost ideal fluid BNL press release, April /04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz Particles don‘t interact, expansion independent of initial shape Particles interact, expansion determined by density gradient „ dust “ fluid Data can be described by hydrodynamics with small Fluid-like Medium

6 Jet Quenching Like in medicine, hard probes can be used to investigate the medium properties If created matter is opaque, a jet depositing its energy should eventually disappear jet suppression STAR, Phys. Rev. Lett. 91 (2003) < p T trigger < 6 GeV/c p T assoc > 2 GeV/c What can the energy lost tell us about the medium properties and the initial conditions? Trigger particle University Wuppertal, “Schul-Vorlesungen zur Physik” 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz

7 The Medium 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz

8 Jets in HIC I By observation:  Confirm fast thermalization  Study EoS of the fluid Mach cone angle sensitive to EoS Can energy lost by jets tell us something about medium properties? IF the medium behaves like a fluid: Mach cones have to occur because of fluid dynamics

4 < p T trigger < 6 GeV/c 0.15 < p T assoc < 4 GeV/c Au+Au / p+p = 200 GeV PHENIX, Phys. Rev. C 77, (2008) 9 Jets in HIC II STAR, Nucl. Phys. A 774, 129 (2006) Reflect interaction of jet with medium Redistribution of energy to lower p T - particles Re-appearance of the away-side for low and intermediate p T assoc H. Stöcker, Nucl. Phys. A 750, 121 (2005), J. Casalderrey-Solana et al. Nucl. Phys. A 774, 577 (2006) 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz

10 Experimental Studies 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz

Many more studies: path-length dependence, centrality dependence, energy dependence 11 STAR, Phys. Rev. C 82, (2010) see also PHENIX, Phys. Rev. C 77, (2008) Position of away-side peaks does not change strongly with p T assoc Not due to Cherenkov gluon radiation What happens to larger p T trigger ? Jet - Studies in HIC I 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz A. Sickeles [PHENIX], Eur. Phys. J. C 61, 583 (2009); PHENIX, Phys. Rev. Lett. 97, (2006); J. Jia, Eur. Phys. J. C 62, 255 (2009)

12 Some caveats 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz

13 Background Subtraction How can one proof/disproof the two-source model? J. Ulery [STAR], PoS LHC07, 036 (2007) D. d’Enterria and BB., Springer Lecture Notes (2008) 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz  Assumption (Two-source model) : No correlations between flow anisotropy and jets ZYAM (Zero Yield At Minimum)  Subtraction of: estimated elliptic flow modulated background  can leads to: double peaked structure Background: Particle correlation from elliptic flow Other methods A. Sickles et al, Phys. Rev. C 81, (2010) STAR, arXiv: [nucl-ex]

14 3-Particle Correlations J. Ulery [STAR], Int. J. Mod. Phys. E 16, 2005 (2007) p trig T =3 – 4 GeV, p assoc T =1 – 2 GeV  Three-particle correlations seem to corroborate Mach cone idea  What’s the effect of ZYAM?  No agreement with 3-particle cumulant method C. Pruneau, Phys. Rev. C 79, (2009) 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz Deflected jetMach Cone p trig T >3 GeV, p assoc T =1 – 2 GeV C. Pruneau, Talk at the Workshop on ‘Critical Asessment of Theory and Experiment on Correlations at RHIC’, BNL, February 2009

15 Theoretical Approach 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz

16 Modelling of Jets STAR, Phys. Rev. Lett. 95, (2005) residue of energy and momentum given by the jet Assumption of isochronous/isothermal freeze-out No interaction afterwards mainly flow driven  Conversion into particles Freeze-out: Jets can be modelled using (ideal) hydrodynamics: e +p v.  Medium created in a HIC can be described using hydrodynamics 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz

17 The Static Medium 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz

18 Stopped Jet I Applying a static medium and an ideal Gas EoS for massless gluons Assume: Near-side jet is not modified by medium Maximal fluid response Jet decelerating from v=0.999 according to Bethe-Bloch formalism a=-1.36 GeV/fm Simplest back-reaction from the medium Bragg Peak adjusts path length BB et al., Phys. Rev. C 79, (2009) 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz

19 Stopped Jet II Mach cone for sound waves Diffusion wake t=4.5/v fm BB et al., Phys. Rev. C 79, (2009) 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz

20 Stopped Jet III Diffusion wake causes peak in jet direction Normalized, background-subtracted isochronous Cooper-Frye at mid-rapidity Energy Flow Distribution Assuming: Particles in subvolume will be emitted into the same direction p T = 5 GeV BB et al., Phys. Rev. C 79, (2009) Any conclusions about deposition mechanism??? 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz

