Hard probes of the Quark Gluon Plasma

Part 1: Introduction, RAA

Marco van Leeuwen, Nikhef & Utrecht University

Lectures at: Quark Gluon Plasma and Heavy Ion Collisions

Siena, 8-13 July 2013

2

Particle Data Group topical reviewshttp://pdg.lbl.gov/2004/reviews/contents_sports.html

QCD and jets: CTEQ web page and summer school lectures http://www.phys.psu.edu/~cteq/

Handbook of Perturbative QCD, Rev. Mod. Phys. 67, 157–248 (1995)http://www.phys.psu.edu/~cteq/handbook/v1.1/handbook.ps.gz

QCD and Collider Physics, R. K. Ellis, W. J. Sterling, D.R. Webber, Cambridge University Press (1996)

An Introduction to Quantum Field Theory, M. Peskin and D. Schroeder, Addison Wesley (1995)

Introduction to High Energy Physics, D. E. Perkins, Cambridge University Press, Fourth Edition (2000)

General QCD references

3

Heavy Ion references

RHIC overviews:P. Jacobs and X. N. Wang, Prog. Part. Nucl. Phys. 54, 443 (2005)B. Mueller and J. Nagle, Ann. Rev. Nucl. Part. Sci. 56, 93 (2006)

Jet quenching reviews:M. Spousta, arXiv:1305.6400

J. Caselderrey-Solana and C. Salgado, arXiv:0712.3443U. Wiedemann, arXiv:0908.2306A. Majumder and M. v. L. arXiv:1002.2206Accardi, Arleo et al, arXiv:0907.3534

RHIC experimental white papersBRAHMS: nucl-ex/0410020PHENIX: nucl-ex/0410003PHOBOS: nucl-ex/0410022STAR: nucl-ex/0501009

LHC Yellow Reports

4

Soft QCD matter and hard probes

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

Heavy-ion collisions produceQCD matter

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

‘Hard Probes’: sensitive to medium density, transport properties

5

Part I: Hard processes in fundamental collisions

6

Accelerators and colliders

• p+p colliders (fixed target+ISR, SPPS, TevaTron, LHC)– Low-density QCD

– Broad set of production mechanisms

• Electron-positron colliders (SLC, LEP)– Electroweak physics

– Clean, exclusive processes

– Measure fragmentation functions

• ep, p accelerators (SLC, SPS, HERA)– Deeply Inelastic Scattering, proton structure

– Parton density functions

• Heavy ion accelerators/colliders (AGS, SPS, RHIC, LHC)– Bulk QCD and Quark Gluon Plasma

Many decisive QCD measurements done

7

Seeing quarks and gluons

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

8

Singularities in pQCD

Closely related to hadronisation effects

(massless case)

Soft divergence Collinear divergence

9

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

10

The first and only ep collider in the world

e± p

27.5 GeV 920 GeV

√s = 318 GeV

Equivalent to fixed target experiment with 50 TeV e±

Loca

ted

in

Ham

bu

rg

H1

Zeus

The HERA Collider

11

XpeXepe ee )( :CC , :NC

NC:

CC:

DIS: Measured electron/jet momentum fixes kinematics: x, Q2

Example DIS events

12

Proton structure F2

Q2: virtuality of the x = Q2 / 2 p q‘momentum fraction of the struck quark’

F2: essentially a cross section/scattering probability

13

Factorisation in DIS

Integral over x is DGLAP evolution with splitting kernel Pqq

14

Parton density distributionLow Q2: valence structure

Valence quarks (p = uud)x ~ 1/3

Soft gluons

Q2 evolution (gluons)

