Power Week pQCD+Energy LossIntroduction

Marco van Leeuwen,Utrecht University

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Hard probes of QCD matter

Use the strength of pQCD to explore QCD matter

Hard-scatterings produce ‘quasi-free’ partons Initial-state production known from pQCD Probe medium through energy loss

Heavy-ion collisions produce‘quasi-thermal’ QCD matter

Dominated by soft partons p ~ T ~ 100-300 MeV

Sensitive to medium density, transport properties

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Plan of the next few days

• Perturbative QCD tools:– PDFs, matrix elements, Fragmentation

• DGLAP evolution and Monte-Carlo showers• Geometry

– Woods-Saxon geometry, tools

• Energy loss models– Using Quenching weights; multiple gluon radiation

Goals: • Provide hands-on experience with all ingredients of a simple energy loss model• Increase understanding of the models, the assumptions and uncertainties• Provide a basic knowledge and experience that allows you to answer your own questions

Plus introduction to MC techniques

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Hard processes in QCD

• Hard process: scale Q >> QCD

• Hard scattering High-pT parton(photon) Q~pT

• Heavy flavour production m >> QCD

Cross section calculation can be split into • Hard part: perturbative matrix element• Soft part: parton density (PDF), fragmentation (FF)

Soft parts, PDF, FF are universal: independent of hard process

QM interference between hard and soft suppressed (by Q2/2 ‘Higher Twist’)

Factorization

c

chbbaa

abcdba

T

hpp

z

Dcdab

td

dQxfQxfdxdxK

pdyd

d

0

/222

)(ˆ

),(),( parton density matrix element FF

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Jet Quenching

1) How is does the medium modify parton fragmentation?• Energy-loss: reduced energy of leading hadron – enhancement of yield at

low pT?

• Broadening of shower?• Path-length dependence• Quark-gluon differences• Final stage of fragmentation

outside medium?

2) What does this tell us about the medium ?• Density• Nature of scattering centers? (elastic vs radiative; mass of scatt. centers)• Time-evolution?

High-energy

parton(from hard scattering)

Hadrons

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0 RAA – high-pT suppression

Hard partons lose energy in the hot matter

: no interactions

Hadrons: energy loss

RAA = 1

RAA < 1

0: RAA ≈ 0.2

: RAA = 1

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A simple model

)/()( , jethadrTjetshadrT

EpDEPdEdN

dpdN

`known’ from e+e-knownpQCDxPDF

extract

Parton spectrum Fragmentation (function)Energy loss distribution

This is where the information about the medium isP(E) combines geometry with the intrinsic process

– Unavoidable for many observables

Notes:• This formula is the simplest ansatz – Independent fragmentation

after E-loss assumed• Jet, -jet measurements ‘fix’ E, removing one of the convolutions

We will explore this model during the week; was ‘state of the art’ 3-5 years ago

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Two extreme scenarios

p+p

Au+Au

pT

1/N

bin

d2 N/d

2 pT

Scenario IP(E) = (E0)

‘Energy loss’

Shifts spectrum to left

Scenario IIP(E) = a (0) + b (E)

‘Absorption’

Downward shift

(or how P(E) says it all)

P(E) encodes the full energy loss process

RAA not sensitive to energy loss distribution, details of mechanism

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Energy loss distribution

BrickL = 2 fm, E/E = 0.2E = 10 GeV

Typical examples with fixed L

E/E> = 0.2 R8 ~ RAA = 0.2

Significant probability to lose no energy (P(0))

Broad distribution, large E-loss (several GeV, up to E/E = 1)

Theory expectation: mix of partial transmission+continuous energy loss– Can we see this in experiment?

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Geometry

Density profile

Profile at ~ form known

Density along parton path

Longitudinal expansion dilutes medium Important effect

Space-time evolution is taken into account in modeling

(Glauber geometry)

11

Some existing calculationsB

ass e

t al, P

RC

79

, 02

49

01

ASW:

HT:

AMY:

/fmGeV2010ˆ 2q

/fmGeV5.43.2ˆ 2q

/fmGeV4ˆ 2q

Large density:AMY: T ~ 400 MeVTransverse kick: qL ~ 10-20 GeV

All formalisms can match RAA, but large differences in medium density

At RHIC: E large compared to E, differential measurements difficult

After long discussions, it turns out that these differences are mostly due to uncontrolled approximations in the calculations Best guess: the truth is somewhere in-between

This week: looking behind the scenes for such calculations

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RAA at LHC

RAA at LHC: increase with pT first sign of sensitivity to P(E)

Nuclear modificationfactor ppTcoll

PbPbTAA dpdNN

dpdNR

/

/

By the way: RAA is also pT-dependent at RHIC?

