Zero th Order Heavy Quark Photon/Gluon Bremsstrahlung

WWND 2008

14/9/08

William Horowitz

Zeroth Order Heavy Quark Photon/Gluon

Bremsstrahlung

William HorowitzColumbia University

Frankfurt Institute for Advanced Studies (FIAS)April 9, 2008

With many thanks to Miklos Gyulassy, Simon Wicks, Ivan Vitev, Hendrik van Hees

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24/9/08

William Horowitz

A Talk in Two Parts

pQCD vs. AdS/CFT Drag

0th Order Production Radiation

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34/9/08

William Horowitz

Testing pQCD vs. AdS/CFT Drag Energy Loss Mechanisms

(In Five Slides)

arXiv:0706.2336 (LHC predictions)arXiv:0710.0703 (RHIC predictions)

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44/9/08

William Horowitz

(Proper) Subset of Mechanisms

• DGLV, AdS/CFT Drag, Diffusion…

• Use heavy quark RAA to test these twodpT/dt ~ -(T2/Mq) pTLPM: dpT/dt ~ -LT3 log(pT/Mq)

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William Horowitz

– LHC Prediction Zoo: What a Mess!– Let’s go through step by step

– Unfortunately, large suppression pQCD similar to AdS/CFT– Large suppression leads to flattening– Use of realistic geometry and Bjorken expansion allows saturation below .2– Significant rise in RAA(pT) for pQCD Rad+El– Naïve expectations met in full numerical calculation: dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST

LHC c, b RAA pT Dependence

WH, M. Gyulassy, arXiv:0706.2336

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64/9/08

William Horowitz

LHC RcAA(pT)/Rb

AA(pT) Prediction

• Recall the Zoo:

– Taking the ratio cancels most normalization differences seen previously– pQCD ratio asymptotically approaches 1, and more slowly so for

increased quenching (until quenching saturates)– AdS/CFT ratio is flat and many times smaller than pQCD at only

moderate pT

WH, M. Gyulassy, arXiv:0706.2336 [nucl-th]


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William Horowitz

RHIC Rcb Ratio

• Wider distribution of AdS/CFT curves at RHIC due to large n power law production: increased sensitivity to input parameters

• Advantage of RHIC: lower T => higher AdS speed limits


pQCD

AdS/CFT

pQCD

AdS/CFT

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William Horowitz

Conclusions• AdS/CFT Drag observables calculated• Generic differences (pQCD vs.

AdS/CFT Drag) seen in RAA

– Masked by extreme pQCD

• Enhancement from ratio of c to b RAA

– Discovery potential in Year 1 LHC Run

• Understanding regions of self-consistency crucial

• RHIC measurement possible

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94/9/08

William Horowitz

Some Investigations of 0th Order Production Radiation

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104/9/08

William Horowitz

Motivation• Previous work: test pQCD or

AdS/CFT energy loss– Heavy quark RQ

AA and RcAA/Rb

AA

• Future goal: additional energy loss test using photon bremsstrahlung

• Zeroth Order Calculation– Recent p + p fragmentation data– Good warm-up and test problem

• Investigate running , low-pT, etc.

– Reevaluate magnitude of Ter-Mikayelian

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114/9/08

William Horowitz

New Fragmentation Data

A. Hanks, QM2008

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124/9/08

William Horowitz

Motivating Example: Running s

– Fixed s is simplification to speed up code• Not a free parameter

– Running s will most likely introduce a large error

– Want to understand systematics in 0th Order

S. Wicks, WH, M. Djordjevic, M Gyulassy, Nucl.Phys.A783:493-496,2007

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William Horowitz

• Quark mass => Dead cone– Ultrarelativistic “searchlight” rad.

pattern

• Gluon mass => Longitudinal modes, QCD Ter-Mikayelian

– Reduction of production radiation compared to vacuum• Alters DGLAP kernel

Quark and Gluon/Photon Mass Effects

~ Mq/E

Y. Dokshitzer and D. Kharzeev, Phys.Lett.B519:199-206,2001

M. Djordjevic and M. Gyulassy, Phys.Rev.C68:034914,2003

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William Horowitz

Previous Calculation of Ter-Mikayelian

• Reduction of E-loss for charm quarks by ~ 30%• E-loss from full HTL well approx. by fixed mg = m∞

• Small-x pQCD 0th Order result:


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William Horowitz

Compare Classical E&M to “pQCD”

– Classical E&M• Recall Jackson:

• Soft photon limit =>

– Note charge conserved

– Usual pQCD approach

– Charge explicitly not conserved=> Ward identity ( ) violated

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William Horowitz

Classical/QFT Inconsistency

– For mQ = mg = 0 and in the small x, large E+ limit, both are equal:

– For mQ, mg ≠ 0 and the small x, large E+ limit, they differ:

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William Horowitz

Not a Classical Error– Wrong classical calculation?