Gluon content of proton risesquickly with Q2

15

p+p dijet at Tevatron

Tevatron: p + p at √s = 1.9 TeV

Jets produced with several 100 GeV

16

Testing QCD at high energy

small x

large x

x = partonic momentum fraction

Dominant ‘theory’ uncertainty: PDFs

Theory matches data over many orders of magnitude

Universality: PDFs from DIS used to calculate jet-production

Note: can ignore fragmentation effects in jet production

CDF, PRD75, 092006

DIS to measure PDFs

17

pQCD illustrated

c

chbbaa

abcdba

T

hpp

z

Dcdab

td

dQxfQxfdxdxK

pdyd

d

0

/222

)(ˆ

),(),(

CDF, PRD75, 092006

jet spectrum ~ parton spectrum

nTTT ppdp

dN

ˆ

1

ˆˆ

jet

hadronT

P

pz ,

fragmentation

18

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

19

Part II: Nuclear Modification Factor RAA

20

RHIC and LHC

STARSTAR

RHIC, Brookhaven

LHC, GenevaAu+Au sNN= 200 GeV Pb+Pb sNN= 2760 GeV

First run: 2000 First run: 2009/2010

21

Nuclear geometry: Npart, Ncoll

b

Two limiting possibilities:- Each nucleon only interacts once, ‘wounded nucleons’

Npart = nA + nB (ex: 4 + 5 = 9 + …)

Relevant for soft production; long timescales: Npart

- Nucleons interact with all nucleons they encounterNcoll = nA x nB (ex: 4 x 5 = 20 + …)

Relevant for hard processes; short timescales: Nbin

Transverse view

Eccentricity

Density profile : part or coll

22

22

xy

xy

x

y

L

22

Centrality dependence of hard processes

d/dNch

200 GeV Au+Au

Rule of thumb for A+A collisions (A>40) 40% of the hard cross section

is contained in the 10% most central collisions

Binary collisions weight towards small impact parameter

Total multiplicity: soft processes

23

Testing volume (Ncoll) scaling in Au+Au

PHENIX

Direct spectra

Scaled by Ncoll

PHENIX, PRL 94, 232301

ppTcoll

AuAuTAA dpdNN

dpdNR

/

/

Direct in A+A scales with Ncoll

Centrality

A+A initial state is incoherent superposition of p+p for hard probes

24

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

25

Nuclear modification factor

ppTcoll

PbPbTAA dpdNN

dpdNR

/

/

Suppression factor 2-6Significant pT-dependenceSimilar at RHIC and LHC?

So what does it mean?

26

Nuclear modification factor RAA

p+p

Au+Au

pT

1/N

bin

d2 N/d

2 pT

‘Energy loss’

Shifts spectrum to left

‘Absorption’

Downward shift

Measured RAA is a ratio of yields at a given pT

The physical mechanism is energy loss; shift of yield to lower pT

ppTcoll

PbPbTAA dpdNN

dpdNR

/

/

27

Getting a sense for the numbers – RHIC

Oversimplified calculation:- Fit pp with power law- Apply energy shift or relative E lossNot even a model !

Ball-park numbers: E/E ≈ 0.2, or E ≈ 3 GeV for central collisions at RHIC

0 spectra Nuclear modification factor

PH

EN

IX, P

RD

76, 051106, arXiv:0801.4020

28

From RHIC to LHCRHIC: 200 GeVLHC: 2.76 TeV

per nucleon pair

Energy ~24 x higher

LHC: spectrum less steep, larger pT reach

nT

TT

pdpdN

p

21

RHIC: n ~ 8.2LHC: n ~ 6.4

Fractional energy loss:2

1

n

AA EE

R

RAA depends on n, steeper spectra, smaller RAA

29

From RHIC to LHC

RHIC LHC

RHIC: n ~ 8.2 LHC: n ~ 6.4

20.023.01 2.6 32.023.01 4.4

Remember: still ‘getting a sense for the numbers’; this is not a model!

