1. Comparing energy loss models Marco van Leeuwen Utrecht University What have we learned from the TECHQM brick problem? With many contributions from TEHCQM collaborators

2. 2 Flashback to Hard Probes 2006 It was becoming clear that GLV, ASW, AMY require different densities to describe the R AA measurements at RHIC and, after discussion, it also became clear that nobody really knew why!

3. 3 Energy loss formalisms I PHENIX, arXiv:0801.1665, J. Nagle WWND08 PQM = 13.2 GeV 2 /fm +2.1 - 3.2 ^ WHDG dN g /dy = 1400 +200 - 375 ZOWW  0 = 1.9 GeV/fm +0.2 - 0.5 AMY  s = 0.280 +0.016 - 0.012 GLV, AMY: T = 300-400 MeV BDMPS: T ~ 1000 MeV Large difference in medium density: Different calculations use different geometries – not clear what dominates

4. 4 Energy loss formalisms II Bass et al, PRC79, 024901 ASW: HT: AMY: AMY: T ~ 400 MeV Compare 3 formalisms with `same’ Hydro geometry: Different formalisms give different energy loss using same geometry Why: Different physics implemented? Or `technical’ differences? Differences indicate theoretical uncertainty? or: Some of the formalisms are ‘wrong’?

5. 5 The Brick Problem Gluon(s) Compare outgoing gluon, quark distributions - Same density - Same suppression Compare energy-loss in a well-defined model system: Fixed length L = 2, 5 fm Density T, q Quark, E = 10, 20 GeV https://wiki.bnl.gov/TECHQM/index.php/Main_Page TECHQM: Theory-Experiment Collaboration on Hot Quark Matter and interpret/understand the differences Two types of comparison:

6. 6 Four formalisms Hard Thermal Loops (AMY) –Dynamical (HTL) medium –Single gluon spectrum: BDMPS-Z like path integral –No vacuum radiation Multiple soft scattering (BDMPS-Z, ASW-MS) –Static scattering centers –Gaussian approximation for momentum kicks –Full LPM interference and vacuum radiation Opacity expansion ((D)GLV, ASW-SH) –Static scattering centers, Yukawa potential –Expansion in opacity L/ (N=1, interference between two centers default) –Interference with vacuum radiation Higher Twist (Guo, Wang, Majumder) –Medium characterised by higher twist matrix elements –Radiation kernel similar to GLV –Vacuum radiation in DGLAP evolution Multiple gluon emission Fokker-Planck rate equations Poisson ansatz (independent emission) DGLAP evolution

7. 7 Large differences in medium density for R 7 = 0.25 Some brick results Outgoing quark spectrum T=300 MeV R AA > P 0  Difference between formalisms sizable even in simple geometry

8. 8 Large angle radiation Emitted gluon distribution Opacity expansion k T < k Calculated gluon spectrum extends to large k  at small k Outside kinematic limits GLV, ASW, HT cut this off ‘by hand’ Estimate uncertainty by varying cut; sizeable effect Gluon momentum k Gluon perp momentum k 

9. 9 Limitations of soft collinear approach Soft: Collinear: Need to extend results to full phase space to calculate observables (especially at RHIC) Soft approximation not problematic: For large E, most radiation is soft Also:  > E  full absorption Cannot enforce collinear limit: Small ,   k T always a part of phase space with large angles Calculations are done in soft collinear approximation:

10. 10 Opacity expansions GLV and ASW-SH x + ~ x E in soft collinear limit, but not at large angles Different large angle cut-offs: k T <  = x E E k T <  = 2 x + E Blue: k Tmax = xE Red: k Tmax = 2x(1-x)E Single-gluon spectrum Blue: m g = 0 Red: m g =  /√2 Horowitz and Cole, PRC81, 024909 Single-gluon spectrum Different definitions of x: ASW: GLV: Factor ~2 uncertainty from large-angle cut-off Horowitz and Cole, PRC81, 024909

11. 11 HT and GLV Single-gluon kernel GLV and HT similar HT: kernel diverges for k T  0  √(E/L) GLV: HT: GLV similar structure, phase factor  However HT assumes k T >> q T, so no explicit integral over q T GLV HT gives more radiation than GLV