• Plugged in massive 4-vectors into massless formulae

• Rederive classical result using Proca Lagrangian

– After several pages of work…

• Identical to

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William Horowitz

Error from QFT Ward Violation• Identical expressions are not a

surprise• QFT Calculation

– Photon momentum carried away crucial for cancellation of photon mass• Classical case neglects both; effects

cancel

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William Horowitz

Resulting Expression– To lowest order in 1/E+

– New:• (1-x)2 prefactor: naturally kills hard

gluons

• mg2 in numerator: fills in the dead cone!?!

– What are the sizes of these effects?Call this LO

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LO Gluon Production Radiation

• Prefactor => 50-150% effect

– Implications for in-medium radiative loss?

• Filling in dead code => 5-20%

– Numerics includes kT and x limits

» x large enough to create mg

» x small enough that EJet > Mq

– Fixed = .5 GeV and s = .5» Similar to Magda full HTL

propagator with running s

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William Horowitz

LO vs. All Orders Production Rad.

• Ter-Mikayelian similar for both

• Different normalizations– 0-60% effect

• All orders calculation self-regulates for mg = 0 and pT → 0

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William Horowitz

Conclusions• No single satisfactory energy loss model• Search for tests sensitive to mechanism

– Ratio of charm to bottom RAA for pQCD vs. AdS/CFT

– Future tests using photon bremsstrahlung

• Inclusion of away-side jet fills in dead cone– Ultimately leads to a relatively small (5-

20%) effect

• Radiative calculations integrate over all x; importance of large x behavior?

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William Horowitz

Backups

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William Horowitz

Reasonable Consistency with Magda

b

c


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William Horowitz

0th Order % Differences

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264/9/08

William Horowitz

Testing AdS/CFT Drag and pQCD Heavy Quark Energy Loss

William HorowitzColumbia University

Frankfurt Institute for Advanced Studies (FIAS)February 9, 2008

With many thanks to Miklos Gyulassy and Simon Wicks

arXiv:0706.2336 (LHC predictions)arXiv:0710.0703 (RHIC predictions)

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274/9/08

William Horowitz

Motivation– Many heavy quark energy loss models – Hope to distinguish between two

broad classes:• Standard Model pQCD• AdS/CFT Drag

– Comparison difficult:• nontrivial mapping of AdS/CFT to QCD• predictions for LHC

– Look for robust signal

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pQCD Success at RHIC:

– Consistency: RAA()~RAA()

– Null Control: RAA()~1

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

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

(circa 2005)

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• e- RAA too small

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

• wQGP not ruled out, but what if we try strong coupling?

• Hydro /s too small

• v2 too large

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

Trouble for wQGP Picture

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William Horowitz

Intro to AdS/CFTLarge Nc limit of d-dimensional conformal field theory dual to string theory on the product of d+1-dimensional Anti-de Sitter space with a compact manifold

3+1 SYM

z = 0

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314/9/08

William Horowitz

Strong Coupling Calculation

The supergravity double conjecture:

QCD SYM IIB

– IF super Yang-Mills (SYM) is not too different from QCD, &

– IF Maldacena conjecture is true– Then a tool exists to calculate

strongly-coupled QCD in classical SUGRA

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• Mach wave-like structures• sstrong=(3/4) sweak, similar to Lattice• /sAdS/CFT ~ 1/4 << 1 ~ /spQCD• e- RAA ~ , RAA; e- RAA()

T. Hirano and M. Gyulassy, Nucl. Phys. A69:71-94 (2006)

Qualitative AdS/CFT Successes:

PHENIX, Phys. Rev. Lett. 98, 172301 (2007)

J. P. Blaizot, E. Iancu, U. Kraemmer, A. Rebhan, hep-ph/0611393

AdS/CFT

S. S. Gubser, S. S. Pufu, and A. Yarom, arXiv:0706.0213

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William Horowitz

AdS/CFT Energy Loss Models• Langevin model

– Collisional energy loss for heavy quarks– Restricted to low pT

– pQCD vs. AdS/CFT computation of D, the diffusion coefficient

• ASW model– Radiative energy loss model for all parton species– pQCD vs. AdS/CFT computation of– Debate over its predicted magnitude

• ST drag calculation– Drag coefficient for a massive quark moving through

a strongly coupled SYM plasma at uniform T– not yet used to calculate observables: let’s do it!