30

Towards a more complete picture

• Energy loss not single-valued, but a distribution

• Geometry: density profile; path length distribution

• Energy loss is partonic, not hadronic– Full modeling: medium modified shower– Simple ansatz for leading hadrons: energy loss

followed by fragmentation– Quark/gluon differences

31

Medium-induced radiation

),(ˆ~ EmFLqCE nRSmed

propagating

parton

radiatedgluon

Landau-Pomeranchuk-Migdal effectFormation time important

Radiation sees length ~f at once

Energy loss depends on density: 1

2

ˆ

qq

and nature of scattering centers(scattering cross section)

Transport coefficient

CR: color factor (q, g) : medium densityL: path lengthm: parton mass (dead cone eff)E: parton energy

q̂

2

2

Tf k

Path-length dependence Ln

n=1: elasticn=2: radiative (LPM regime)n=3: AdS/CFT (strongly coupled)

Energy loss

32

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-MS)– Static scattering centers– Gaussian approximation for momentum kicks– Full LPM interference and vacuum radiation

• Opacity expansion ((D)GLV, ASW-SH)– 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

See also: arXiv:1106.1106

33

Large angle radiationEmitted gluon distribution

Opacity expansion

kT < k

Calculated gluon spectrum extends to large k at small kOutside kinematic limits

GLV, ASW, HT cut this off ‘by hand’

Gluon momentum k (GeV)G

luo

n p

erp

mo

men

tum

k (

GeV

)

34

Effect of large angle radiation

Ex

E

xE

Different large angle cut-offs:kT < = xE EkT < = 2 x+ E

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

Single-gluon spectrum

Different definitions of x:

ASW: GLV:

Factor ~2 uncertainty from large-angle cut-off

Ho

row

itz an

d C

ole

, PR

C8

1, 0

24

90

9

Opacity expansion formalisms

Expand in powers ofL

35

Energy loss distributions

Radiated gluon distribution

Main theory uncertainty:Large angle radiation

Multiple gluon emission:Poisson Ansatz

Energy loss probability distribution

Broad distributionSignificant contributions at E=0, E=E

36

Energy loss formalisms

Plenty of room for interesting and relevant theory work!

• Large differences between formalisms understood– Large angle cut-off

– Length dependence (interference effects)

• Mostly ‘technical’ issues; can be overcome– Use path-integral formalism

– Monte Carlo: exact E, p conservation• Full 2→3 NLO matrix elements• Include interference

• Next step: interference in multiple gluon emission

37

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

38

)/()( , 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 is the simplest ansatz – most calculation to date use it (except

some MCs)• Jet, -jet measurements ‘fix’ E, removing one of the convolutions –

more in Lecture 2 and 3

A simplified approach

39

RAA at RHIC: ‘calibrating’ the modelsB

ass e

t al, P

RC

79

, 02

49

01ASW:

HT:

AMY:

/fmGeV2010ˆ 2q

/fmGeV5.43.2ˆ 2q

/fmGeV4ˆ 2q

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

Large uncertainty in absolute medium density

PH

EN

IX, a

rXiv:1

20

8.2

25

4

All calculations describe the dataNot very sensitive to

energy loss distribution

40

RAA at LHC & models

ALICE: arXiv:1208.2711CMS: arXiv:1202.2554

Broad agreement between models and

LHC RAA

Extrapolation from RHIC

tends to give too much suppression at LHC

Many model curves: need more constraints and/or selection of models

41

RAA at LHC and JEWEL

Suppression factor 2-6Significant pT-dependence

JEWEL energy loss model agrees with measurements(tuned at RHIC, LHC ‘parameter-free’)

JEWEL: Monte Carlo event generator with radiative+collisional energy loss- Modified showers with MC-LPM implementation- Geometry: expanding Woods-Saxon density

42

Identified hadron RAA

M. Ivanov, A. Ortiz@QM2012

Low-intermediate pT (1-6 GeV):Large baryon/meson ratio

Probably due to:1) radial flow2) parton recombination

M. Ivanov, A. Ortiz@QM2012

Baryon, meson RAA similar at pT > 8 GeV

As expected from parton energy loss

43

Identified hadron RAA (strangeness)

Kaon, pion RAA

similar

: RAA~1 at pT~3 GeV/cSmaller suppression,/K enhanced at low pT

pT ~8 GeV/c:All hadrons similar

partonic energy loss + pp-like fragmentation?