12. 12 Opacity expansion vs multiple soft Salgado, Wiedemann, PRD68, 014008 Different limits: SH (N=1 OE): interference between neighboring scattering centers MS: ‘all orders in opacity’, gaussian scattering approximation Quantitative differences sizable OE and MS related via path integral formalism Two differences at the same time

13. 13 AMY, BDMPS, and ASW-MS Single-gluon kernel from AMY based on scattering rate: BMPS-Z use harmonic oscillator: BDMPS-Z: Salgado, Wiedemann, PRD68, 014008 Finite-L effects: Vacuum-medium interference + large-angle cut-off

14. 14 AMY and BDMPS Using based on AMY-HTL scattering potential L=2 fm Single gluon spectraL=5 fm Single gluon spectra AMY: no large angle cut-off + sizeable difference at large  at L=2 fm

15. 15 L-dependence; regions of validity? Emission rate vs  (=L) Caron-Huot, Gale, arXiv:1006.2379 AMY, small L, no L 2, boundary effect Full = numerical solution of Zakharov path integral = ‘best we know’ GLV N=1 Too much radiation at large L (no interference between scatt centers) H.O = ASW/BDMPS like (harmonic oscillator) Too little radiation at small L (ignores ‘hard tail’ of scatt potential) E = 16 GeV k = 3 GeV T = 200 MeV

16. 16 Single gluon spectra Same temperature @Same temperature: AMY > OE > ASW-MS L = 2 fm L = 5 fm Size of difference depends on L, but hierarchy stays

17. 17 Outgoing quark spectra Same temperature: T = 300 MeV @Same T: suppression AMY > OE > ASW-MS Note importance of P 0

18. 18 Outgoing quark spectra Same suppression: R 7 = 0.25 At R 7 = 0.25: P 0 small for ASW-MS P 0 = 0 for AMY by definition

19. 19 Conclusion AMY gives most radiation –No L 2 effect at small L –No large-angle cut Opacity expansions (GLV/ASW-SH) intermediate –Good at short lengths (L < 2-3 fm) –Likely too much at large L Multiple-soft scattering radiates least –Too much suppression at short L ? Higher Twist more difficult to compare –Gives more radiation than GLV at single-gluon level Current calculations: Large uncertainties associated with large-angle radiation at low to moderate x We now know where the differences between formalisms come from ! Unfortunately: differences not dominated by physics, but by approximations

20. 20 What next ? Use improved methods: full path-integral, higher order opacity Need to improve treatment of large angle radiation (recoil?) –Some ideas exist, e.g. use MC with LPM + full matrix elements Systematically explore sensitivity to medium model (scattering potential) In preparation: TECHQM publication with more detailed report Plenty of room of original work ! Some suggested future directions: Thanks to all in TECHQM who contributed

21. 21 Extra slides

22. 22 L=2 fm, T=250, 350 MeV GLV, HT, ASW-MS similar AMY: large suppression L=2 fm, T=250, 350 MeV AMY, HT larger suppression than OE, MS Fragmentation function Majumder, van Leeuwen, arXIv:1002.2206

23. 23 Qhat vs T Some leeway in calculation of q from T:(N f = 0) or

24. 24 X+ vs xE

25. 25 TECHQM Forum to discuss comparison between theory and experiment in areas where there is a potential significant quantitative understanding Two subgroups: –Parton energy loss –Elliptic flow/Hydro Workshops/meetings: –BNL May 2008 –LBL Dec 2008 –CERN July 2009 –BNL (with CATHIE) Dec 2009 https://wiki.bnl.gov/TECHQM/index.php/Main_Page Theory-Experiment Collaboration on Hot Quark Matter This talk is about Parton Energy loss

26. 26 Single gluon spectra Same temperatureSame suppression @Same suppression: OE (AMY?) peaked at low  ASW-MS not so much @Same temperature: AMY > OE > ASW-MS

27. 27 Conclusion Tentative summary: –AMY shows strongest suppression Lack of vacuum radiation? –ASW-MS: smallest suppression Soft scattering or interference or both? –OE, HT similar, between MS and AMY Large uncertainties associated with large angle radiation in all formalisms Differences between formalisms large at single-gluon level R AA probably not sensitive to details of multi-gluon treatment Thanks to all in TECHQM who contributed ! In preparation: TECHQM publication with more detailed report