Jet Quenching and Jet FindingMarco van Leeuwen, UU

2

Fragmentation and parton showers

large Q2 Q ~ mH ~ QCDF

Analytical calculations: Fragmentation Function D(z, ) z=ph/EjetOnly longitudinal dynamics

High-energy

parton(from hard scattering)

Hadrons

MC event generatorsimplement ‘parton showers’

Longitudinal and transverse dynamics

3

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

4

Medium-induced radition

If < f, multiple scatterings add coherently

2ˆ~ LqE Smed

22

Tf k

Zapp, QM09

Lc = f,max

propagating parton

radiatedgluon

Landau-Pomeranchuk-Migdal effectFormation time important

Radiation sees length ~f at once

Energy loss depends on density: 1

2

ˆq

q

and nature of scattering centers(scattering cross section)

Transport coefficient

5

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

6

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

7

Two extreme scenarios

p+p

Au+Au

pT

1/N

bin d

2 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

8

Jet reconstructionSingle, di-hadrons: focus on a few fragments of the shower No information about initial parton energy in each event

Jet finding: sum up fragments in a ‘jet cone’Main idea: recover radiated energy – determine energy of initial partonFeasibility depends on background fluctuations, angular broadening of jets

Need: tracking or Hadron Calorimeter and EMCal (0)

9

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?

10

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

11

Collinear and infrared safetyIllustration by G

. Salam

Jets should not be sensitive to soft effects (hadronisation and E-loss)

- Collinear safe- Infrared safe

12

Collinear safety

Note also: detector effects, such as splitting clusters in calorimeter (0 decay)

Illustration by G. S

alam

13

Infrared safety

Infrared safety also implies robustness against soft background in heavy ion collisions

Illustration by G. S

alam

14

Clustering algorithms – kT algorithm

15

kT algorithm

• Calculate – For every particle i: distance to beam– For every pair i,j : distance

• Find minimal d– If diB, i is a jet

– If dij, combine i and j

• Repeat until only jets

Various distance measures have been used, e.g. Jade, Durham, Cambridge/Aachen

Current standard choice:

2,itiB pd

2

22,

2, ),min(

RR

ppd ijjtitij

16

kT algorithm demo

17

kT algorithm properties• Everything ends up in jets• kT-jets irregular shape

– Measure area with ‘ghost particles’• kT-algo starts with soft stuff

– ‘background’ clusters first, affects jet• Infrared and collinear safe• Naïve implementation slow (N3). Not necessary

Fastjet

Alternative: anti-kT 2,

1

itiB pd

2

2

2,

2,

1,1minRR

ppd ij

jtitij

2

2

RR

d ijij Cambridge-Aachen:

18

Cone algorithm

• Jets defined as cone• Iterate until stable:

(,)Cone = <,>particles in cone

• Starting points for cones, seeds, e.g. highest pT particles

• Split-merge prescription for overlapping cones

19

Cone algorithm demo

20

Seedless cone

Limiting cases occur when two particles are on the edge of the cone

1D: slide cone over particles and search for stable coneKey observation: content of cone only changes when the cone boundary touches a particle

Extension to 2D (,)

21

IR safety is subtle, but important

G. S

alam, arX

iv:0906.1833

22

Split-merge procedure

• Overlapping cones unavoidable• Solution: split-merge procedure

Evaluate Pt1, Pt,shared

– If Pt,shared/Pt1> f merge jets

– Else split jets (e.g. assign Pt,shared to closest jet or split Pt,shared according to Pt1/Pt2)

Jet1 Jet2

Merge: Pt,shared large fraction of Pt1

Jet1 Jet2

Split: Pt,shared small fraction of Pt1

f = 0.5 … 0.75

23

Note on recombination schemes

ET-weighted averaging:Simple

Not boost-invariant for massive particles

Most unambiguous scheme: E-scheme, add 4-vectors

Boost-invariantNeeds particle masses (e.g. assign pion mass)Generates massive jets