2103/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz The Expanding Medium

22 Expanding Medium I Consider different jet paths b=0 Apply Glauber initial conditions and an ideal Gas EoS for massless gluons Focus on radial flow contribution Experimental results based on many events A. K. Chaudhuri, Phys. Rev. C 75, (2007), A. K. Chaudhuri, Phys. Rev. C 77, (2008) Two-particle correlation (T freeze-out < T crit = 130 MeV): near-side jet dE/dt = 1 GeV/fm Jet 150 E tot = 5 GeV 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz

23 Expanding Medium II E tot = 5 GeV broad away-side peak double peaked structure due to non-central jets T trig p T trig = 3.5 GeV PHENIX, Phys. Rev. C 77, (2008) v jet =0.999 BB et al., Phys. Rev. Lett. 105, (2010) 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz

24 Expanding Medium III E tot = 10 GeV Strong impact of the Diffusion wake broad away-side peak double peaked structure Causes smaller dip for p T =2 GeV T trig p T trig = 7.5 GeV 6 < p T trigger < < p T assoc < 2.5  Yield Path length dependence Centrality dependence 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz STAR, Phys. Rev. C 82, (2010) BB, arXiv: [nucl-th]

25 Expanding Medium IV Conical emission angle also appears for subsonic jets Not a Mach cone Considering a bottom quark (M=4.5 GeV), propagating at v jet < c s (energy-momentum deposition scenario) T assoc p T assoc = 2.0 GeV Cu+Cu: Similar away-side shoulder width, T assoc double-peak structure reappars for p T assoc = 3 GeV PHENIX, PRL98, (2007) 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz BB et al., Phys. Rev. Lett. 105, (2010)

26 Some more caveats 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz

27 Hot Spots I Can fluctuating initial condition explain the 2+3-particle correlations? Takahashi et al, PRL 103, (2009) F. Grassi, Talk at the Glasma Workshop, BNL, May 2010 R. Andrade et al., J. Phys. G 37, (2010) 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz

28 Hot Spots II Check with one single hot spot 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz Au,  e/e 0 = 2

29 Hot Spots III Can hot spots explain everything? There is a superposition of jets and fluctuating initial conditions 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz T assoc p T assoc = 2.0 GeV T trig p T trig = 8.0 GeV T trig p T trig = 3.5 GeV Both lead to double-peak structureCoalesced peak only for jet events Heavy quark jets need to be studied BB, arXiv: [nucl-th]

30 Heavy-flavor results 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz e-h correlations from heavy-flavor decay show a double-peak structure on the away-side Clear indication that the signal is not just background fluctuation A. Adare et al. [PHENIX], arXiv: [nucl-ex]

31 Why v 3 deformations cannot be the whole story p trig T =3 – 4 GeV, p assoc T =1 – 2 GeV What are the consequences of triangular flow? The latter case should not be subtracted! v 3 could be due to initial conditions (hot spots) OR due to a jet traversing the medium 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz  Correlation in  1 -  2  1/2 120°  No correlation in  1 -  2 B. Alver et al., Phys. Rev. C 81, (2010) 120° Shock front?? ~ 120 J. Ulery [STAR], Int. J. Mod. Phys. E 16, 2005 (2007) B. Alver, Talk at the Glasma Workshop, BNL, May 2010

32 Fluctuating Initial Conditions 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz

3303/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz Initial Conditions  Studying heavy-ion collisions requires a good understanding of the role of the initial conditions:  Glauber model: incoherent superposition of p+p collisions  Color Glass Condensate (CGC): saturation effects are included  They differ:  initial temperature gradients  initial high-p T parton distribution  distance travelled by each parton Leads to a different opacity estimate B. Alver, Talk at the Glasma Workshop, BNL, May 2010 CGC Glauber L. McLerran, Talk at a the CP Violation Workshop, BNL, April 2010

3403/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz Opacity of the Medium  Exploring the properties of the strongly- coupled sQGP jet quenching: signal for creation of opaque matter (QGP) S. Bass et. al., PRC 79 (2009), defined via:  Current description commonly based on pQCD though medium is supposedly sQGP D. D’Enterria, Lect. Notes Phys.785 (2010), 285

S. Bass et. al., PRC 79 (2009), /04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz Caveat  pQCD descriptions disagree in their prediction of the azimuthal anisotropy of high-p T hadrons, characterizing due to v 2 =v 2 ( l ) v 2 is sensitive to the path length dependence of energy loss, scaling as dE/dx ~ l z : z=1 : pQCD z=2 : AdS/CFT (on-shell partons) z>2 : AdS/CFT (off-shell partons) M. Gyulassy et. al., PRL 85 (2000), 5535 S. Gubser et. al., JHEP 0810 (2008), 052; P. Chesler et.al., PRD 79 (2009)

