Lecture IV: Jet finding techniques and results

Marco van LeeuwenUtrecht University

Jyväskylä Summer School 2008

2

Parton energy from -jet and jet reconstruction

Qualitatively:

)/()( , jethadrTjetshadrT

EpDEPdEdN

dpdN

`known’ from e+e-knownpQCDxPDF

extract

Full deconvolution large uncertainties (+ not transparent)

Fix/measure Ejet to take one factor out

Two approaches: -jet- Jet reconstruction

Second-generation measurements at RHIC – first generation at LHC?

3

Perturbative QCD processes

• Hadron production• Heavy flavours• Jet production

– e+e- → jets – p(bar)+p → jets

• Direct photon production

Measurem

ent difficulty

The

ory

diff

icul

ty

4

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

5

-jet in Au+Au

Use shower shape in EMCal to form 0 sample and -rich sample

Combinatorial subtraction to obtain direct- sample

6

STAR Preliminary

IAA(zT) =DAA (zT)

Dpp (zT)

Direct- recoil suppression

Large suppression for away-side: factor 3-5

Results agree with model predictions

Uncertainties still sizable Some improvements expected for final resultsFuture improvements with increased RHIC luminosity

J. Frantz, H

ard Probes 2008

A. H

amed, H

ard Probes 2008

8 < ET, < 16 GeV

ET,

2 < pTassoc < 10 GeV

7

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

8

Collinear and infrared safetyIllustration by G

. Salam

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

- Collinear safe- Infrared safe

9

Collinear safety

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

Illustration by G. S

alam

10

Infrared safety

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

Illustration by G. S

alam

11

Clustering algorithms – kT algorithm

12

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(

R

Rppd ij

jtitij

13

kT algorithm demo

14

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,

1min

R

R

ppd ij

jtitij

15

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

16

Cone algorithm demo

17

IR safety is subtle, but important

G. S

alam, arX

iv:0906.1833

18

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 (,)

19

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: Ptshared large fraction of Pt1

Jet1 Jet2

Split: Ptshared small fraction of Pt1

f = 0.5 … 0.75

20

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

21

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)

22

Speed matters

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

G. S

alam, arX

iv:0906.1833

23

Relating jets and single hadrons

High-pT hadrons from jet fragmentation

Qualitatively: )/( ,, jetThadrT

jetsThadrT

ppDdpdN

dpdN

Single hadrons are suppressed:

- Suppression of jet yield (out-of-cone radiation) RAAjets < 1

- Modification of fragment distribution (in-cone radiation) softening of fragmentation function and/or broadening of jet structure

24

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

25

p+p Au+Au central

STAR Preliminary

Jet spectra

STAR Preliminary

Note kinematic reach out to 50 GeV

• Jet energy depends on R, affects spectra• kT, anti-kT give similar results

Take ratios to compare p+p, Au+Au

26

Jet RAA at RHIC

Jet RAA >> 0.2 (hadron RAA)

Jet finding recovers most of the energy loss measure of initial parton energy

M. P

loskon, ST

AR

, QM

09

Some dependence on jet-algorithm? Under study…

27

Radius dependence

RAA depends on jet radius:Small R jet is single hadron

M. P

loskon, ST

AR

, QM

09

Jet broadening due to E-loss?

28

Fragmentation functions

STAR Preliminary

pt,rec(AuAu)>25 GeV20<pt,rec(AuAu)<25 GeV

Use recoil jet to avoid biases

Suppression of fragmentation also small (>> 0.2)

E. B

runa, ST

AR

, QM

09

29

Di-jet spectra

29

Ele

na B

run

a fo

r the S

TA

R C

olla

bora

tion

- Q

M0

9STAR PreliminarySTAR Preliminary

E. B

runa, ST

AR

, QM

09

Jet IAA

Away-side jet yield suppressed partons absorbed

... due to large path lentgh(trigger bias)

30

Emerging picture from jet results

• Jet RAA ~ 1 for sufficiently large R – unbiased parton selection

• Away side jet fragmentation ummodified – away-side jet emerges without E-loss

• Jet IAA ~ 0.2 – Many jets are absorded (large E-loss)

Study vs R, E to quantify P(E) and broadening

31

Modeling in-medium fragmentation

From C. Salgado

32

Sudakov prescription

From C. Salgado

33

Sudakov prescription

From C. Salgado

34

Sudakov MC implementation

Used by most MC event generators (PYTHIA, HERWIG)

From C. Salgado

35

Full MC event

From C. Salgado

36

MC resultsQ-PYTHIA

N. A

rme

sto e

t al, a

rXiv:0

90

7.1

01

4

Softening of fragmentation(pT-spectra)

Broadening

Caveat: all plot are parton-level. Effect of hadronisation may be large

37

Summary

• Jet-finding, -jet to fix parton energy Sensitivity to P(E), jet broadening

• -hadron results agree with predictionNeed more statistics for P(E)

• Jet-algorithm requirements: Infrared and Collinear safe

• Jet results from RHIC:– Can recover full parton energy (R=0.4)– Indicate large broadening

– Away-side jet IAA ~ 0.2, jet absorption?

• Full event MC genartors are being developed important reference/benchmark for jet-analyses

38

Extra slides

39

Direct- recoil yields

A. H

amed, H

ard Probes 2008

Run 4 p+p/Au+Au @ 200 GeV

M. N

guyen, Quark M

atter 2006

Direct-–jet measurements being pursued by STAR and PHENIXRequires large data samples

Suppression of away-side yield visible

Similar to di-hadrons, but now with selected parton energy