9/22/06William Horowitz 1 Surface or Volume Emission at RHIC: Is Jet Tomography Possible? William Horowitz Columbia University September 22, 2006 With.

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9/22/06 William Horowitz

Surface or Volume Emission at RHIC:

Is Jet Tomography Possible? William Horowitz

Columbia UniversitySeptember 22, 2006

With many thanks to Simon Wicks, Azfar Adil, Magdalena Djordjevic, and Miklos

Gyulassy.

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Outline

• Possibility of Tomography– Surface vs. Volume

• Time Permitting– LHC Pion Predictions– Azimuthal Anisotropy Puzzle

– Heavy Quark RAA Puzzle

– LHC Heavies Predictions

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The Big Picture

• Ultimate goal: Jet Tomography

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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RAA()=RAA(1+2v2Cos(2)+…)

•RAA: ratio of Au+Au to binary scaled p+p

•Modest Goal: reproduce RAA to estimate the medium density

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Jets as a Tomographic Probe

• Requires:– Theoretical understanding of

underlying physics (esp. quenching mechanisms)

– Mapping from the controlling parameter of the theory to the medium density

– Sensitivity in the model + data for the measurement used

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Surface Emission:A Simple (Specious?) Picture

• Claim: only jets originating close to the medium edge escape– No matter the input density,

a corona of jets always escape• Surface Emission => • Fragile Probe =>• No Tomography

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2/3

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2

2

( (1 ) /(1 )

( ) /

1

1 '

T TAA

T

pa

T

t

n

r

d p dyd pR

d p dyd p

N

20( ) nn

T T T

d a a

dyd p p p p

2 /3/ 23 ' part

gE L dNA k

E A dyN

Baseline:

Fractional energy loss:

I. Vitev, Phys.Lett.B in press, hep-ph/0603010

Prediction: 2/3ln AA partR N

Natural variables1/31/3 2/3 2/3,part part

g

t

g

par

L dNL A A

A dy

dNA

dy

N N

N

Scalings:

Suppression:

Approximately universal behavior

Simplistic Volume Emission

I. Vitev, HP2006

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Reframe the Debate

• Disentangle Surface Bias from Surface Emission– All energy loss models must have surface

bias

• Fragility is a poor descriptor of a theory– All energy loss models with a formation time

saturate at some RminAA > 0

– The questions asked should be quantitative : • Where is Rdata

AA compared to RminAA?

• How much can one change a model’s controlling parameter so that it still agrees with a measurement within error? How sensitive are the jets?

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BDMPS-Z-SWEnergy Loss

• Highly Biased? • Insensitive Jets?

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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Significance of Nuclear Profile

• Simpler densities create a surface biasHard Cylinder Hard Sphere Woods-Saxon

Illustrative Only! Toy model for purely geometric radiative loss from Drees, Feng, Jia, Phys. Rev. C.71:034909

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A Closer Look at BDMPS

– Difficult to draw conclusions on inherent surface bias in BDMPS from this plot for three reasons: • No Bjorken expansion• Glue and light quark

contributions not disentangled

• Plotted against Linput (complicated mapping from Linput to physical distance)


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A Closer Look at BDMPS (cont’d)


The lack of sensitivity needs to be more closely examined because of the use of unrealistic geometry (hard cylinders) and no expansion

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Our Extended Theory

• Convolve Elastic with Inelastic energy loss fluctuations

• Include path length fluctuations in diffuse nuclear geometry with 1+1D Bjorken expansion

• Separate calculations with BT and TG collisional formulae provide a measure of the elastic theoretical uncertainty

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Elastic Can’t be Neglected!

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

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Length Definitions– Define a mapping from the line integral

through the realistic medium to the theoretical block

– where

– Then

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Geometry Can’t be Neglected!

