1. Lecture II: spectra and di-hadrons
Marco van Leeuwen, Utrecht University
Lectures for Helmholtz School Feb/March 2011

2. Hard probes of QCD matter
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. Centrality examples peripheral mid-central central
... and this is what you see in a presentation
This is what you really measure

4. Nuclear geometry: Npart, Nbin, L, e
Npart: nA + nB (ex: = 9 + …)
Nbin: nA x nB (ex: 4 x 5 = 20 + …)
Two limits:
- Complete shadowing, each nucleon only interacts once, s  Npart
No shadowing, each nucleon interact with all nucleons it encounters, s  Nbin
Soft processes: long timescale, large s, stot  Npart
Hard processes: short timescale, small s, stot  Nbin
Transverse view
Density profile r: rpart or rcoll y L
Eccentricity x
Path length L, mean <L>

5. Centrality dependence of hard processes
Total multiplicity: soft processes
Binary collisions weight
towards small impact parameter
ds/dNch
200 GeV Au+Au
Rule of thumb for A+A collisions (A>40)
40% of the hard cross section is contained in the 10% most central collisions

6. Testing volume (Ncoll) scaling in Au+Au
Direct g spectra
PHENIX, PRL 94,
PHENIX
Centrality
Scaled by Ncoll
Direct g in A+A scales with Ncoll
A+A initial state is incoherent superposition of p+p for hard probes

7. Testing Ncoll scaling II: Charm
PRL 94 (2005)
NLO prediction:
m ≈ 1.3 GeV, reasonably hard scale at pT=0
Total charm cross section scales with Nbin in A+A
Sizable disagreement between STAR and PHENIX – scaling error in one experiment?

8. Generic expectations from energy loss
Ejet
kT~m l
fragmentation after energy loss?
Longitudinal modification:
out-of-cone  energy lost, suppression of yield, di-jet energy imbalance
in-cone  softening of fragmentation
Transverse modification
out-of-cone  increase acoplanarity kT
in-cone  broadening of jet-profile

9. Energy loss in QCD matter
radiated gluon
QCD bremsstrahlung (+ LPM coherence effects)
propagating parton
Energy loss probes:
Density of scattering centers:
Nature of scattering centers, e.g. mass: radiative vs elastic loss
Transport coefficient

10. Radiation senses region with extent tf
LPM interference
Landau-Pomeranchuk-Migdal effect
Formation time important l
Zapp, QM09
radiated gluon
propagating parton
Radiation senses region with extent tf
Lc = tf,max
If l < tf, multiple scatterings add coherently:
Energy loss
w = 3 GeV, kT = 0.2 GeV, tf =20 fm/c
Typical length in nucleus 2-5 fm

11. Questions about energy loss
What is the dominant mechanism: radiative or elastic?
Heavy/light, quark/gluon difference, L2 vs L dependence
How important is the LPM effect?
L2 vs L dependence
Can we use this to learn about the medium?
Density of scattering centers?
Temperature?
Or ‘strongly coupled’, fields are dominant?
Phenomenological questions:
Large vs small angle radiation
Mean DE?
How many radiations?
Virtuality evolution/interplay with fragmentation?

12. p0 RAA – high-pT suppression
: no interactions
Hadrons: energy loss
RAA = 1
RAA < 1
Hard partons lose energy in the hot matter

13. Two extreme scenarios RAA not sensitive to details of mechanism
(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
RAA not sensitive to details of mechanism
P(DE) encodes the full energy loss process

14. Parton energy loss and RAA modeling
Qualitatively:
Parton spectrum
Energy loss distribution
Fragmentation (function)
known
pQCDxPDF
extract
`known’ from e+e-
medium effect
Medium effect P(DE) is only part of the story
Parton spectrum and fragmentation function are steep
 non-trivial relation between RAA and P(DE)

15. Four theory approaches
Multiple-soft scattering (ASW-BDMPS)
Full interference (vacuum-medium + LPM)
Approximate scattering potential
Opacity expansion (GLV/WHDG)
Interference terms order-by-order (first order default)
Dipole scattering potential 1/q4
Higher Twist
Like GLV, but with fragmentation function evolution
Hard Thermal Loop (AMY)
Most realistic medium
LPM interference fully treated
No interference between vacuum frag and medium