44

Summary

• QCD calculations: factorisation of perturbative and universal non-perturbative components (PDFs, FFs)– Except e+e-: no PDF needed

• Heavy ion collisions: jet quenching– First observable: RAA

– Qualitatively: large effect, several GeV lost or E/E ~ 0.2

– Detailed modeling: • Some ‘intrinsic’ uncertainties• In progress – more in next lectures

45

Effects in RAA

• Parton pT spectra– Less steep at LHC less suppression

– Steepness decreases with pT: RAA rises

• Quark vs gluon jets– More gluon jets at LHC more suppression

– More quark jets at high pT: RAA rises

• Medium density (profile)– Larger density at LHC more suppression

(profile similar?)

– Path length dependence of energy loss

• Parton energy dependence– Expect slow (log) increase of E with E RAA rises with pT

– Running of S (A Buzzatti@QM2012) ?

• Energy loss distribution– Expect broad distribution P(E); kinematic bounds important

‘Known’, external

input

Energy loss theory

Determine/constrain from measurements

Use different observables to disentangle effects contributions

46

Extra slides

47

Intermezzo: Centrality

Central collisionPeripheral collision

top view:

front view:

b~0 fm

b

b finite

Nuclei are large compared to the range of strong force

Size of reaction zone, density depends on centrality:No QGP effects in peripheral collisions

48

Centrality continuedcentralperipheral

Multiplicity distribution

Experimental measure of centrality: multiplicity

49

Note: difference p+p, e++e-

p+p: steeply falling jet spectrumHadron spectrum convolution of jet spectrum with fragmentation

e+ + e- QCD events: jetshave p=1/2 √sDirectly measure frag function

50

Multiple soft scattering: BDMPS, AMY

Using based on AMY-HTL scattering potential

L=2 fm Single gluon spectra L=5 fm Single gluon spectra

AMY: no large angle cut-off

)(ˆ Tq

+ sizeable difference at large at L=2 fm

51

L-dependence; regions of validity?Emission rate vs (=L)

Caron-Huot, Gale, arXiv:1006.2379

AMY, small L,no L2, boundary effect

Full = numerical solution of

Zakharov path integral = ‘best we know’

GLV N=1Too much radiation at large L(no interference between scatt centers)

H.O = ASW/BDMPS like (harmonic oscillator)Too little radiation at small L

(ignores ‘hard tail’ of scatt potential)

E = 16 GeVk = 3 GeVT = 200 MeV

52

So what are we trying to do...

• First: understand (parton) energy process– Magnitude, dominant mechanism(s)– Probability distribution

• Lost energy• Radiated gluons/fragments

– Path length dependence– Flavour/mass dependence– Large angle radiation?

• Future: use this to learn about the medium

53

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

54

RAA at RHIC and LHCP

HE

NIX

: arXiv:1208.2254

RA

A

LHC RAA < RHIC

Larger suppression+ spectrum less steep:larger density

Increase of RAA with pT similar at RHIC and LHCIncrease of RAA with pT:Decrease of relative energy loss ΔE/E with pT

and/or decrease of power law index with pT (e.g. change from gluon to quark)

55

Jets in pp at √s=2.76 TeV

R. Ma@HPCharged tracks+EMCAL, R=0.4

EMCAL installed in Dec 2010: ||<0.8, ~/3

R=0.2/R=0.4

Reasonable agreement with NLO calculationsNeed to include hadronisation for jet shapes

56

Singularities in phase space

57

Mechanisms for modified jet chemistry

Expect large baryon/meson ratio associated with high-pT trigger

(Hwa, Yang)

Baryon pT=3pT,parton

MesonpT=2pT,parton

Hard parton

Hot matter

‘Shower-thermal’ recombination

Sapeta, Wiedemann, arXiv:0707.3494Milhano et al

In-medium color flow/reconnection