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Comparing energy loss models

Comparing energy loss models. What have we learned from the TECHQM brick problem?. Marco van Leeuwen Utrecht University. With many contributions from TEHCQM collaborators. Flashback to Hard Probes 2006.

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Comparing energy loss models

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

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

  3. Energy loss formalisms I +2.1 - 3.2 ^ PQM <q> = 13.2 GeV2/fm +0.2 - 0.5 ZOWW e0 = 1.9 GeV/fm +0.016 - 0.012 +200 - 375 AMY as = 0.280 WHDG dNg/dy = 1400 PHENIX, arXiv:0801.1665,J. Nagle WWND08 Large difference in medium density: GLV, AMY: T = 300-400 MeV BDMPS: T ~ 1000 MeV Different calculations use different geometries – not clear what dominates

  4. Energy loss formalisms II ASW: HT: AMY: Compare 3 formalisms with `same’ Hydro geometry: Bass et al, PRC79, 024901 AMY: T ~ 400 MeV 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. The Brick Problem TECHQM: Theory-Experiment Collaboration on Hot Quark Matter https://wiki.bnl.gov/TECHQM/index.php/Main_Page Gluon(s) Compare energy-loss in a well-defined model system: Fixed length L = 2, 5 fm Density T, q Quark, E = 10, 20 GeV Compare outgoing gluon, quark distributions - Same density - Same suppression Two types of comparison: and interpret/understand the differences

  6. Four formalisms Multiple gluon emission • 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/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 Fokker-Planckrate equations Poisson ansatz (independent emission) DGLAP evolution

  7. Some brick results Large differences in medium density for R7 = 0.25 Outgoing quark spectrum T=300 MeV RAA > P0  Difference between formalisms sizable even in simple geometry

  8. Large angle radiation Emitted gluon distribution Opacity expansion kT < k Gluon perp momentum k Gluon momentum 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

  9. Limitations of soft collinear approach Calculations are done in soft collinear approximation: 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: w > E  full absorption Cannot enforce collinear limit: Small w, w kT always a part of phase space with large angles

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

  11. HT and GLV HT: kernel diverges for kT 0 t < L  kT > √(E/L) HT: GLV: Single-gluon kernel GLV and HT similar HT: GLV GLV similar structure, phase factor W However HT assumes kT >> qT,so no explicit integral over qT HT gives more radiation than GLV

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

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

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

  15. L-dependence; regions of validity? AMY, small L, no L2, boundary effect H.O = ASW/BDMPS like (harmonic oscillator) Too little radiation at small L (ignores ‘hard tail’ of scatt potential) Emission rate vs t (=L) GLV N=1 Too much radiation at large L (no interference between scatt centers) Caron-Huot, Gale, arXiv:1006.2379 E = 16 GeV k = 3 GeV T = 200 MeV Full = numerical solution of Zakharov path integral = ‘best we know’

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

  17. Outgoing quark spectra Same temperature: T = 300 MeV @Same T: suppression AMY > OE > ASW-MS Note importance of P0

  18. Outgoing quark spectra Same suppression: R7 = 0.25 At R7 = 0.25: P0 small for ASW-MS P0 = 0 for AMY by definition

  19. Conclusion • AMY gives most radiation • No L2 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. What next ? In preparation: TECHQM publication with more detailed report • 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) Some suggested future directions: Plenty of room of original work ! Thanks to all in TECHQM who contributed

  21. Extra slides

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

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

  24. X+ vs xE

  25. TECHQM https://wiki.bnl.gov/TECHQM/index.php/Main_Page • 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 Theory-Experiment Collaboration on Hot Quark Matter This talk is about Parton Energy loss

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

  27. Conclusion • Tentative summary: • AMY shows strongest suppressionLack of vacuum radiation? • ASW-MS: smallest suppressionSoft 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 levelRAA probably not sensitive to details of multi-gluon treatment In preparation: TECHQM publication with more detailed report Thanks to all in TECHQM who contributed !

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