36 Energy-Loss Mechanisms 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz A. Adare et al, Phys. Rev. Lett. 105, (2010)  First investigation of v 2 (N part ) and R AA (N part ) for p T > 5 GeV hadrons is based on J. Jia et. al., PRC 82 (2010), simple jet absorption model  Once R AA (N part =350) ~ 0.18 for 0-5%  0 data  pQCD-like energy loss fails to reproduce v 2 (N part )  AdS/CFT-like energy loss describes data for CGC initial conditions pQCD-likeAdS/CFT-like

37 Generic Energy Loss Model 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz

38 Generic Energy Loss Model 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz Choosing an ansatz for the energy loss   = 2fm, one can determine the R AA (N part ), v n (N part ) P: momentum of the jet(s) a,z: parameters controlling the jet-energy and path-length dependence  : being fixed thus that R AA (N part =350) ~ 0.18 for most central data and considering Bjorken expansion via CGC/KLN: H. Drescher et. al., PRC 76 (2007) Glauber: B.Betz et.al., arXiv: [nucl-th]

39 R AA and v 2 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz z=1z=2 Having fixed  for R AA (N part =350) ~ 0.18 R AA (N part ) can be reproduced z=1: v 2 not reproduced z=2: v 2 reproduced for CGC initial cond. B.Betz et.al., arXiv: [nucl-th] a=0.3 Small fluctuations for R AA (N part ) large fluctuations for v 2 (N part ) Not straightforward to distinguish between initial conditions

4003/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz R AA vs. I AA, and v n vs. v n I AA  Extend to dijet analysis, but considering  away =  In contrast to Jia’s model, we fit the R AA vs. I AA  v n vs. v n I AA :  clear shift between Glauber and CGC model  saturation effect for larger z B.Betz et.al., arXiv: [nucl-th] J. Jia et.al., arXiv: [nucl-th]  It is necessary to always determine the mean and the with of a correlation!

41 Higher Harmonics 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz z=1z=2  v 3 ≠0 event-by- event,  v 4 similar for average and event-by-event initial conditions Not suitable to distinguish between Glauber and CGC initial conditions Higher harmonics are more sensitive to local gradients, but also to event- by-event fluctuations larger v 3,4 fluctuations B.Betz et.al., arXiv: [nucl-th]

42 Path-length dependence 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz  Study the path-length dependence at b=8fm:  Once R AA is fixed via ,  sensitivity remains mostly for v 2 and v 3 saturation effect occurs for larger z described by AdS/CFT off-shell partons S. Gubser et. al., JHEP 0810 (2008), 052; P. Chesler et.al., PRD 79 (2009)  Measurement of virtuality in jet-photon collisions & v 2,3 could lead to signature of AdS/CFT dynamics & microscopic mechanism of energy loss. B.Betz et.al., arXiv: [nucl-th]

Summary  „Conical“ signal can be created (general effect): by averaging over deflected wakes created by jets. Structure cannot directly be related to EoS, but is a measure for the flow even for subsonic jets Necessary to study heavy-flavor tagged jets. 43  „Conical“ correlations could arise from multiple non-Mach sources 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz  Investigated higher Fourier harmonics of jet quenching Showing that they are remarkably insensitive to the Glauber and KLN/CGC model initial conditions  Studied the path-length dependence for larger exponents a saturation effect occurs for larger exponents favoring an AdS/CFT energy loss

44 Backup 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz

45 Investigation of path length dependence: Double-peaked structure becomes more pronounced out-of-plane A. Sickeles [PHENIX], Eur. Phys. J. C 61, 583 (2009) Jet - Studies in HIC 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz Could be due to deflection

46 Centrality dependence: double-peaked structure for central collisions one peak structure for very peripheral collisions PHENIX, Phys. Rev. Lett. 97, (2006) J. Jia, Eur. Phys. J. C 62, 255 (2009) Jet - Studies in HIC Energy Scan: double-peaked structure occurs at about the same angle for different collision energies Mach cone??? 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz

47 Stopped Jet Jet stops after t=4.5/v fm Vorticity conservation t FO =4.5/v fmt FO =6.5/v fmt FO =8.5/v fm Diffusion wake still present BB et al., Phys. Rev. C 79, (2009) 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz

48 Stopped Jet t FO =4.5/v fmt FO =6.5/v fmt FO =8.5/v fm Diffusion wake causes peak in jet direction Larger impact of thermal smearing BB et al., Phys. Rev. C 79, (2009) 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz

4903/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz Still influence of diffusion wake Transverse momentum deposition: from explosion of matter t=4.5/v fm Vorticity conservation Punch – Through Jet BB et al., Phys. Rev. C 79, (2009)

50 BAMPS: Boltzmann Approach of MultiParton Scatterings A transport algorithm solving the Boltzmann equations for on-shell partons with pQCD interactions C. Greiner, Talk at the Opening Symposium of the JET Collaboration, Berkeley, June 2010 Box scenario, no expansion, massless Boltzmann gas interactions, 2 -> 2 The shock front (Mach front) gets broader and vanish with more dissipation 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz Mach Cones in Transport

