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

4. Energy loss formalisms II
Compare 3 formalisms with `same’ Hydro geometry:
ASW:
HT:
AMY:
Bass et al, PRC79,
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 Gluon(s) Compare outgoing gluon, quark distributions
TECHQM: Theory-Experiment Collaboration on Hot Quark Matter
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. (independent emission)
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-Planck rate equations
Poisson ansatz
(independent emission)
DGLAP
evolution

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

8. Large angle radiation kT < k
Emitted gluon distribution
Opacity expansion
kT < k
Gluon momentum k
Gluon perp 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,
Single-gluon spectrum
Blue: kTmax = xE
Red: kTmax = 2x(1-x)E
Horowitz and Cole, PRC81,
Different definitions of x:
ASW:
GLV:
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:
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: kernel diverges for kT 0
t < L  kT > √(E/L)
GLV:
HT:
HT gives more radiation than GLV

12. Opacity expansion vs multiple soft
OE and MS related via path integral formalism
Salgado, Wiedemann, PRD68,
Different limits:
SH (N=1 OE): interference between neighboring scattering centers
MS: ‘all orders in opacity’, gaussian scattering 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,
BMPS-Z use harmonic oscillator:
BDMPS-Z:
Finite-L effects:
Vacuum-medium interference
+ large-angle cut-off

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

15. L-dependence; regions of validity?
Emission rate vs t (=L)
GLV N=1
Too much radiation at large L
(no interference between scatt centers)
Caron-Huot, Gale, arXiv:
E = 16 GeV
k = 3 GeV
T = 200 MeV
Full =
numerical solution of Zakharov path integral
= ‘best we know’
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)

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 ? Some suggested future directions:
In preparation: TECHQM publication with more detailed report
Some suggested future directions:
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)
Plenty of room of original work !
Thanks to all in TECHQM who contributed

21. Extra slides

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

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
Theory-Experiment Collaboration on Hot Quark Matter
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
This talk is about Parton Energy loss

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

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