1. Heavy Quark Energy Loss
William Horowitz
Columbia University
June 6, 2006
With many thanks to Simon Wicks, Azfar Adil, Miklos Gyulassy, Magdalena Djordjevic, and Brian Cole
Azfar Adil
Simon Wicks
RHIC & AGS Annual Users’ Meeting ‘06

2. RAA(j)=RAA(1+2v2Cos(2j)+…)
Glue and Lights
Charm and Bottom
Correlations of back-to-back jets, etc.
RHIC & AGS Annual Users’ Meeting ‘06

3. Jets as a Tomographic Probe
Probe the unknown rQGP with energy loss
Tomography requires precision measurements AND precision, pQCD theory
Quark or Glue Jet probes:
(h, pT, j - jreac, MQ) init
Hadron jet fragments:
(h, pT, j – jreac ) final
RHIC & AGS Annual Users’ Meeting ‘06

4. Jets as a Tomographic Probe (cont’d)
If pQCD makes the correct predictions, we can use
to understand the medium
Otherwise, jet suppression is just another non-perturbative anomaly of A+A collisions (like J/Y suppression)
RHIC & AGS Annual Users’ Meeting ‘06

5. Before the e- RAA, the picture looked pretty good:
Y. Akiba for the PHENIX collaboration, hep-ex/
Null Control: RAA(g)~1
Consistency: RAA(h)~RAA(p)
GLV Prediction: Theory~Data for reasonable fixed L~5 fm and dNg/dy~dNp/dy
RHIC & AGS Annual Users’ Meeting ‘06

6. But with Hints of Trouble:
Theory v2 too small
Fragile Probe?
A. Drees, H. Feng, and J. Jia, Phys. Rev. C71: (2005)
(first by E. Shuryak, Phys. Rev. C66: (2002))
K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747:511:529 (2005)
RHIC & AGS Annual Users’ Meeting ‘06

7. What Can Heavies Teach Us?
Provide a unique test of our understanding of energy loss
Mass => Dead Cone => Reduction in E loss =
Bottom Quark
(Gratuitous Pop Culture Reference)
RHIC & AGS Annual Users’ Meeting ‘06

8. Entropy-constrained radiative-dominated loss FALSIFIED by e- RAA
Problem: Qualitatively, p0 RAA~ e- RAA
RHIC & AGS Annual Users’ Meeting ‘06

9. Inherent Uncertainties in Production Spectra
How large is bottom’s role?
M. Djordjevic, M. Gyulassy, R. Vogt, S. Wicks, Phys. Lett. B632:81-86 (2006)
Vertex detectors could de-convolute the e- contributions
N. Armesto, M. Cacciari, A. Dainese, C. A. Salgado, U. A. Wiedemann, hep-ph
RHIC & AGS Annual Users’ Meeting ‘06

10. The BDMPS-Z-WS Approach
Increase to 14 to push curve down
Fragility in the model allows for consistency with pions
N. Armesto, M. Cacciari, A. Dainese, C. A. Salgado, U. A. Wiedemann, hep-ph
RHIC & AGS Annual Users’ Meeting ‘06

11. RHIC & AGS Annual Users’ Meeting ‘06
What Does Mean?
We believe it’s nonperturbative:
a = .5 => dNg/dy ~ 13,000
“Proportionality constant ~ 4-5 times larger than perturbative estimate”
K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747:511:529 (2005)
“Large numerical value of not yet understood”
R. Baier, Nucl. Phys. A715: (2003)
U. A. Wiedemann, SQM 2006
RHIC & AGS Annual Users’ Meeting ‘06

12. Is this Plausible? Maybe
Flow nonperturbative at low-pT
v2 possibly nonperturbative at mid-pT
Asymptotic Freedom MUST occur
But at what momentum?
WH, nucl-th/
D. Winter, QM2005
RHIC & AGS Annual Users’ Meeting ‘06

13. But what if we Neglected an Important Effect?
M. Mustafa, Phys. Rev. C72: (2005) S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/
RHIC & AGS Annual Users’ Meeting ‘06