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Comparing to theory

Many theory calculations available

Ingredients:- pQCD production- Medium density profile

tuned to RHIC data, scaled- Energy loss model

Large spread of predictions:• Will be narrowed down

by discussion/thought• Need to understand

models/calculations to sort it out

All calculations show increase with pT

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Path length dependence: RAA vs LPHENIX, PRC 76, 034904

In Plane

Out of Plane

3<pT<5 GeV/c

RAA as function of angle with reaction plane

Suppression depends on angle, path length

Relation between RAA() and v2:

)(2cos21 2 vRR AAAA

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Path length dependence and v2

PH

EN

IX P

RL

10

5, 1

42

30

1

v2 at high pT due to energy loss

Most calculations give too small effectPath length dependence stronger than expected?

Depends strongly on geometry – stay tuned

3ˆ LqE 2ˆ LqE

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Di hadron correlations

associated

trigger

8 < pTtrig < 15 GeV

pTassoc > 3 GeV

Use di-hadron correlations to probe the jet-structure in p+p, d+Au

Near side Away side

and Au+Au

Combinatorialbackground

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pT

assoc > 3 G

eVp

Tassoc >

6 GeV

d+Au Au+Au 20-40% Au+Au 0-5%

Suppression of away-side yield in Au+Au collisions: energy loss

High-pT hadron production in Au+Au dominated by (di-)jet fragmentation

Di-hadrons at high-pT: recoil suppression

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Di hadron yield suppression

Away-side: Suppressed by factor 4-5 large energy loss

Near side Away side

STAR PRL 95, 152301

8 < pT,trig < 15 GeV

Yield of additional particles in the jet

Yield in balancing jet, after energy loss

Near side: No modification Fragmentation outside medium?

Near sideassociated

trigger

Away side associated

trigger

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Path length II: ‘surface bias’

Near side trigger, biases to small E-loss

Away-side large L

Away-side suppression IAA samples longer path-lengths than inclusives RAA

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L scaling: elastic vs radiative

T. Renk, PRC76, 064905

RAA: input to fix density Radiative scenario fits data; elastic scenarios underestimate suppression

Indirect measure of path-length dependence: single hadrons and di-hadrons probe different path length distributions

Confirms L2 dependence radiative loss dominates

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Factorisation in perturbative QCD

c

chbbaa

abcdba

T

hpp

z

Dcdab

td

dQxfQxfdxdxK

pdyd

d

0

/222

)(ˆ

),(),(

Parton density functionNon-perturbative: distribution of partons in protonExtracted from fits to DIS (ep) data

Matrix elementPerturbative component

Fragmentation functionNon-perturbativeMeasured/extracted from e+e-

Factorisation: non-perturbative parts (long-distance physics) can be factored out in universal distributions (PDF, FF)

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PYTHIA (by Adam Kocoloski)

gg

qq

gq

Subprocesses and quark vs gluon

p+pbar dominantly from gluon fragmentation?

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PRL 97, 152301 (2006)STAR Preliminary, QM08

Curves: X-N. Wang et al PRC70(2004) 031901

Baryon & meson NMF

STAR Preliminary

Comparing quark and gluon suppression

Protons less suppressed than pions, not more

No sign of large gluon energy loss

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Quark vs gluon suppression

+ renk plot

WHDG

Renk and Eskola, PRC76,027901

GLV formalism BDMPS formalism

Quark/gluon difference larger in GLV than BDMPS(because of cut-off effects E < Ejet?)

~10% baryons from quarks, so baryon/meson effect smaller than gluon/quarkAre baryon fragmentation functions under control?

Conclusion for now: some homework to do... Day 1, 3 of this week

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Equalibration of rare probes

• Rare probes: not chemically equilibrated in the jet spectrum.• Example 1: flavor not contained in the medium, but can be produced

off the medium (e.g. photons)

– Need enough yield to outshine other sources of Nrare.

• Example 2: flavor chemically equilibrated in the medium

– E.g. strangeness at RHIC– Coupling of jets (flavor not equilibrated) to the equilibrated medium should

drive jets towards chemical equilibrium.

L

N

NN

dt

dN

jet

excess rare,jet

rare

1

gssg e.g. %50

for RHIC GeV 10 @ %5

mediumce

jetjet

du

sw

du

sw

dug ,,

dug ,, s

R. Fries, QM09

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Determining the initial energy

)/()( , jethadrTjetshadrT

EpDEPdEdN

dpdN

`known’ from e+e-knownpQCDxPDF

extract

Parton spectrum Fragmentation (function)Energy loss distribution

This is where the information about the medium isP(E) combines geometry with the intrinsic process

Jet, -jet measurements ‘fix’ E, removing one of the convolutions

Allows to study energy loss as function of E(at least in principle)

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Generic expectations from energy loss

• Longitudinal modification:– out-of-cone energy lost, suppression of yield, di-jet energy

imbalance– in-cone softening of fragmentation

• Transverse modification– out-of-cone increase acoplanarity kT

– in-cone broadening of jet-profile

kT~Ejet

fragmentation after energy loss?

