Standard Candles: Jets

QCD at the LHCECT* - Trento - September 2010

Standard Candles: Jets

Matteo CacciariLPTHE - Paris 6,7 and CNRS

Matteo Cacciari - LPTHE QCD at the LHC - ECT* - September 2010

Taming reality

2

QCD predictions

W candidate (ATLAS)

Real data

??

Jets

One purpose of a ‘jet clustering’ algorithm is toreduce the complexity of the final state, simplifying many hadrons

to simpler objects that one can hope to calculate

Multileg + PS


Standard candles

3

Jets as observables


Snowmass

4

Speed

Snowmass set standards, but didn’t provide solutions

Infrared and collinear safety

[Addition of a soft particle or a collinear splitting should not

change final hard jets]


Cone algorithms

5

Finding all stable cones (and hence produce an infrared and collinear (IRC) safe cone algorithm)

would naively take N2N operations

This is roughly the age of the universe for just 100 particles

Resort to approximate methods:use seeds

Too slow

➥leads to unsafe algorithms


Recombination algorithms

6

‣ Calculate the distances between the particles:

‣ Calculate the beam distances:

‣ Combine particles with smallest distance or, if diB is smallest, call it a jet

‣ Find again smallest distance and repeat procedure until no particles are left

This is infrared and collinear safe, but finding all the distances is an N2 operation, to be repeated N times

⇒ naively, recombination algorithms scale like N3

Faster than the cone, but still too slow:about 60 seconds for 4000 particles

di j =min(k2pti ,k2pt j )Δy2+Δφ2

R2diB = k2pti

(original prototype: kt algorithm, with p=1)


FastJet and SISCone

7

Both the N3/speed problem of kt and the N2N/speed/IRC safety of the cone were solved by shifting the problem

from combinatorics to geometry

‣ kt was made fast by reducing the problem to near-neighbour searches, and using Voronoi diagrams to reduce complexity to NlnN

‣ Cone was made fast (and IRC safe) by inventing circular enclosures to find stable cones and reduce complexity to N2lnN

(MC, Salam, hep-ph/0512210)

(Salam, Soyez, arXiv: 0704.0292)


Recombination algorithms

8

di j =min(k2pti ,k2pt j )Δy2+Δφ2

R2

p = 1 kt algorithm S. Catani, Y. Dokshitzer, M. Seymour and B. Webber, Nucl. Phys. B406 (1993) 187S.D. Ellis and D.E. Soper, Phys. Rev. D48 (1993) 3160

p = 0 Cambridge/Aachen algorithm Y. Dokshitzer, G. Leder, S.Moretti and B. Webber, JHEP 08 (1997) 001M. Wobisch and T. Wengler, hep-ph/9907280

diB = k2pti

p = -1 anti-kt algorithm MC, G. Salam and G. Soyez, arXiv:0802.1189

NB: in anti-kt pairs with a hard particle with cluster first: if no other hard particles are close by, the algorithm will give perfect cones

Quite ironically, a sequential recombination algorithm is the perfect cone algorithm


IRC safe algorithms

9

kt

SRdij = min(kti2,ktj2)ΔRij2/R2

hierarchical in rel pt

Catani et al ‘91Ellis, Soper ‘93 NlnN

Cambridge/Aachen

SRdij = ΔRij

2/R2

hierarchical in angle

Dokshitzer et al ‘97Wengler, Wobish ‘98 NlnN

anti-kt

SRdij = min(kti-2,ktj-2)ΔRij

2/R2

gives perfectly conical hard jets

MC, Salam, Soyez ’08(Delsart, Loch) N3/2

SISConeSeedless iterative cone

with split-mergegives ‘economical’ jets

Salam, Soyez ‘07 N2lnN

All are available in FastJet, http://fastjet.fr, as well as SpartyJet

‘second-generation’ algorithms

http://fastjet.fr

http://fastjet.fr

kt Cam/Aa

SISCone anti-kt

10


Cover of EPJ C67 (2010)

1110


Inclusive jets at HERA

12

arXiv:1003.2923 [hep-ex]


Inclusive jets in ATLAS and CMS

13

CMS and ATLAS have settled on one of the new algorithms as their default

Amazingly, they are using the same one, anti-kt

However, and perhaps unsurprisingly, CMS uses R = 0.5 and 0.7, and ATLAS 0.4 and 0.6!