14. RHIC & AGS Annual Users’ Meeting ‘06
Elastic History
People have thought about Elastic Loss for a long time, and in different ways—all assume parton starts in asymptotic past
J. D. Bjorken, FERMILAB-PUB THY (Quantal)
M. H. Thoma and M. Gyulassy, Nucl. Phys. B351: (1991) (Classical)
E. Braaten and M. H. Thoma, Phys. Rev. D24: (1991) (Quantal)
P. Romatschke and M. Strickland, Phys. Rev. D71: (2005) (Quantal)
Bottom Charm
Most correct (infinite time) elastic loss calculation approximately bounded by BT and TG curves
RHIC & AGS Annual Users’ Meeting ‘06

15. Include Path Length Fluctuations with Realistic Geometry
For fixed L~5 fm, Collisional+Radiative leads to pion overquenching
Use Woods-Saxon density
hard production ~ TAA
medium ~ rparticipant
This allows a self-
consistent pion prediction
without “fixed L”approx
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/
RHIC & AGS Annual Users’ Meeting ‘06

16. RHIC & AGS Annual Users’ Meeting ‘06
Our Extended Theory
Convolve Elastic with Inelastic energy loss fluctuations
Include path length fluctuations in diffuse nuclear geometry
Separate calculations with BT and TG collisional formulae provide a measure of the elastic theoretical uncertainty
RHIC & AGS Annual Users’ Meeting ‘06

17. RHIC & AGS Annual Users’ Meeting ‘06
Conservative Results
Elastic loss improves quench
keeping
dNg/dy = 1000
as = .3
and No change in c or b production cross sections
Extended Theory is consistent with data for pT > 7 GeV
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/
RHIC & AGS Annual Users’ Meeting ‘06

18. Consistency Test with Pions
Not flat, which requires a balance of many competing effects (Cronin, EMC, etc.) but not at odds with data
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/
RHIC & AGS Annual Users’ Meeting ‘06

19. El+Rad+Geom NOT a Fragile Probe
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
Why? First, experimental error bars have shrunk considerably since Second, sDE,el < sDE,rad
RHIC & AGS Annual Users’ Meeting ‘06

20. RHIC & AGS Annual Users’ Meeting ‘06
Why Widths are Vital
The whole distribution is important:
, but sDE,el < sDE,rad
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/
RHIC & AGS Annual Users’ Meeting ‘06

21. RHIC & AGS Annual Users’ Meeting ‘06
Elastic Objections
All derivations start parton at asymptotic past: are there formation time effects?
Peigne et al. (Classical):
This is unintuitive: one expects effects to disappear by L ~ 1/mD ~ .5 fm, the screening scale; but perhaps there is a hidden g factor
What about interference effects?
They claim NO elastic loss until L > 10 fm!
S. Peigne, P.-B. Gossiaux, and T. Gousset, JHEP0604:011 (2006)
RHIC & AGS Annual Users’ Meeting ‘06

22. Adil et al. Classical Refutation of Peigne et al.
Two issues:
Peigne et al. do not disentangle known radiative effects
small
Peigne et al. neglect a term in
their classical current, thereby
violating current conservation
and resulting in a spurious
A. Adil, M. Gyulassy, WH, and S. Wicks, nucl-th/
subtraction of the (negative) binding energy of the quark-antiquark pair
HUGE
RHIC & AGS Annual Users’ Meeting ‘06

23. Classical Finite Time Results
By L ~ 1/mD, stable field reaches ~ 90% of the asymptotic
10 GeV Charm
10 GeV Charm
A. Adil, M. Gyulassy, WH, and S. Wicks, nucl-th/
RHIC & AGS Annual Users’ Meeting ‘06

24. Quantal Finite Time Results
Again, formation effects negligible beyond 1/mD
M. Djordjevic, nucl-th/
X. N. Wang, nucl-th/
No one as yet fully combines El+Rad with interference
RHIC & AGS Annual Users’ Meeting ‘06

25. Heavy Quark Tomography of the LHC
Additional systematic tests of the energy loss theory
2-3 times RHIC medium densities
Enormous pT range
At very high momenta, GLV and BDMPS-Z-WS results converge, but elastic effects persist!
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
RHIC & AGS Annual Users’ Meeting ‘06