16. Determining the medium density
PHENIX, arXiv: , J. Nagle WWND08
PQM (Loizides, Dainese, Paic), Multiple soft-scattering approx (Armesto, Salgado, Wiedemann) Realistic geometry
For each model:
Vary parameter and predict RAA
Minimize 2 wrt data
Models have different but ~equivalent parameters:
Transport coeff.
Gluon density dNg/dy
Typical energy loss per L: e0
Coupling constant aS
GLV (Gyulassy, Levai, Vitev), Opacity expansion (L/l), Average path length
WHDG (Wicks, Horowitz, Djordjevic, Gyulassy) GLV + realistic geometry
ZOWW (Zhang, Owens, Wang, Wang) Medium-enhanced power corrections (higher twist) Hard sphere geometry
AMY (Arnold, Moore, Yaffe)
Finite temperature effective field theory (Hard Thermal Loops)

17. Medium density from RAA^
+2.1
- 3.2
PQM <q> = GeV2/fm
+270
- 150
+0.2
- 0.5
GLV dNg/dy = 1400
ZOWW e0 = GeV/fm
+200
- 375
+0.016
WHDG dNg/dy = 1400
AMY as = 0.280
Data constrain model parameters to 10-20%
Method extracts medium density given the model/calculation Theory uncertainties need to be further evaluated
e.g. comparing different formalisms, varying geometry
But models use different medium parameters
– How to compare the results?

18. Some pocket formula results
GLV/WHDG: dNg/dy = 1400
T(t0) = 366 MeV
PQM: (parton average)
T = 1016 MeV
AMY: T fixed by hydro (~400 MeV), as = 0.297
Large differences between models

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

20. Determining ASW: HT: AMY:
Bass et al, PRC79,
Large density:
AMY: T ~ 400 MeV
Transverse kick: qL ~ GeV
All formalisms give RAA ~ constant, but large differences in medium density
Need more differential measurements to test formalisms
At RHIC: DE large compared to E, differential measurements difficult

21. Energy loss spectrum <DE/E> = 0.2 R8 ~ RAA = 0.2
Typical examples with fixed L
<DE/E> = 0.2
R8 ~ RAA = 0.2
Brick
L = 2 fm, DE/E = 0.2
E = 10 GeV
Significant probability to lose no energy (P(0))
Broad distribution, large E-loss (several GeV, up to DE/E = 1)
Theory expectation: mix of partial transmission+continuous energy loss
-- Can we see this in experiment?

22. Need to ask critical questions!
Brian Cole, QM08 summary:
Scrutinise theory, experiment and interpretation
What do we know?
What do we not know?
How can we improve?
Good understanding needed to communicate our results with other scientists (e.g. particle physicists)

23. Path length dependence I
Collision geometry
Au+Au
Centrality
Cu+Cu
Out of plane
<L>, density increase with centrality
Vary L and density independently by changing Au+Au  Cu+Cu
In-plane
Change L in single system in-plane vs out of plane

24. Path length I: centrality dependence
Comparing Cu+Cu and Au+Au
RAA: inclusive suppression
Away-side suppression
B. Sahlmüller, QM08
6 < pT trig < 10 GeV
O. Catu, QM2008
Modified frag: nucl-th/ H.Zhang, J.F. Owens, E. Wang, X.N. Wang
Inclusive and di-hadron suppression seem to scale with Npart
Some models expect scaling, others (PQM) do not

25. Npart scaling? PQM: no scaling of with Npart
PQM - Loizides – private communication
Geometry (thickness, area) of central Cu+Cu similar to peripheral Au+Au
PQM: no scaling of with Npart

26. Path length II: RAA vs L RAA as function of angle with reaction plane
PHENIX, PRC 76,
Out of Plane
In Plane Le
3<pT<5 GeV/c
Suppression depends on angle, path length

27. RAA Le Dependence Au+Au collisions at 200GeV
0-10%
50-60%
PHENIX, PRC 76,
The pathlength weighted integral over the density is done on a Glauber model by assuming that the density goes like the Ncoll density.
The data seem to imply that we don’t reach a regime that matches the energy dependence of purely radiative energy loss until high pT. Is this a signal that at lower pT’s collisional losses are significant? This is all in pretty good agreement with Magdelena’s calculations (see backup slide).
Phenomenology: RAA scales best with Le
Little/no energy loss for Le < 2 fm ?

