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

2. Soft QCD matter and hard probes
Heavy-ion collisions produce ‘quasi-thermal’ QCD matter
Dominated by soft partons p ~ T ~ 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

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: RAA vs IAA
Some results for LHC

4. 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

5. Energy loss models Multiple soft scattering approximation ASW-MS
Opacity expansions (OE)
ASW-SH
(D)GLV
Phys.Rev.D
Nucl.Phys.A
AMY, HT only in brick part
(discussed at JET symposium)

6. Some (overly) simple arguments
p0 spectra
Nuclear modification factor
PHENIX, PRD 76, , arXiv:
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

7. 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

8. 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

9. (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)

10. 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

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

12. 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

13. 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?

14. 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

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

16. 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.

17. 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

18. 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

19. 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)

20. 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

21. 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

22. 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

23. 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.

24. 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)

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  R7 < 0.2 in full geom

26. 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

27. 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

28. 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?

29. LHC estimates
RHIC best fits

30. Conclusion
Energy loss models (OE and MS) give different suppression at same density
For R7 = 0.25, need L=5, T= MeV or L=2, T= 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

31. Extra slides

32. Where does the log go?

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 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

34. 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

35. 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

36. 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

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

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

39. Model input parameters~