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Current best jet algorithms

• Only three good choices:– kT algorithm (sequential recombination, non-circular jets)

– Anti-kT algoritm (sequential recombination, circular jets)– SISCone algorithm (Infrared Safe Cone)

+ some minor variations: Durham algo, differentcombination schemes

These are all available in the FastJet package:http://www.lpthe.jussieu.fr/~salam/fastjet/

Really no excuse to use anything else (and potentially run into trouble)

25

Speed matters

At LHC, multiplicities are largeA lot has been gained from improving implementations

G. S

alam, arX

iv:0906.1833

26

Jet algorithm examplesC

acciari, Salam

, Soyez, arX

iv:0802.1189simulated p+p event

27

Jet reco

p+p 200 GeV, pTrec ~ 21 GeV

p+p: no or little background

Cu+Cu: some background

STAR

PHENIX

28

Jet finding in heavy ion events

η

p t p

er g

rid c

ell [

GeV

]

STAR preliminary~ 21 GeV

FastJet:Cacciari, Salam and Soyez; arXiv: 0802.1188http://rhig.physics.yale.edu/~putschke/Ahijf/A_Heavy_Ion_Jet-Finder.html

Jets clearly visible in heavy ion events at RHIC

Use different algorithms to estimate systematic uncertainties:• Cone-type algorithms

simple cone, iterative cone, infrared safe SISCone

• Sequential recombination algorithmskT, Cambridge, inverse kT

Combinatorial backgroundNeeds to be subtracted

29

Jet finding with background

By definition: all particles end up in a jetWith background: all - space filled with jets

Many of these jets are ‘background jets’

30

Background estimate from jets

M. Cacciari, arXiv:0706.2728

Single event: pT vs area = pT/area

Jet pT grows with area Jet energy density ~ independent of

Backgroundlevel

31

Example of pT distribution

Response over ~5 orders of magnitude

Response over range of ~40 GeV (sharply falling jet spectrum)

SIngle particle ‘jet’pT=20 GeVembedded in 8M real events

Gaussian fit to LHS:• LHS: good representation• RHS: non-Gaussian tail

• Centroid non-zero(~ ±1 GeV) contribution to jet energy scale uncertainty

32

Unfolding background fluctuations

unfolding

Pythia

Pythia smeared

Pythia unfolded

Simulation

PT distribution: ‘smearing’ of jet spectrumdue to background fluctuations

Large effect on yieldsNeed to unfold

Test unfolding with simulation – works

33

RAA at LHC

ALICE, H. Appelshauser, QM11

34

RAA at LHC

• pronounced pT dependence of RAA at LHC

sensitivity to details of the energy loss distribution

35

Jets at LHC

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

1 ‘short’ run

Large energy asymmetry observed for central events

36

Jet RCP at LHC

Significant suppression of reconstructed jets in AAOut to large pT~250 GeV

No indication of rise vs pT like single hadrons

Significant out-of-cone radiation

ATLAS, B, Cole, QM11

37

Jet fragmentation

38

Di-jet (im)balance

CMS, arXiv:1102.1957

12

12

EEEEAJ

Jet-energy asymmetry Large asymmetry seen for central events

ATLA

S, arX

iv:1011.6182 (PR

L), QM

update

39

Di-jet (im)balance

CMS, arXiv:1102.1957

40

Di-Jet fragmentation

41

Summary

42

Extra slides

43

Four theory approaches

• Multiple-soft scattering (ASW-BDMPS)– Full interference (vacuum-medium + LPM)– Approximate scattering potential

• Opacity expansion (GLV/WHDG)– Interference terms order-by-order (first order default)– Dipole scattering potential 1/q4

• Higher Twist– Like GLV, but with fragmentation function evolution

• Hard Thermal Loop (AMY)– Most realistic medium– LPM interference fully treated– No finite-length effects (no L2 dependence)

44

Energy loss spectrum

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?

45

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

46

Determining B

ass et al, PR

C79, 024901

q̂

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

47