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William Horowitz

AdS/CFT Drag• Model heavy quark jet energy loss

by embedding string in AdS space

dpT/dt = - pT

= T2/2Mq

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William Horowitz

Energy Loss Comparison

– AdS/CFT Drag:dpT/dt ~ -(T2/Mq) pT

– Similar to Bethe-HeitlerdpT/dt ~ -(T3/Mq

2) pT

– Very different from LPMdpT/dt ~ -LT3 log(pT/Mq)

tx

Q, m v

D7 Probe Brane

D3 Black Brane(horizon)

3+1D Brane Boundary

Black Holez = 0

zh = T

zm = 2m / 1/2

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William Horowitz

RAA Approximation

– Above a few GeV, quark production spectrum is approximately power law:• dN/dpT ~ 1/pT

(n+1), where n(pT) has some momentum dependence

– We can approximate RAA(pT):

• RAA ~ (1-(pT))n(pT),

where pf = (1-)pi (i.e. = 1-pf/pi)

y=0

RHIC

LHC

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William Horowitz

– Use LHC’s large pT reach and identification of c and b to distinguish between pQCD, AdS/CFT• Asymptotic pQCD momentum loss:

• String theory drag momentum loss:

– Independent of pT and strongly dependent on Mq!

– T2 dependence in exponent makes for a very sensitive probe

– Expect: pQCD 0 vs. AdS indep of pT!!

• dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST

rad s L2 log(pT/Mq)/pT

Looking for a Robust, Detectable Signal

ST 1 - Exp(- L), = T2/2Mq

S. Gubser, Phys.Rev.D74:126005 (2006); C. Herzog et al. JHEP 0607:013,2006

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384/9/08

William Horowitz

Model Inputs– AdS/CFT Drag: nontrivial mapping of QCD to SYM

• “Obvious”: s = SYM = const., TSYM = TQCD

– D 2T = 3 inspired: s = .05– pQCD/Hydro inspired: s = .3 (D 2T ~ 1)

• “Alternative”: = 5.5, TSYM = TQCD/31/4

• Start loss at thermalization time 0; end loss at Tc

– WHDG convolved radiative and elastic energy loss• s = .3

– WHDG radiative energy loss (similar to ASW)• = 40, 100

– Use realistic, diffuse medium with Bjorken expansion

– PHOBOS (dNg/dy = 1750); KLN model of CGC (dNg/dy = 2900)

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William Horowitz

– LHC Prediction Zoo: What a Mess!– Let’s go through step by step

– Unfortunately, large suppression pQCD similar to AdS/CFT– Large suppression leads to flattening– Use of realistic geometry and Bjorken expansion allows saturation below .2– Significant rise in RAA(pT) for pQCD Rad+El– Naïve expectations met in full numerical calculation: dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST

LHC c, b RAA pT Dependence


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William Horowitz

• But what about the interplay between mass and momentum?– Take ratio of c to b RAA(pT)

• pQCD: Mass effects die out with increasing pT

– Ratio starts below 1, asymptotically approaches 1. Approach is slower for higher quenching

• ST: drag independent of pT, inversely proportional to mass. Simple analytic approx. of uniform medium gives

RcbpQCD(pT) ~ nbMc/ncMb ~ Mc/Mb ~ .27– Ratio starts below 1; independent of pT

An Enhanced Signal

RcbpQCD(pT) 1 - s n(pT) L2 log(Mb/Mc) ( /pT)

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414/9/08

William Horowitz

LHC RcAA(pT)/Rb

AA(pT) Prediction

• Recall the Zoo:

– Taking the ratio cancels most normalization differences seen previously– pQCD ratio asymptotically approaches 1, and more slowly so for

increased quenching (until quenching saturates)– AdS/CFT ratio is flat and many times smaller than pQCD at only

moderate pT



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William Horowitz

– Speed limit estimate for applicability of AdS drag• < crit = (1 + 2Mq/1/2 T)2

~ 4Mq2/(T2)

– Limited by Mcharm ~ 1.2 GeV

• Similar to BH LPM– crit ~ Mq/(T)

– No Single T for QGP• smallest crit for largest T

T = T(0, x=y=0): “(”

• largest crit for smallest T

T = Tc: “]”

Not So Fast!