28. Modelling azimuthal dependence
A. Majumder, PRC75,
RAA
RAA
pT (GeV)
pT (GeV)
RAA vs reaction plane sensitive to geometry model

29. RAA vs reaction plane angle
Majumder, van Leeuwen, arXiv:
Azimuthal modulation, path length dependence largest in ASW-BDMPS
But why? – No clear answer yet
Data prefer ASW-BDMPS

30. Path length dependence and v2
PHENIX PRL105,
v2 at high pt due to energy loss
Most calculations give too small effect

31. Path length III: ‘surface bias’
Near side trigger, biases to small E-loss
Away-side large L
Away-side suppression IAA samples different path-length distribution than inclusives RAA

32. Di­hadron correlations
8 < pTtrig < 15 GeV
Combinatorial background
associated
pTassoc > 3 GeV 
trigger
Near side
Away side
Use di-hadron correlations to probe the jet-structure in p+p, d+Au
and Au+Au

33. Di-hadrons at high-pT: recoil suppression
d+Au
Au+Au 20-40%
Au+Au 0-5%
pTassoc > 3 GeV
pTassoc > 6 GeV
High-pT hadron production in Au+Au dominated by (di-)jet fragmentation
Suppression of away-side yield in Au+Au collisions: energy loss

34. Di­hadron yield suppression
Away side
Near side
8 < pT,trig < 15 GeV
Yield in balancing jet, after energy loss
Yield of additional particles in the jet
trigger
Near side
associated
trigger
STAR PRL 95,
Away side associated
Near side: No modification  Fragmentation outside medium?
Away-side: Suppressed by factor 4-5  large energy loss

35. Interpreting di-hadron measurements
Scenario I:
Some lose all,
Some lose nothing
Scenario II:
All lose something
Di-hadron measurement:
Away-side yield is (semi-)inclusive, so does not measure fluctuations of energy loss
Multi-hadron measurements potentially more sensitive
All is encoded in energy loss distribution P(DE)

36. A closer look at azimuthal peak shapes
8 < pT(trig) < 15 GeV/c
pT(assoc)>6 GeV
Vitev, hep-ph/ p Df
Broadening due to fragments of induced radiation
Induced acoplanarity (BDMPS):
No away-side broadening:
No induced radiation
No acoplanrity (‘multiple-scattering’)

37. Comparing single- and di-hadron results
Armesto, Cacciari, Salgado et al.
RAA and IAA fit with similar density
Calculation uses LPM-effect, L2 dependence

38. Near side trigger, biases to small E-loss
Surface bias
Near side trigger, biases to small E-loss
(No suppression seen)
Away-side large L
Away-side suppression IAA samples longer path lengths than inclusives RAA

39. L scaling: elastic vs radiative
T. Renk, PRC76,
RAA: input to fix density
Radiative scenario fits data; elastic scenarios underestimate suppression
Indirect measure of path-length dependence:
single hadrons and di-hadrons probe different path length distributions
Confirms L2 dependence  radiative loss dominates

40. RAA at LHC ALICE PHENIX RAA at LHC has much stronger pT-dependence ?
ALICE, PLB 696, 30
RAA at LHC has much stronger pT-dependence ?

41. RAA RHIC and LHC II
Overlaying the two results: PHENIX p0 and ALICE h± pT-dependence not too different…
N.B.: Large uncertainties in RHIC result at high pT

42. LHC results vs models
ASW N=1 opacity
DGLV N=1 opacity
ASW MS
Calculations: M. Verweij
Radiative energy loss calculations do not reproduce the rise with pT

43. Heavy quark suppression
Using non-photonic electrons
Expected energy loss
light
M.Djordjevic PRL 94
Wicks, Horowitz et al, NPA 784, 426
PHENIX nucl-ex/ , STAR nucl-ex/
Expect: heavy quarks lose less energy due to dead-cone effect
Most pronounced for bottom
Measured suppression of non-photonic electrons larger than expected
Djordjevic, Phys. Lett. B632, 81
Armesto, Phys. Lett. B637, 362
Radiative (+collisional) energy loss not dominant? E.g.: in-medium hadronisation/dissociation (van Hees, et al)