While the use of an IRC safe algorithm is welcome, it’s fairly unfortunate that there isn’t some overlap for immediate comparisons

(I’m told discussions are in progress to fix this)


Inclusive jets in ATLAS and CMS

14

Good agreement, no surprises (nor any was expected)


Jets

15

Jets can serve two purposes

‣ They can be observables, that one can measure and calculate

‣ They can be tools, that one can employ to extract specific properties of the final state


Less standard candles

16

Jets as tools

CENSO

RED

CENSO

RED


Less standard candles

17

A more modern candle

ToolsRemove soft

contamination from a hard jet

Tag heavy objects originating the jet

Eventually leading to ‘third-generation’ jet algorithms

Measure invariant masses


Best R in dijet-mass reconstruction

1940

1/N

dN

/db

in

dijet mass [GeV]

0

0.01

0.02

0.03

0.04

0.05

80 100 120

kt, R=1.0

Q1/fw=1.25!M = 8.6

dijet mass [GeV]

80 100 120

kt, R=0.5

Q1/fw=1.25!M = 6.3

qq 1

00 G

eV

dijet mass [GeV]

80 100 120

SISCone, R=0.5, f=0.75

Q1/fw=1.25!M = 5.8 qq jets

at 100 GeV

R=1: BAD R=0.5: BETTER MC, Rojo, Salam, Soyez, 2008



1940

1/N

dN

/db

in

dijet mass [GeV]

0

0.01

0.02

0.03

0.04

0.05

80 100 120

kt, R=1.0

Q1/fw=1.25!M = 8.6

dijet mass [GeV]

80 100 120

kt, R=0.5

Q1/fw=1.25!M = 6.3

qq 1

00 G

eV

dijet mass [GeV]

80 100 120


Q1/fw=1.25!M = 5.8 qq jets

at 100 GeV

R=1: BAD R=0.5: BETTER

gg jets at 2 TeV

MC, Rojo, Salam, Soyez, 2008



1940

1/N

dN

/db

in

dijet mass [GeV]

0

0.01

0.02

0.03

0.04

0.05

80 100 120

kt, R=1.0

Q1/fw=1.25!M = 8.6

dijet mass [GeV]

80 100 120

kt, R=0.5

Q1/fw=1.25!M = 6.3

qq 1

00 G

eV

dijet mass [GeV]

80 100 120


Q1/fw=1.25!M = 5.8 qq jets

at 100 GeV

R=1: BAD R=0.5: BETTER

gg jets at 2 TeV

1/N

dN

/db

in

dijet mass [GeV]

0

0.01

0.02

0.03

0.04

1900 2000 2100

kt, R=0.5

Q1/fw=1.25!M = 15.9

dijet mass [GeV]

1900 2000 2100

kt, R=1.0

Q1/fw=1.25!M = 9.5 g

g 2

TeV

dijet mass [GeV]

1900 2000 2100


Q1/fw=1.25!M = 7.9

R=0.5: BAD R=1: BETTER

Gluons (and heavy objects) prefer larger R

MC, Rojo, Salam, Soyez, 2008



2041

Filtering can help in mass reconstruction too

(and can also be further subtracted)

1.0

1.5

2.0

2.5

!L

kt

noPU-sub

noPU

!L from Qwf=z

C/A anti-kt SISCone

qq

10

0 G

eV

C/A-filt

1.0

1.5

2.0

2.5

0.5 1.0 1.5

!L

R

0.5 1.0 1.5

R

0.5 1.0 1.5

R

0.5 1.0 1.5

R

0.5 1.0 1.5

gg

2 T

eV

REffect of subtraction: bad jet

definitions are improved.Gain in effective luminosity about 20-30%(i.e. they were ‘bad’ due to a large extent to their

behaviour with respect to the background)

ρL = factor of luminosity needed to obtain equivalent signal/background significance


R-dependent effects

21

Perturbative radiation: ∆pt !αs(CF , CA)

πpt lnR

∆pt !(CF , CA)

R× 0.4 GeV

∆pt !R2

2× (2.5−−15 GeV)

Hadronisation:

Underlying Event:

Analytical estimates,Dasgupta, Magnea, Salam, arXiv:0712.3014

Tevatron LHC


Best R

22

Minimize Σ(Δpt)2

Best R Best RDasgupta, Magnea, Salam, arXiv:0712.3014


Boosted Higgs tagger

2331

Butterworth, Davison, Rubin, Salam, 2008

Cluster with a large RUndo the clustering into subjets,

until a large mass drop is observed

Re-cluster with smaller R, and keep only 3 hardest

jets


Jet substructure as tagger

24

Studying the jet substructure (i.e. the subjets obtained by undoing the clustering of a sequential recombination algorithm)

can lead to identification capabilities of specific objects (as opposed to ‘standard’ QCD background)