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Fragmentation functions

Qualitatively: )()()( zDEPzD vacmed

Fragmentation functions sensitive to P(E)Distinguish GLV from BDMPS?

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Modified fragmentation functionsSmall-z enhancement from gluon fragments (only included in HT, not important for RAA)

Differences between formalisms large, both magnitude of supresion and z-dependence

Can we measure this directly? Jet reconstruction

A. M

ajum

der, M

vL, arXiv:100

2.2206

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Jet shapes

Energy distribution in sub-jets

Energy loss changes radial distribution of energy

Several ‘new’ observables considered Discussion: sensitivity viability … ongoing

q-P

ythia

, Eu

r Ph

ys J C 6

3, 6

79

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Fixing the parton energy with -jet eventsT. Renk, PRC74, 034906

-jet: know jet energy sensitive to P(E)

RAA insensitive to P(E)

Nuclear modification factor

Away-side spectra in -jet

E = 15 GeV

Away-side spectra for -jet are sensitive to P(E)

Input energy loss distribution

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IAA(zT) =DAA (zT)

Dpp (zT)

Direct- recoil suppression

Large suppression for away-side: factor 3-5

Reasonable agreement with model predictions

8 < ET, < 16 GeV

ST

AR

, arXiv:0912

.1871

NB: gamma pT = jet pT still not very large

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Jet reconstruction algorithms

Two categories of jet algorithms:

• Sequential recombination kT, anti-kT, Durham

– Define distance measure, e.g. dij = min(pTi,pTj)*Rij

– Cluster closest

• Cone– Draw Cone radius R around starting point

– Iterate until stable ,jet = <,>particles

For a complete discussion, see: http://www.lpthe.jussieu.fr/~salam/teaching/PhD-courses.html

Sum particles inside jet Different prescriptions exist, most natural: E-scheme, sum 4-vectors

Jet is an object defined by jet algorithmIf parameters are right, may approximate parton

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Jets at LHC

LHC: jet energies up to ~200 GeV in Pb+Pb from

1 ‘short’ run

Large energy asymmetry observed for central events

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Jets at LHCCentrality

12

12

EEEE

AJ

AT

LA

S, a

rXiv:1

01

1.6

18

2 (P

RL

)

Jet-energy asymmetry Large asymmetry seen for central events

N.B. only measures reconstructed di-jetsDoes not show ‘lost’ jets

Large effect on recoil: qualitatively consistent with RHIC jet IAA

Energy losses: tens of GeV, ~ expected from BDMPS, GLV etcbeyond kinematic reach at RHIC

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Jets at LHC

CM

S, arX

iv:1102.19

57

CMS sees similar asymmetries

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Jet RCP

R=0.2 R=0.4

RCP < 1: jet production suppressed, even at high pT

Out-of-cone radiation with R=0.4 significantNB: Jet-measurements are difficult: important experimental questions about

(trigger) bias and background fluctuations

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Jet imbalance calculationsQin, Muller, arXiv:1012.5280

Radiation plus evolution

Parton transport (brick)

Coleman-Smith, Qin, Bass, Muller, arXiv:1108.5662

MARTINI: AMY+MC

Young, S

chenke, Jeon, Gale, arX

iv:1103.5769

Several calculations describemeasured imbalance

Need to keep track of all fragments:Various approximations made

Most natural approach: parton showers(qPYTHIA, qHERWIG, JEWEL ?)

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Fragmentation and parton showers

large Q2 Q ~ mH ~ QCDF

Analytical calculations: Fragmentation Function D(z, ) z=ph/Ejet

Only longitudinal dynamics

High-energy

parton(from hard scattering)

Ha

dro

ns

MC event generatorsimplement ‘parton showers’

Longitudinal and transverse dynamics

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Getting ready

Software set-up:• ROOT• LHAPDF• Fragmentation function libraries• AliFastGlauber• AliQuenchingWeights

Day 1

See also http://www.staf.science.uu.nl/~leeuw179/powerweek/software

Day 2Day 3

Make sure that you have the code and that the test macros work

Questions/problems See me or Andreas

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Extra slides

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Seeing quarks and gluons

In high-energy collisions, observe traces of quarks, gluons (‘jets’)