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Heavy Quark Energy Loss

William HorowitzColumbia University

June 6, 2006

With many thanks to Simon Wicks, Azfar Adil, Miklos Gyulassy, Magdalena

Djordjevic, and Brian ColeSimon Wicks Azfar Adil

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RAA()=RAA(1+2v2Cos(2)+…)• Glue and Lights • Charm and

Bottom

•Correlations of back-to-back jets, etc.

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Jets as a Tomographic Probe

• Tomography requires precision measurements AND precision, pQCD theory

Probe the unknown QGP with energy loss

Quark or Glue Jet probes: (, pT, - reac, MQ) init

Hadron jet fragments: (, pT, – reac ) final

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to understand the medium

• If pQCD makes the correct predictions, we can use

Jets as a Tomographic Probe (cont’d)

•Otherwise, jet suppression is just another non-perturbative anomaly of A+A collisions (like J/ suppression)

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Before the e- RAA, the picture looked pretty good:

– Null Control: RAA()~1

– Consistency: RAA()~RAA()

– GLV Prediction: Theory~Data for reasonable fixed L~5 fm and dNg/dy~dN/dy

Y. Akiba for the PHENIX collaboration, hep-ex/0510008

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But with Hints of Trouble:

• Theory v2 too small

• Fragile Probe?

A. Drees, H. Feng, and J. Jia, Phys. Rev. C71:034909 (2005)(first by E. Shuryak, Phys. Rev. C66:027902 (2002))

K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747:511:529 (2005)

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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)

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Entropy-constrained radiative-dominated loss FALSIFIED by e- RAA

Problem: Qualitatively, RAA~ e- RAA

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Inherent Uncertainties in Production Spectra

M. Djordjevic, M. Gyulassy, R. Vogt, S. Wicks, Phys. Lett. B632:81-86 (2006)

How large is bottom’s role?

– Vertex detectors could de-convolute the e- contributions

N. Armesto, M. Cacciari, A. Dainese, C. A. Salgado, U. A. Wiedemann, hep-ph-0511257

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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-0511257

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What Does Mean?

We believe it’s nonperturbative:– = .5 => dNg/dy ~ 13,000

R. Baier, Nucl. Phys. A715:209-218 (2003)

“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”

U. A. Wiedemann, SQM 2006

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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/0511052 D. Winter, QM2005

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But what if we Neglected an Important Effect?

M. Mustafa, Phys. Rev. C72:014905 (2005) S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076

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Elastic History

(a) J. D. Bjorken, FERMILAB-PUB-82-059-THY (Quantal)(b) M. H. Thoma and M. Gyulassy, Nucl. Phys. B351:491-506 (1991) (Classical)(c) E. Braaten and M. H. Thoma, Phys. Rev. D24:2625-2630 (1991) (Quantal)(d) P. Romatschke and M. Strickland, Phys. Rev. D71:125008 (2005) (Quantal)

People have thought about Elastic Loss for a long time, and in different ways—all assume parton starts in asymptotic past

Bottom Charm

Most correct (infinite time) elastic loss calculation approximately bounded by BT and TG curves

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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 ~ participant

– This allows a self-consistent pion prediction

without “fixed L”approx

S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076

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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

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Conservative Results

S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076

•Elastic loss improves quench•keeping dNg/dy = 1000 s = .3• and No change in c or b production cross sections•Extended Theory is consistent with data for pT > 7 GeV

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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/0512076

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El+Rad+Geom NOT a Fragile Probe

• Why? First, experimental error bars have shrunk considerably since 2004. Second, el < rad

WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

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Why Widths are Vital

– The whole distribution is important: , but el < rad

S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076

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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/D ~ .5 fm, the screening scale; but perhaps there is a hidden factor

• What about interference effects?

S. Peigne, P.-B. Gossiaux, and T. Gousset, JHEP0604:011 (2006)

They claim NO elastic loss until L > 10 fm!

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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 intheir classical current, therebyviolating current conservationand resulting in a spurious A. Adil, M. Gyulassy, WH, and S.

Wicks, nucl-th/0606010

subtraction of the (negative) binding energy of the quark-antiquark pair

•HUGE

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Classical Finite Time Results

A. Adil, M. Gyulassy, WH, and S. Wicks, nucl-th/0606010

By L ~ 1/D, stable field reaches ~ 90% of the asymptotic10 GeV Charm 10 GeV Charm

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Quantal Finite Time Results

Again, formation effects negligible beyond 1/D

X. N. Wang, nucl-th/0604040M. Djordjevic, nucl-th/0603066

No one as yet fully combines El+Rad with interference

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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

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LHC Predictions

WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

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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

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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

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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

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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 must be allowed to run; the size of the irreducible error due to integration over low, nonperturbative momenta, where > .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?

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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. C72:014906 (2005)

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Backup Slides

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WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

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S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076

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WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

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WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

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WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

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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. C38:461-474 (2005)

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N. Armesto, M. Cacciari, A. Dainese, C. A. Salgado, U. A. Wiedemann, hep-ph-0511257

A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005)

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A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005)

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S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076