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Marco van Leeuwen, Marta Verweij, Utrecht University Energy loss in a realistic geometry
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2 Soft QCD matter and hard probes Use the strength of pQCD to explore QCD matter Hard-scatterings produce ‘quasi-free’ partons Initial-state production known from pQCD Probe medium through energy loss Heavy-ion collisions produce ‘quasi-thermal’ QCD matter Dominated by soft partons p ~ T ~ 100-300 MeV Sensitive to medium density, transport properties
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3 Plan of talk Energy loss in a brick: reminder of main differences between formalisms How do these carry over to full geometry Surface bias? Can we exploit full geometry, different observables to constrain/test formalisms? Case study: R AA vs I AA Some results for LHC
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4 The Brick Problem 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 kTkT
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5 Energy loss models Multiple soft scattering approximation ASW-MS Opacity expansions (OE) ASW-SH (D)GLV Phys.Rev.D68 014008 Nucl.Phys.A784 426 AMY, HT only in brick part (discussed at JET symposium)
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6 Some (overly) simple arguments 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, 051106, arXiv:0801.4020 Note: slope of ‘input’ spectrum changes with p T : use experimental reach to exploit this
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7 Energy loss distributions 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
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8 Large impact of P(0); broad distribution 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 R AA with E/E= 0.2
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9 R n to summarize E-loss n: power law index n ~ 8 at RHIC R 8 ~ R AA Use R n to characterise P( E) (Brick report uses R 7, numerical differences small)
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10 Suppression vs For all models: Use temperature T to set all inputs TECHQM preliminary Gluon gas N f = 0
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11 Single gluon spectrum For all models this is the starting point P(∆E) originates from spectrum of radiated gluons Models tuned to the same suppression factor R 7 Gluon spectrum different for ASW-MS and OE TECHQM preliminary
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12 Energy loss probability P(∆E) is generated by a Poisson convolution of the single gluon spectrum: 3 distinct contributions: p 0 = probability for no energy loss = e - 〈 Ngluons> p(∆E) = continuous energy loss = parton loses ∆E ∆E > E: parton is absorbed by the medium
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13 Outgoing quark spectrum Outgoing quark spectrum: x E = 1 - ∆E/E x E = 0: Absorbed quarks x E = 1: No energy loss Suppression factor R 7 dominated by: ASW-MS: partons w/o energy loss OEs: p 0 and soft gluon radiation TECHQM preliminary Can we measure this? Continuous part of energy loss distribution more relevant for OE than MS
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14 Geometry Density profile Density along parton path Longitudinal expansion 1/ dilutes medium Important effect Space-time evolution Wounded Nucleon Scaling with optical Glauber Formation time: 0 = 0.6 fm
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15 Effective medium parameters PQM: ASW-MS: c, R Generalisation , : GLV, ASW-OE: GLV, ASW-OE
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16 Medium as seen by parton Path average variables which characterize the energy loss. Exercise: Parton is created at x 0 and travels radially through the center of the medium until it leaves the medium or freeze out has taken place.
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17 Medium as seen by parton Different treatment of large angle radiation cut-off: qperp<E Now: Partons in all directions from all positions Medium characterized by c and L ASW-MSDGLV
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18 Medium as seen by parton Medium characterized by typical gluon energy c and path length L Radially outward from surface Radially outward from intermediate R Radially inward from surface ASW-MS DGLV
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19 Medium as seen by parton ASW-MSDGLV There is no single ‘equivalent brick’ that captures the full geometry Some partons see very opaque medium (R 7 < 0.05) R 7 isolines
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20 Why measure I AA ? Bias associated particle towards longer path length Probe different part of medium Trigger to larger parton p t Probe different energy loss probability distribution Associate Trigger Single hadron
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21 Surface bias I ASW-MSWHDG rad 22% surviving partons 48% surviving partons OE more surviving partons → more fractional energy loss OE probe deeper into medium E < E: Surviving partons
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22 Surface bias II: L trig vs L assoc For R AA and I AA different mean path length. P t Trigger > P t Assoc Triggers bias towards smaller L Associates bias towards longer L L eff [fm]
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23 R AA vs I AA : Trigger bias Parton spectra resulting in hadrons with 8<p t hadron <15 GeV for without (vacuum) and with (ASW-MS/WHDG) energy loss. I AA : conditional yield Need trigger hadron with p T in range E < E I AA selects harder parton spectrum
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24 R AA and I AA at RHIC Models fitted to R AA using modified 2 analysis 1 uncertainty band indicated q 0 for multiple-soft approx 4x opacity expansion (T 0 factor 1.5)
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25 Brick vs full geometry Brick: Full geometry Factor between MS and OE larger in full geom than brick OE give larger suppression at large L NB: large L R 7 < 0.2 in full geom
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26 R AA and I AA at RHIC R AA – fitted I AA – predicted Measured I AA (somewhat) larger than prediction Differences between models small; DGLV slightly higher than others I AA < R AA due to larger path length – difference small due to trigger bias
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27 R AA and I AA at LHC 50 < p t,Trig < 70 GeV Using medium density from RHIC R AA increases with p T at LHC larger dynamic range E/E decreases with p T I AA : decrease with p T,assoc Slopes differ between models
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28 R AA and I AA at LHC Reduced p T dependence Slope similar for different models I AA < R AA Some p T dependence? 50 < p t,Trig < 70 GeV Density 2x RHIC
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29 LHC estimates RHIC best fits
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30 Conclusion Energy loss models (OE and MS) give different suppression at same density For R 7 = 0.25, need L=5, T=300-450 MeV or L=2, T=700-1000 MeV Full geometry: Large paths, large suppression matter Surface bias depends on observable, energy loss model Measured I AA above calculated in full geometry At LHC: p T -dependence of R AA sensitive to P( E | E) Only if medium density not too large R AA, I AA limited sensitivity to details of E-loss mode (P(E)) Are there better observables? Jets: broadening, or long frag? -hadron
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31 Extra slides
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32 Where does the log go?
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33 Single gluon spectrum P(∆E) originates from spectrum of radiated gluons. ASW-MS and ASW-SH the same at large. WHDG smooth cutoff depending on E parton. Opacity expansions more soft gluon radiation than ASW-MS. N gluons,ASW-SH ~ N gluons,WHDG 〈〉 ASW-SH > 〈〉 WHDG N gluons,ASW-MS < N gluons,OE TECHQM preliminary
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34 Suppression Factor in a brick Hadron spectrum if each parton loses energy: Weighted average energy loss: For RHIC: n=7 R 7 approximation for R AA. p t ' = (1-) p t
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35 Multi gluon spectrum 1 2 3 4 5 6 7 = N max,gluon Poisson convolution of single gluon to multi gluon spectrum N max,gluon = (2*N gluon +1) Iterations N gluon follows Poisson distribution – model assumption Normalize to get a probability distribution.
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36 Geometry of HI collision Woods-Saxon profile Wounded Nucleon Scaling with optical Glauber Medium formation time: 0 = 0.6 fm Longitudinal Bjorken Expansion 1/ Freeze out temperature: 150 MeV Temperature profile Input parton spectrum Known LO pQCD Fragmentation Factor Known from e+e- Energy loss geometry medium Measurement
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37 Opacity Expansion Calculation of parameters through Few hard interactions. All parameters scale with a power of T:
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38 Schematic picture of energy loss mechanism in hot dense matter path length L kTkT Radiated energy x Outgoing quark x x)
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39 Model input parameters ~
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