Comparing energy loss phenomenology Marco van Leeuwen Utrecht University

2 Energy loss in QCD matter radiated gluon propagating parton 22 QCD bremsstrahlung (+ LPM coherence effects) Density of scattering centers: Nature of scattering centers, e.g. mass: radiative vs elastic loss Or no scattering centers, but fields  synchrotron radiation? Transport coefficient Energy loss Energy loss probes:

3 Determining the medium density PQM (Loizides, Dainese, Paic), Multiple soft-scattering approx (Armesto, Salgado, Wiedemann) Realistic geometry GLV (Gyulassy, Levai, Vitev), Opacity expansion (L/ ), Average path length WHDG (Wicks, Horowitz, Djordjevic, Gyulassy) GLV + realistic geometry ZOWW (Zhang, Owens, Wang, Wang) Medium-enhanced power corrections (higher twist) Hard sphere geometry AMY (Arnold, Moore, Yaffe) Finite temperature effective field theory (Hard Thermal Loops) For each model: 1.Vary parameter and predict R AA 2.Minimize  2 wrt data Models have different but ~equivalent parameters: Transport coeff. Gluon density dN g /dy Typical energy loss per L:  0 Coupling constant  S PHENIX, arXiv: , J. Nagle WWND08

4 Medium density from R AA PQM = 13.2 GeV 2 /fm ^ GLV dN g /dy = WHDG dN g /dy = ZOWW  0 = 1.9 GeV/fm AMY  s = Data constrain model parameters to 10-20% Method extracts medium density given the model/calculation Theory uncertainties need to be further evaluated e.g. comparing different formalisms, varying geometry Side-by-side comparison needed to progress Different medium density parameters are used Each model ‘lives in its own world’

5 Some pocket formula results Large difference between models ? GLV/WHDG: dNg/dy = 1400 T(  0 ) = 366 MeV PQM: (parton average) AMY: T fixed by hydro (~400 MeV),  s = T = 1016 MeV

6 TECHQM Brick problem Use simple geometry: –Brick of QGP: L = 2 fm, L = 5 fm –Various densities Plot P(  E) for quark of 10, 100 GeV Theory-Experiment Collaboration on Hot Quark Matter Goal: apples-to-apples comparison of energy loss formalisms Some models do not calculate P(  E) use fragmentation function instead Next slides: brick results (disregard nuclear geometry)

7 Back to data: oversimplified approach This is a cartoon! Hadronic, not partonic energy loss No quark-gluon difference Energy loss not probabilistic P(  E) Ball-park numbers:  E/E ≈ 0.2, or  E ≈ 2 GeV for central collisions at RHIC  0 spectra Nuclear modification factor PHENIX, PRD 76, , arXiv: Note: slope of ‘input’ spectrum changes with p T : use experimental reach to exploit this

8 Energy distribution from theory TECHQM ‘brick problem’ L = 2 fm,  E/E = 0.2 E = 10 GeV ‘Typical for RHIC’ Not a narrow distribution:  Significant probability for  E ~ E  Conceptually/theoretically difficult Significant probability to lose no energy P(0) = 0.5 – 0.6 ASW: Armesto, Salgado, Wiedemann WHDG: Wicks, Horowitz, Dordjevic, Gyulassy

9 R AA with  E/E= 0.2 Large impact of P(0)? Spread in  E reduces suppression (R AA ~0.6 instead of 0.2) 〈  E/E 〉 not very relevant for R AA at RHIC Quarks only

10 How to summarize E-loss? (Suggested by B. Mueller) n: power law index n ~ 8 at RHIC  R 8 ~ R AA Use R n to characterise P(  E)

11 T-dependence ASW vs WHDG WHDG (GLV) and ASW (BDMPS) give similar suppression, but  T~200 MeV With L = 2 fm, R AA >> 0.2 ASW: Armesto, Salgado, Wiedemann WHDG: Wicks, Horowitz, Dordjevic, Gyulassy

12 T-dependence ASW vs WHDG (L=5 fm) L=5 fm: Reach R AA ~ 0.2 at T = 370 MeV (WHDG) and T = 500 MeV (ASW) So, why ~ 14 GeV 2 /fm, T~1000 MeV in PQM?  Geometry ASW: Armesto, Salgado, Wiedemann WHDG: Wicks, Horowitz, Dordjevic, Gyulassy

