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Radiative energy loss

Radiative energy loss. Marco van Leeuwen, Utrecht University. Medium-induced radiation. Zapp, QM09. L c = t f,max. Radiation sees length ~ t f at once. Landau-Pomeranchuk-Migdal effect Formation time important. radiated gluon. propagating parton.

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Radiative energy loss

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  1. Radiative energy loss Marco van Leeuwen, Utrecht University

  2. Medium-induced radiation Zapp, QM09 Lc = tf,max Radiation sees length ~tf at once Landau-Pomeranchuk-Migdal effect Formation time important radiated gluon propagating parton If l < tf, multiple scatterings add coherently Energy loss depends on density: and nature of scattering centers (scattering cross section) Transport coefficient

  3. A simple model Parton spectrum Energy loss distribution Fragmentation (function) known pQCDxPDF extract `known’ from e+e- This is where the information about the medium is P(DE) combines geometry with the intrinsic process– Unavoidable for many observables • Notes: • This formula is the simplest ansatz – Independent fragmentationafter E-loss assumed • Jet, g-jet measurements ‘fix’ E, removing one of the convolutions We will explore this model during the week; was ‘state of the art’ 3-5 years ago

  4. Two extreme scenarios (or how P(DE) says it all) Scenario I P(DE) = d(DE0) Scenario II P(DE) = a d(0) + b d(E) 1/Nbin d2N/d2pT ‘Energy loss’ ‘Absorption’ p+p Downward shift Au+Au Shifts spectrum to left pT P(DE) encodes the full energy loss process RAA not sensitive to energy loss distribution, details of mechanism

  5. What can we learn from RAA? p0 spectra Nuclear modification factor PHENIX, PRD 76, 051106, arXiv:0801.4020 This is a cartoon! Hadronic, not partonic energy loss No quark-gluon difference Energy loss not probabilistic P(DE) Ball-park numbers: DE/E ≈ 0.2, or DE ≈ 2 GeVfor central collisions at RHIC Note: slope of ‘input’ spectrum changes with pT: use experimental reach to exploit this

  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 See also: arXiv:1106.1106

  7. Kinematic variables Gluon(s) L: medium length T, q: Density E: incoming parton energy/momentum w: (total) momentum of radiated gluon (=DE) kT: transverse momentum of radiated gluon p: outgoing parton momentum = E-DE = E-w

  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. 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

  12. 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

  13. 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

  14. 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’

  15. 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

  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. Multiple gluon emission Poisson convolution example Average number of gluons: Poisson fluctuations: (assumed) Total probability:

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

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

  20. Model inputs: medium density Multiple soft scattering (ASW-MS): Quenching weights (AliQuenchingWeights) Inputs: N.B: keep track of factors hc = 197.327 MeVfm Quenching weights: Opacity expansion (DGLV, ASW-SH): Gluon spectra +Poisson Ansatz for multiple gluon radiation

  21. Medium properties Some pocket formulas gluon gas, Baier scheme: HTL: See also: arXiv:1106.1106

  22. Geometry Density along parton path Density profile Profile at t ~ tform known Longitudinal expansion dilutes medium  Important effect Space-time evolution is taken into account in modeling

  23. Geometry II L-moments of density along path:

  24. ‘Analytic’ calculations vs MC Event Generators • Analytic calculations (this lecture) • Easy to include interference • So far: only soft-collinear approx • Energy-momentum conservation ad-hoc • Monte Carlo event generators (modified parton showers) • Energy-momentum conservation exact • May be able to introduce recoil (dynamic scatt centers) • More difficult to introduce interference • Examples: JEWEL, qPYTHIA, YaJEM

  25. AliQuenchingWeights Based on Salgado, Wiedemann, hep-ph/0302184 AliQuenchingWeights::InitMult() Initialises multiple soft scattering Quenching Weights AliQuenchingWeights::CalcMult(ipart, R, x, cont, disc) Multiple soft scattering Quenching Weights input: ipart 0=gluon, 1=quark x = w/wc return: cont: w dI/dw disc: P(0)

  26. Extra slides

  27. Thoughts about black-white scenario Or: Hitting the wall with P(DE) • At RHIC, we might have effectively a ‘black-white scenario’ • Large mean E-loss • Limited kinematic range • Different at LHC? • Mean E-loss not much larger, kinematic range is? • Or unavoidable: steeply falling spectra In addition: the more monochromatic the probe, the more differential sensitivity g-jet, jet-reco promising!

  28. Opacity expansion Opacity expansion (DGLV, ASW-SH): Gluon spectra Poisson Ansatz:

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