44. Light flavour reference
Armesto, Cacciari, Salgado et al.
Note again: RAA and IAA fit same density

45. Heavy Quark comparison
No minimum – Heavy Quark suppression too large for ‘normal’ medium density

46. Charm/bottom separation
X.Y. Lin, hep-ph/
Idea: use e-h angular correlations to tag semi-leptonic D vs B decay B
D → e + hadrons
B peak broader due to larger mass D
The two points at delta phi = 0 are due to photonic electrons sneaking through, Shingo has an updated plot where the points are with the fit.
Shingo Sakai
Reference QM06 paper
Extract B contribution by fitting: 46

47. Charm/bottom separation
STAR, PRL 105,
Almost fifty-fifty B and D contributions to non-photonic e’s at 5.5 < pT < 9 GeV/c and FONLL prediction is consistent with our data within errors.
Combine rB and RAA to determine RAA for charm and bottom 47 47

48. RAA for c  e and b  e Combined data show: electrons from both
pT > 5 GeV/c
Combined data show:
electrons from both
B and D suppressed
STAR, PRL 105,
Large suppression suggests additional energy loss mechanism
(resonant scattering, dissociative E-loss)
Red line is using the mean value for RAA_eb and RAA_ec
I: Djordjevic, Gyulassy, Vogt and Wicks, Phys. Lett. B 632 (2006) 81; dNg/dy = 1000
II: Adil and Vitev, Phys. Lett. B 649 (2007) 139
III: Hees, Mannarelli, Greco and Rapp, Phys. Rev. Lett. 100 (2008) 48 48

49. D/B from e-K correlations
B → e + D
D → e + K
Use e-K invariant mass to separate charm and bottom
Signal: unlike-sign near-side correlations
Subtract like-sign pairs to remove background
Use Pythia to extract D, B yields
arXiv: hep-ex
Ntag counted as all pairs within 0.4 < M < 1.9.

50. Charm-to-Bottom Ratio
arXiv: hep-ex
At pt greater than 5, fraction of bottom found to be > 33% to 90% confidence level.
**explain axes
How are systematic errors estimated? Pythia dependent?
**arrows
PHENIX p+p measuments agree with pQCD (FONLL) calculation

51. Heavy-to-Light ratios at LHC
Colour-charge and mass dep. of E loss
Heavy-to-light ratios:
mass effect
For pT > 10 GeV charm is ‘light’
RD/h : colour-charge dependence of E loss
RB/h : mass dependence of E loss
Armesto, Dainese, Salgado, Wiedemann, PRD71 (2005)

52. Color factors QCD : For SU(3) : Nc = 3 CA = 3, CF = 4/3 CA/CF=9/4
Color factors measured at LEP
QCD : For SU(3) :
Nc = 3
CA = 3, CF = 4/3
CA/CF=9/4
CF ~ strength of a gluon coupling to a quark
CA ~ strength of the gluon self coupling
TF ~ strength of gluon splitting into a quark pair
Expect
gluons radiate ~ twice more energy than quarks

53. Subprocesses and quark vs gluon
PYTHIA (by Adam Kocoloski) gg qq gq
p+pbar dominantly from gluon fragmentation

54. Comparing quark and gluon suppression
Baryon & meson NMF
PRL 97, (2006)
STAR Preliminary, QM08
STAR Preliminary
Curves: X-N. Wang et al PRC70(2004)
Protons less suppressed than pions, not more
No sign of large gluon energy loss

55. Quark vs gluon suppression
GLV formalism
BDMPS formalism
WHDG
+ renk plot
Renk and Eskola, PRC76,027901
Quark/gluon difference larger in GLV than BDMPS
(because of cut-off effects DE < Ejet?)
~10% baryons from quarks, so baryon/meson effect smaller than gluon/quark
Are baryon fragmentation functions under control?
Conclusion for now: some homework to do...

56. Equalibration of rare probes
Rare probes: not chemically equilibrated in the jet spectrum.
Example 1: flavor not contained in the medium, but can be produced off the medium (e.g. photons)
Need enough yield to outshine other sources of Nrare.
Example 2: flavor chemically equilibrated in the medium
E.g. strangeness at RHIC
Coupling of jets (flavor not equilibrated) to the equilibrated medium should drive jets towards chemical equilibrium.
R. Fries, QM09

57. Equilibration process: jet conversion
Flavour of leading parton changes
through interactions with medium
hard
parton
path length L
Quark
gluon
W. Liu, R.J. Fries, Phys. Rev. C77 (2008)