26. RHIC & AGS Annual Users’ Meeting ‘06
LHC Predictions
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
RHIC & AGS Annual Users’ Meeting ‘06

27. RHIC & AGS Annual Users’ Meeting ‘06
Conclusions
Fantastic new RHIC data challenging, surprising
Better understanding of heavy quark loss mechanisms, production critical for interpreting experimental results
Large uncertainties in ratio of charm to bottom contribution to non-photonic electrons
Direct measurement of D spectra would help separate the different charm and bottom jet dynamics
FONNLL would provide better information on theoretical production error
RHIC & AGS Annual Users’ Meeting ‘06

28. RHIC & AGS Annual Users’ Meeting ‘06
Conclusions (cont’d)
BDMPS-Z-WS:
IF extreme is assumed
IF elastic loss is assumed to vanish
IF they assume fragility
Then not inconsistent with data
No hope for tomography
RHIC & AGS Annual Users’ Meeting ‘06

29. RHIC & AGS Annual Users’ Meeting ‘06
Conclusions (cont’d)
DGLV:
Include elastic, inelastic, and path length fluctuations
Consistent results for high-pT e- RAA
Pion RAA predictions agree well with data over large momentum range, are sensitive to changes in medium density, consistent with multiplicity constraints
RHIC & AGS Annual Users’ Meeting ‘06

30. RHIC & AGS Annual Users’ Meeting ‘06
Conclusions (cont’d)
Far from finished:
Coherence and correlation effects between elastic and inelastic processes that occur in a finite time over multiple collisions must be sorted out
Fixed a must be allowed to run; the size of the irreducible error due to integration over low, nonperturbative momenta, where a > .5, needs to be determined
Where will e- RAA data and theoretical calculations settle down as research progresses and error bars are reduced over time?
RHIC & AGS Annual Users’ Meeting ‘06

31. RHIC & AGS Annual Users’ Meeting ‘06
Conclusions (cont’d)
AMY: a third approach?
Produced a pion RAA; no calculation of e- RAA, a crucial consistency check
The LHC will provide an excellent new testing ground for systematic study (falsification?) of energy loss theory
Jet tomography is an elusive, but achievable goal
P. Arnold, G.D. Moore, and L. Yaffe, JHEP 011:057 (2001)
S. Turbide, C. Gale, S. Jeon, G. D. Moore, Phys. Rev. C72: (2005)
RHIC & AGS Annual Users’ Meeting ‘06

32. RHIC & AGS Annual Users’ Meeting ‘06

33. RHIC & AGS Annual Users’ Meeting ‘06
Backup Slides
RHIC & AGS Annual Users’ Meeting ‘06

34. RHIC & AGS Annual Users’ Meeting ‘06
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
RHIC & AGS Annual Users’ Meeting ‘06

35. RHIC & AGS Annual Users’ Meeting ‘06
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/
RHIC & AGS Annual Users’ Meeting ‘06

36. RHIC & AGS Annual Users’ Meeting ‘06
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
RHIC & AGS Annual Users’ Meeting ‘06

37. RHIC & AGS Annual Users’ Meeting ‘06
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
RHIC & AGS Annual Users’ Meeting ‘06

38. RHIC & AGS Annual Users’ Meeting ‘06
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
RHIC & AGS Annual Users’ Meeting ‘06

39. RHIC & AGS Annual Users’ Meeting ‘06
K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747:511:529 (2005)
A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38: (2005)
RHIC & AGS Annual Users’ Meeting ‘06

40. RHIC & AGS Annual Users’ Meeting ‘06
N. Armesto, M. Cacciari, A. Dainese, C. A. Salgado, U. A. Wiedemann, hep-ph
A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38: (2005)
RHIC & AGS Annual Users’ Meeting ‘06

41. RHIC & AGS Annual Users’ Meeting ‘06
A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38: (2005)
RHIC & AGS Annual Users’ Meeting ‘06

42. RHIC & AGS Annual Users’ Meeting ‘06
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/
RHIC & AGS Annual Users’ Meeting ‘06