D3 Black Brane

D7 Probe Brane Q

Worldsheet boundary Spacelikeif > crit

TrailingString

“Brachistochrone”

“z”

x5

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William Horowitz

LHC RcAA(pT)/Rb

AA(pT) Prediction(with speed limits)

– T(0): (O), corrections unlikely for smaller momenta

– Tc: (|), corrections likely for higher momenta


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444/9/08

William Horowitz

Measurement at RHIC– Future detector upgrades will allow for

identified c and b quark measurements

y=0

RHIC

LHC

• • NOT slowly varying

– No longer expect pQCD dRAA/dpT > 0

• Large n requires corrections to naïve

Rcb ~ Mc/Mb

– RHIC production spectrum significantly harder than LHC

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RHIC c, b RAA pT Dependence

• Large increase in n(pT) overcomes reduction in E-loss and makes pQCD dRAA/dpT < 0, as well


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William Horowitz

RHIC Rcb Ratio

• Wider distribution of AdS/CFT curves due to large n: increased sensitivity to input parameters

• Advantage of RHIC: lower T => higher AdS speed limits


pQCD

AdS/CFT

pQCD

AdS/CFT

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474/9/08

William Horowitz

Conclusions• AdS/CFT Drag observables calculated• Generic differences (pQCD vs.

AdS/CFT Drag) seen in RAA

– Masked by extreme pQCD

• Enhancement from ratio of c to b RAA

– Discovery potential in Year 1 LHC Run

• Understanding regions of self-consistency crucial

• RHIC measurement possible

WWND 2008

484/9/08

William Horowitz

Backups

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494/9/08

William Horowitz

Geometry of a HI Collision

Medium density and jet production are wide, smooth distributions

Use of unrealistic geometries strongly bias results

M. Gyulassy and L. McLerran, Nucl.Phys.A750:30-63,2005

1D Hubble flow => () ~ 1/=> T() ~ 1/1/3

S. Wicks, WH, M. Djordjevic, M. Gyulassy, Nucl.Phys.A784:426-442,2007

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504/9/08

William Horowitz

Langevin Model– Langevin equations (assumes v ~ 1 to

neglect radiative effects):

– Relate drag coef. to diffusion coef.:– IIB Calculation:

• Use of Langevin requires relaxation time be large compared to the inverse temperature:

AdS/CFT here

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William Horowitz

But There’s a Catch (II)• Limited experimental pT reach?

– ATLAS and CMS do not seem to be limited in this way (claims of year 1 pT reach of ~100 GeV) but systematic studies have not yet been performed

ALICE Physics Performance Report, Vol. II

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LHC Predictions

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

• Our predictions show a significant increase in RAA as a function of pT

• This rise is robust over the range of predicted dNg/dy for the LHC that we used

• This should be compared to the flat in pT curves of AWS-based energy loss (next slide)

• We wish to understand the origin of this difference

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William HorowitzWH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

Asymptopia at the LHCAsymptotic pocket formulae:Erad/E 3 Log(E/2L)/EEel/E 2 Log((E T)1/2/mg)/E

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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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William Horowitz

Pion RAA

• Is it a good measurement for tomography?

– Yes: small experimental error

• Claim: we should not be so immediately dis-missive of the pion RAA as a tomographic tool

– Maybe not: some models appear “fragile”

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William Horowitz

Fragility: A Poor Descriptor

• All energy loss models with a formation time saturate at some Rmin

AA > 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?

– Define sensitivity, s = min. param/max. param that is consistent with data within error

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Different Models have Different Sensitivities to the Pion RAA

• GLV: s < 2

• Higher Twist:s < 2

• DGLV+El+Geom:s < 2

• AWS:s ~ 3 WH, S. Wicks, M. Gyulassy, M. Djordjevic, in

preparation

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T Renk and K Eskola, Phys. Rev. C 75, 054910 (2007)

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

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A Closer Look at ASW



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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William Horowitz

– Surface Emission: one phrase explanation of fragility• All models become surface emitting with infinite E

loss

– Surface Bias occurs in all energy loss models• Expansion + Realistic geometry => model probes a

large portion of medium

Surface Bias vs. Surface Emission

A. Majumder, HP2006 S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076

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William Horowitz

A Closer Look at ASW

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

contributions not disentangled

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


Zero th Order Heavy Quark Photon/Gluon Bremsstrahlung

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