13 Typical P(  E) at RHIC x → 1 important for phenomenology at RHIC Not well controlled in theory

14 Note on geometry WHDGPQM (BDMPS)  part gives longer ‘typical’ pathlengths  coll more sharply peaked

15 Geometry II  part : larger ‹L eff ›  part : qhat more sharply peaked Changing  coll to  part may reduce needed to reproduce data (Note: distributions only for illustration, need to tune  part to reproduce data)

16 More differential measurements Di-hadron correlations R AA vs reaction plane (elliptic flow)  -jet Jet reconstruction R AA integrates out parton kinematics, energy loss distribution Energy loss distribution P(  E) integrates out geometry More differential measurements help probe P(  E), geometry:

17 Di­hadron correlations associated  trigger Near sideAway side Combinatorial background 8 < p T trig < 15 GeV p T assoc > 3 GeV STAR PRL 95, < p T,trig < 15 GeV No z T -dependence of away-side suppression  indicates importance of P(0) ?

18 d-Au Au-Au Medium density from di-hadron measurement I AA constraint D AA constraint D AA + scale uncertainty J. Nagle, WWND2008 associated  trigger  0 =1.9 GeV/fm single hadrons Higher twist: Medium density from away-side suppression and R AA Theory: ZOWW, PRL98, Caveats: -Theory curve does not match d+Au: need to evaluate systematics -p T relatively low (recombination?) Data: STAR PRL 95, < p T,trig < 15 GeV z T =p T,assoc /p T,trig Would like to see other models!

19 Model predictions for R AA (  ) ASW shows larger variation vs  Geometry is additional handle on/for models Bass et al. arXiv:

20 Parton energy from  -jet and jet reconstruction Qualitatively: `known’ from e + e - known pQCDxPDF extract Full deconvolution large uncertainties (+ not transparent) Fix/measure E jet to take one factor out Two approaches:  -jet -Jet reconstruction  second-generation measurements at RHIC See talks by Putschke, Hamed (and others) for results and more discussion

21 Towards LHC L = 5 fm E = 10 GeV RHIC: n = 8LHC: n = 6 p T -6 instead of p T -8 spectrum has only small effect on R AA R 8 ≈ R 6

22 LHC:  E vs E L = 5 fm E = 10 GeV L = 5 fm E = 100 GeV Dependence of R 6 on E,T different in ASW, WHDG Due to added log(√(ET)) in WHDG (trivial) or more fundamental?

23 R AA at LHC S. Wicks, W. Horowitz, QM2006 T. Renk, QM2006 GLVBDMPS RHIC Dependence of R 6 on E,T different in ASW, WHDG Due to added log(√(ET)) in WHDG (trivial) or more fundamental?... or even something else? Should clarify before first data at LHC  Predictions, not postdictions

24 Conclusion Nuclear suppression data (R AA, I AA ) are becoming accurate – Need accurate theory Side-by-side comparison: TECHQM brick problem makes a clean start BDMPS-ASW and GLV-WHDG give  T~200 MeV (results for Higher Twist and AMY still need to be put on same scale –expected soon) Next step: uniform treatment of geometry, time evolution Thanks to: W. Horowitz, C. Salgado, N. Armesto, U. Wiedemann, A. Majumder Beware of P(0) and P(  E = E): both are important for phenomenology Are they under control?

25 Thank you for your attention

26 Fragmentation functions Include some FF plots?

27 STAR Preliminary I AA (z T ) = D AA (z T ) D pp (z T ) Direct-  recoil suppression Large suppression for away-side: factor 3-5 Results agree with model predictions Uncertainties still sizable Some improvements expected for final results Future improvements with increased RHIC luminosity J. Frantz, Hard Probes 2008 A. Hamed, Hard Probes 2008  8 < E T,  < 16 GeV E T,  2 < p T assoc < 10 GeV Expected recoil for various P(  E) T. Renk Measurement sensitive to energy loss distribution P(  E) Need precision to distinguish scenarios

28 Energy loss in QCD matter D. d’Enterria Hard partons lose energy in the hot matter  : no interactions Hadrons: energy loss R AA = 1 R AA < 1 Yield per collision  0 : R AA ≈ 0.2  : R AA = 1 Nuclear modification factor C. Vale, K. Okada, Hard Probes 2008