Status of the TECHQM‘brick problem’

Marco van Leeuwen,Utrecht University

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TECHQM

• Forum to discuss comparison between theory and experiment in areas where there is a potential significant quantitative understanding

• Two subgroups:– Parton energy loss

– Elliptic flow/Hydro• Workshops/meetings:

– BNL May 2008

– LBL Dec 2008

– CERN July 2009

– BNL (with CATHIE) Dec 2009

https://wiki.bnl.gov/TECHQM/index.php/Main_Page

Theory-Experiment Collaboration on Hot Quark Matter

This talk is about Parton Energy loss

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Energy loss formalisms I

PHENIX, arXiv:0801.1665,J. Nagle WWND08

PQM <q> = 13.2 GeV2/fm +2.1- 3.2

^

WHDG dNg/dy = 1400 +200- 375

ZOWW 0 = 1.9 GeV/fm +0.2- 0.5

AMY s = 0.280 +0.016- 0.012

GLV, AMY: T = 300-400 MeV BDMPS: T ~ 1000 MeV

Large difference in medium density:

Different calculations use different geometries – not clear what dominates

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Energy loss formalisms IIB

ass e

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RC

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49

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ASW:

HT:

AMY:

/fmGeV2010ˆ 2q

/fmGeV5.43.2ˆ 2q

/fmGeV4ˆ 2q

AMY: T ~ 400 MeV

Compare 3 formalisms with `same’ Hydro geometry:

Different formalisms give different energy loss at given density, path length

Why:Different physics implemented? Or `technical’ differences?What are the main uncertainties?

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The Brick Problem

Gluon(s)

Plot: outgoing gluon, quark distributions

Two types of comparison: - Same density- Same suppression

Compare energy-loss in a well-defined model system:Fixed-length L (2, 5 fm)Density T, qQuark, E = 10, 20 GeV

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Four formalisms

• Hard Thermal Loops (AMY)– Dynamical (HTL) medium– Single gluon spectrum: BDMPS-Z like path integral– No vacuum radiation

• Multiple soft scattering (BDMPS-Z, ASW)– Static scattering centers– Gaussian approximation for momentum kicks– Full LPM interference and vacuum radiation

• Opacity expansion ((D)GLV, ASW-OE)– Static scattering centers, Yukawa potential – Expansion in opacity L/

(N=1, interference between two centers default)– Interference with vacuum radiation

• Higher Twist (Guo, Wang, Majumder)– Medium characterised by higher twist matrix elements– Radiation kernel similar to GLV– Vacuum radiation in DGLAP evolution

Multiple gluon emission

Fokker-Planckrate equations

Poisson ansatz(independent emission)

DGLAPevolution

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1

0

1 )()1( PdR nn

spectrum 1

for nT

AAn pRR

Large differences in medium densityfor R7 = 0.25

Some brick resultsOutgoing quark spectrum

T=300 MeV

RAA > P0

Difference between formalisms sizable even in simple geometry

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Limitations of soft collinear approach

Soft: Collinear:

Need to extend results to full phase space to calculate observables(especially at RHIC)

Soft approximation not problematic:For large E, most radiation is softAlso: > E full absorption

Cannot enforce collinear limit:Small , kT always a part of phase space with large angles

E TkCalculations are done in soft collinear approximation:

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Opacity expansions GLV and ASW-SH

Expressions dN/dxdk ASW-OE and GLV are the same

Ex

E

xE

However, GLV use x = x+, while ASW use x=xE

x+ ~ xE in soft collinear limit, but not at large anglesDifferent large angle cut-offs:

kT < = xEEkT < = 2x+E

Blue: kTmax = xERed: kTmax = 2x(1-x)E

Blue: mg = 0Red: mg = /√2

Ho

row

itz an

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ole

, PR

C8

1, 0

24

90

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Single-gluon spectrum Single-gluon spectrum

Different definitions of x:

ASW: GLV:

Factor ~2 uncertainty from large-angle cut-off

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Opacity expansion vs multiple soft

Salgado, Wiedemann, PRD68, 014008

Different limits:SH (N=1 OE): interference betweenneighboring scattering centersMS: ‘all orders in opacity’, gaussianscattering approximation

Quantitative differences sizable

OE and MS related via path integral formalism

So far, not clear which difference dominates.

Would like: OE with gaussian and/or all orders (Wicks)

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AMY and BDMPS

Single-gluon kernel from AMY based on scattering rate:

BMPS-Z use harmonic oscillator:

BDMPS-Z:

Salgado, Wiedemann, PRD68, 014008

Finite-L effects:Vacuum-medium interference+ large-angle cut-off

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AMY and BDMPS

Large difference between AMY and ASW at L=2 fm?

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HT and GLV

Single-gluon kernel GLV and HT ‘similar’

L = 5 fm, T = 300 MeV

HT: < L kT > √(E/L) kernel diverges for kT 0

GLV:

TExxkT 3)1(2max, HT:

ExxkT )1(2max, TEqT 3max,

222

2

2

1)(

T

qgFs

T kxP

CdkdxdN

42

1)(

Tggqg

Fs

T kFxP

CdkdxdN

L

T

zzpk

d0

2

)1(2cos1

HT:

OE:

Large uncertainty from kTmax

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Single gluon spectraSame temperature Same suppression

(Not complete)

@Same suppression:OE (AMY?) peaked at low ASW-MS not so much

@Same temperature:AMY > OE > ASW-MS

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Outgoing quark spectraSame temperature Same suppression

ASW-MS less suppression than OE at T=300 MeV

At R7 = 0.25P0 small for ASW-MS

P0 = 0 for AMY by definition

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L=2 fm, T=250, 350 MeVGLV, HT, ASW-MS similar

AMY: large suppression

L=2 fm, T=250, 350 MeVAMY, HT larger suppression

than OE, MS

Fragmentation functionM

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Conclusion

• Tentative summary:– AMY shows strongest suppression

Lack of vacuum radiation?

– ASW-MS: smallest suppressionSoft scattering or interference or both?

– OE, HT similar, between MS and AMY

• Large uncertainties associated with large angle radiation in all formalisms

• Differences between formalisms large at single-gluon levelRAA probably not sensitive to details of multi-gluon treatment

Thanks to all in TECHQM who contributed !

In preparation: TECHQM publication with more detailed report

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Extra slides

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X+ vs xE