5103/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz Different Jet-Energy Loss Modells

5203/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz Modelling Jets using … Conclusion about Mach cones? pQCD AdS/CFT P. Chesler and L. Yaffe, Phys. Rev. D 78, (2008) R. Neufeld et al, Phys. Rev. C 78, (2008) Strongly-coupled theory Pointing vector perturbation Momentum density perturbationEnergy density perturbation Weakly-coupled theory v=0.75 v=

5303/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz Non-Mach correlations caused by Neck region Jets in AdS/CFT J. Noronha et al., Phys. Rev. Lett. 102, (2009)

5403/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz Heavy Quark Jets

5503/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz Heavy Quark Jets Compare weakly and strongly coupled models using heavy punch-through jet pQCD: Neufeld et al. source for a heavy quark AdS/CFT: Stress tables with R. Neufeld et al, Phys. Rev. C 78, (2008) p T = 3.14 GeV BB et al., Phys. Lett. B 675, 340 (2009) No Mach-like peaks: AdS/CFT: Strong influence of the Neck region Static medium and isochronous freeze-out needed for comparison t=4.5/v fm S. Gubser et al, Phys. Rev. Lett. 100, (2008) BB et al., Phys. Lett. B 675, 340 (2009) J. Noronha et al., Phys. Rev. Lett. 102, (2009)

56 Expanding Medium Comparing different deposition scenarios, one sees that „cone“ angle approximately the same for different deposition scenarios T assoc p T assoc = 2.0 GeV: No double-peaked structure for pure energy deposition scenario due to thermal smearking T trig p T trig = 3.5 GeV T assoc p T assoc = 3.0 GeV T assoc p T assoc = 2.0 GeV v jet =0.999 BB et al., arXiv: /04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz

57 Initial Fluctuations I P. Sorensen J. Phys. G 37, (2010), B. Alver et al., Phys. Rev. C 81, (2010) Glauber initial conditions: due to symmetry, odd Fourier components vanish higher Fourier components may occur Fluctuating initial conditions: B. Alver, Talk at the Glasma Workshop, BNL, May /04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz

58 Initial Fluctuations II B. Alver et al., arXiv: B. Alver et al., Phys. Rev. C 81, (2010), B. Alver et al., arXiv: H. Petersen et al., arXiv: v 3 not negligable small v 3 is extensively studied Calculating v 3 using a viscous hydro model with initial conditions deformed according to the eccentricities from a Glauber and a KLM (CGC) model 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz

59 Insensitivity of higher v n ‘s 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz  Why are the v n ‘s at high-p T so insensivite to initial conditions while the v n ‘s of soft particles are?  viscous forces are driven by local gradients  jet absorption is driven by global differences in the integrated These two effects are different, especially event-by-event  Glauber and CGC in. cond. are tuned to reproduce the observed multiplicites is similar, even if local gradients of T are different Hydrodynamics and tomography lead to very different results.

60 Flow Subtraction Subtraction of v 2 and v 3 leads to double-peak structure 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz Jun Xu et al, Phys. Rev. C 83, (2011) Subtraction of larger v n only leads to one broad away-side peak 4 < p T trigger < 6 GeV/c 0.15 < p T assoc < 4 GeV/c STAR, Nucl. Phys. A 774, 129 (2006) similar shape

61 (2+1)d correlations 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz H. Agakishiev et al. [STAR], arXiv: [nucl-ex] 2 trigger, opposite to each other + 1 associated jet Still using ZYAM Trigger particle Trigger particle It needs to be shown that jet quenching results can be reproduced for larger p T assoc Structure on the away-side 1.5 GeV < p T assoc < p T trig1 5 < p T trig1 < 10 GeV/c p T trig2 < 4 GeV/c

6203/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz Full Jet Reconstruction I J. Putschke, Talk at RHIC and AGS Users Meeting 2009 Full jet reconstruction questions ZYAM

6303/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz Full Jet Reconstruction II No apparent v 2 modulation in jet-hadron vs. di-hadron correlations J. Putschke, Talk at RHIC and AGS Users Meeting 2009

6403/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz Full Jet Reconstruction III Jet-hadron away-side significantly narrower J. Putschke, Talk at RHIC and AGS Users Meeting 2009

65 Generic Energy Loss Model 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz n ~ 6: spectral index K =  (1-a) Nuclear modification factor with T AA : Glauber T AA =  2 / P 0 2 : CGC H. Drescher et. al., PRC 76 (2007)

66 Generic Energy Loss Model 03/04/10 Nuclear Theory and RIKEN seminar, BNL Barbara Betz Having fixed , the harmonics can be calculated B. Alver, Talk at the Glasma Workshop, BNL, May 2010 determining the angle with the reaction plane and the Fourier density components are given by