• P(L) is a wide distribution– Flavor

independent

• Flavor dependent fixed length approximations LQ’s not a priori obvious

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

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Our Jets Probe the Volume and are Sensitive to the Medium

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


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Elastic Width Increases Sensitivity

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


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Other Models Probe the Volume

• Higher Twist • BDMPS w/ Geom

A. Majumder, HP2006 T. Renk, hep-ph/0608333

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Conclusions I

• In order to make nontrivial statements about fragility, one must use diffuse nuclear geometries with Bjorken expansion– Otherwise surface emission is a

reflection of the inherent surface bias of the geometry

– RHIC is not a Brick

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Conclusions I (cont’d)

• Our model emits from the volume and is falsified by data for too-large medium densities– Renk: Volume Emission– Majumder: Volume Emission and

Sensitive– Vitev: Sensitive

• Pion RAA is a good tomographic probe of the medium

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LHC Pion Predictions

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Elastic Remains Important

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LHC Pions

• Note the large rise in RAA with energy

• Note the dependence on medium density WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

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BDMPS-Based Predictions

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Conclusions II

• With current predictions, the momentum dependence of RAA at LHC could distinguish between BDMPS and GLV type loss models

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Azimuthal Anisotropy

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What is the Puzzle?–Data– Naïvely combine

published RAA(pT) and v2(pT) data

– Preliminary PHENIX 0 data

– Data centrality classes:• STAR charged hadron

– 0-5%, 10-20%, 20-30%, 30-40%, 40-60%

• PHENIX charged hadron– 0-20%, 20-40%, 40-60%

• PHENIX 0

– 10-20%, 20-30%, …, 50-60% • Note: error regions are only a rough estimate

W. Horowitz, nucl-th/0511052

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What is the Puzzle?–Theory

• Nothing matches the RHIC phenomena• Hydrodynamics

– Not applicable at intermediate and higher pT

– Boltzmann factors crush RAA to 0

• Parton Cascade and Energy Loss– Don’t work: jet quenching and anisotropy

are anti-correlated

– Models over-suppress RAA in order to reproduce large observed v2 or vice-versa

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Model Failures• Models can’t

match intended data point for any value of their free parameter (opacity of the medium)– MPC: calculated for

25-35% centrality– gGLV: 40-50%

centralityW. Horowitz, nucl-th/0511052

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Success!

• Add a small, outward-pointing momentum punch, – Reasonable,

deconfinement-like value of .5 GeV

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Cu+Cu Predictions and Improved PHENIX Data

W. Horowitz, nucl-th/0511052 D. Winter, QM2005

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Conclusions II

• The punch is an interesting toy model that suggests the larger than pQCD intermediate-pT v2 may provide a unique signature of deconfinement

• Work is needed to extend the results out in pT and more closely associate the punch with a deconfinement mechanism

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Heavy Quark Puzzle

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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))


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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


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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”


“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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Our Results

• Inclusion of elastic decreases the discrepancy

• Direct c and b measurements required to truly rule out this approach


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LHC Predictions for Heavies


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Conclusions III

– Elastic loss cannot be neglected when considering pQCD jet quenching• 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

– 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

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This Slide Intentionally Left Blank

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Backup Slides

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Insensitive Jets?



The lack of sensitivity needs to be more closely examined because (a) unrealistic geometry (hard cylinders) and no expansion and (b) no expansion shown against older data (whose error bars have subsequently shrunk

(a) (b)

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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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Let’s Look at the Data• STAR moderate-pt charged hadrons RAA (nucl-ex/0305015)• STAR moderate-pt charged hadrons v2 (nucl-ex/0206006, 0409033)• PHENIX moderate-pt charged hardrons RAA (nucl-ex/0308006)• PHENIX moderate-pt charged hadrons v2 (nucl-ex/0305013)• PHENIX unpublished RAA

9/22/06William Horowitz 1 Surface or Volume Emission at RHIC: Is Jet Tomography Possible? William Horowitz Columbia University September 22, 2006 With.

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