Energy loss in a realistic geometry Marco van Leeuwen, Marta Verweij, Utrecht University

Soft QCD matter and hard probes Heavy-ion collisions produce ‘quasi-thermal’ QCD matter Dominated by soft partons p ~ T ~ 100-300 MeV Hard-scatterings produce ‘quasi-free’ partons  Initial-state production known from pQCD  Probe medium through energy loss Use the strength of pQCD to explore QCD matter Sensitive to medium density, transport properties

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: RAA vs IAA Some results for LHC

The Brick Problem w kT 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

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)

Some (overly) simple arguments 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 GeV for central collisions at RHIC Note: slope of ‘input’ spectrum changes with pT: use experimental reach to exploit this

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

Spread in DE reduces suppression RAA with DE/E= 0.2 Quarks only Spread in DE reduces suppression (RAA~0.6 instead of 0.2) 〈DE/E〉not very relevant for RAA at RHIC Large impact of P(0); broad distribution

(Brick report uses R7, numerical differences small) Rn to summarize E-loss n: power law index n ~ 8 at RHIC  R8 ~ RAA (Brick report uses R7, numerical differences small) Use Rn to characterise P(DE)

Suppression vs For all models: Use temperature T to set all inputs Gluon gas Nf = 0 For all models: TECHQM preliminary Use temperature T to set all inputs

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 R7 Gluon spectrum different for ASW-MS and OE TECHQM preliminary

Energy loss probability P(∆E) is generated by a Poisson convolution of the single gluon spectrum: 3 distinct contributions: p0 = probability for no energy loss = e-〈Ngluons> p(∆E) = continuous energy loss = parton loses ∆E ∆E > E: parton is absorbed by the medium

Outgoing quark spectrum xE = 1 - ∆E/E xE = 0: Absorbed quarks xE = 1: No energy loss Suppression factor R7 dominated by: ASW-MS: partons w/o energy loss OEs: p0 and soft gluon radiation TECHQM preliminary Continuous part of energy loss distribution more relevant for OE than MS Can we measure this?

Wounded Nucleon Scaling Geometry Space-time evolution Density profile Density along parton path Longitudinal expansion 1/t dilutes medium  Important effect Wounded Nucleon Scaling with optical Glauber Formation time: t0 = 0.6 fm

Effective medium parameters PQM: ASW-MS: wc, R GLV, ASW-OE: GLV, ASW-OE Generalisation m, l:

Medium as seen by parton Path average variables which characterize the energy loss. Exercise: Parton is created at x0 and travels radially through the center of the medium until it leaves the medium or freeze out has taken place.

Medium as seen by parton Now: Partons in all directions from all positions Medium characterized by wc and L ASW-MS DGLV Different treatment of large angle radiation cut-off: qperp<E

Medium as seen by parton Medium characterized by typical gluon energy wc and path length L DGLV Radially inward from surface ASW-MS Radially outward from intermediate R Radially outward from surface

Medium as seen by parton ASW-MS DGLV R7 isolines There is no single ‘equivalent brick’ that captures the full geometry Some partons see very opaque medium (R7 < 0.05)

Why measure IAA? Bias associated particle towards longer path length Probe different part of medium Trigger to larger parton pt Probe different energy loss probability distribution Single hadron Trigger Associate

Surface bias I DE < E: Surviving partons ASW-MS 48% surviving partons WHDG rad OE more surviving partons → more fractional energy loss OE probe deeper into medium

Surface bias II: Ltrig vs Lassoc Leff [fm] Leff [fm] Leff [fm] For RAA and IAA different mean path length. Pt Trigger > Pt Assoc Triggers bias towards smaller L Associates bias towards longer L

RAA vs IAA: Trigger bias IAA: conditional yield Need trigger hadron with pT in range  DE < E IAA selects harder parton spectrum Parton spectra resulting in hadrons with 8<pthadron<15 GeV for without (vacuum) and with (ASW-MS/WHDG) energy loss.

RAA and IAA at RHIC Models fitted to RAA using modified c2 analysis 1s uncertainty band indicated q0 for multiple-soft approx 4x opacity expansion (T0 factor 1.5)

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  R7 < 0.2 in full geom

RAA and IAA at RHIC RAA – fitted IAA – predicted Measured IAA (somewhat) larger than prediction Differences between models small; DGLV slightly higher than others IAA < RAA due to larger path length – difference small due to trigger bias

RAA increases with pT at LHC RAA and IAA at LHC Using medium density from RHIC 50 < pt,Trig < 70 GeV RAA increases with pT at LHC larger dynamic range DE/E decreases with pT IAA: decrease with pT,assoc Slopes differ between models

RAA and IAA at LHC Density 2x RHIC Reduced pT dependence 50 < pt,Trig < 70 GeV Reduced pT dependence Slope similar for different models IAA < RAA Some pT dependence?

LHC estimates RHIC best fits

Conclusion Energy loss models (OE and MS) give different suppression at same density For R7 = 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 IAA above calculated in full geometry At LHC: pT-dependence of RAA  sensitive to P(DE | E) Only if medium density not too large RAA, IAA limited sensitivity to details of E-loss mode (P(E)) Are there better observables? Jets: broadening, or long frag? g-hadron

Extra slides

Where does the log go?

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 Eparton. Opacity expansions more soft gluon radiation than ASW-MS. Ngluons,ASW-SH ~ Ngluons,WHDG 〈〉ASW-SH > 〈〉WHDG Ngluons,ASW-MS < Ngluons,OE TECHQM preliminary

Suppression Factor in a brick Hadron spectrum if each parton loses  energy: Weighted average energy loss: For RHIC: n=7 R7 approximation for RAA. pt' = (1-) pt

Multi gluon spectrum Nmax,gluon = (2*Ngluon+1) Iterations Ngluon follows Poisson distribution – model assumption Normalize to get a probability distribution. Poisson convolution of single gluon to multi gluon spectrum 1 2 3 4 5 6 7 = Nmax,gluon

Geometry of HI collision Woods-Saxon profile Wounded Nucleon Scaling with optical Glauber Medium formation time: t0 = 0.6 fm Longitudinal Bjorken Expansion 1/t Freeze out temperature: 150 MeV Temperature profile Measurement Energy loss geometry medium Fragmentation Factor Known from e+e- Input parton spectrum Known LO pQCD

Opacity Expansion Few hard interactions. All parameters scale with a power of T: Calculation of parameters through

Schematic picture of energy loss mechanism in hot dense matter path length L  kT Outgoing quark xE=(1-x)E Radiated energy E=xE

Model input parameters ~