‣ Boosted Higgs tagger

‣ Boosted top tagger

‣ Moderately boosted top and Higgs tagger

‣ + others


Thaler, Wang, 2008Kaplan, Rehermann, Schwartz, Tweedie, 2008

Plehn, Salam, Spannowsky, 2009

Common feature: start with a ‘fat jet’, decluster it and check if it contains a complex ‘hard’ substructure

G. Broojmans, ATLAS 2008



25

pp →ZH → ννbb

Start with the hardest jet

Use C/A with large R=1.2

m = 150 GeVG

. Sal

am

- -



26

pp →ZH → ννbb

Undo last step of clustering

Check how the mass splits between the two subjets

(m1 = 139 GeV, m2 = 5 GeV)

If max(m1,m2)

m> µ repeat



27

pp →ZH → ννbb

m1 = 52 GeV, m2 = 28 GeV

Stop when a large mass drop is observed

(and recombine these two jets)


Jet substructure as filter

28

The jet substructure can be exploited to help removing contamination

from a soft background

‣ Jet ‘filtering’

‣ Jet ‘pruning’

‣ Jet ‘trimming’


Krohn, Thaler, Wang, 2009

S. Ellis, Vermilion, Walsh, 2009

(Filtering, trimming and pruning are actually quite similar)

Aim: limit sensitivity to background while retaining bulk of perturbative radiation


Cambridge/Aachen with filtering

29

An example of a third-generation jet algorithm

‣ Cluster with C/A and a given R

‣ Undo the clustering of each jet down to subjets with radius xfiltR

‣ Retain only the nfilt hardest subjets

Butterworth, Davison, Rubin, Salam, arXiv:0802.2470


Filtering in action

30

Start with a jet

Butterworth, Davison, Rubin, Salam, arXiv:0802.2470

G. S

alam


Filtering in action

31

Recluster the contituents with Rfilt

G. S

alam


Filtering in action

32

Only keep the nfilt hardest jets

The low-momentum stuff surrounding the hard particles has been removedG

. Sal

am


Hard jets and background

3325

In a realistic set-up underlying event (UE) and pile-up (PU) from multiple collisions produce many soft particles which can ‘contaminate’ the hard jet

How does the background affect the hard jet?


Jet areas

3427

Not one, but three definitions of a jet’s size:

‣ Voronoi area

‣ Passive area

‣ Active area

MC, Salam, Soyez, arXiv:0802.1188

Mimics effect of pointlike radiation

Mimics effect of diffuse radiation

(In the large number of particles limit all areas converge to the same value)

A jet area expresses the susceptibility of a jet to contamination from background radiation



3519

Susceptibility (how much bkgd gets picked up)

Resiliency (how much the original jet changes)

How are the hard jets modified by the background?


Background characterization

36

LHC14 pp UE RHIC LHC

HI

ρ transverse momentum per

unit area

2.2 - 43 - 6 100 300

σ/ρσ = background fluctuations per

unit areain a single event

0.70.45 0.1 0.06

σρ√(<ρ2> -<ρ>2 ) dispersion of ρ over many events

2 - 3.82.2 - 4.5 14 40

PYTHIA HERWIG HYDJET(all dimensionful quantities in GeV)



37

background back-reaction

‘susceptibility’ ‘resiliency’

Modifications of the hard jet

MC, Salam, arXiv:0707.1378MC, Salam, Soyez, arXiv:0802.1188

∆pt = ρA± (σ√

A + σρA + ρ√〈A2〉 − 〈A〉2) + ∆pBR

t


Backreaction

38

Without background

“How (much) a jet changes when immersed in a background”


Backreaction

38

Without background



Backreaction

38

Without background

With background



Backreaction lossBackreaction gain

Backreaction

38

Without background

With background



Backreaction

39

0.001

0.01

0.1

1

-20 -15 -10 -5 0 5 10 15

1/N

dN/d

p t (G

eV-1

)

!pt(B) (GeV)

R=1

Pythia 6.4LHC (high lumi)2 hardest jetspt,jet> 1 TeV

|y|<2

SISCone (f=075)Cam/Aachenktanti-kt

pT gainpT loss

Anti-kt jets are much more resilient to changes from background immersion

MC, Salam, Soyez, arXiv:0802.1188


The IRC safe algorithms

40

Speed Regularity UE Backreaction Hierarchicalsubstructure

kt ☺☺☺ ☂ ☂☂ ☁☁ ☺☺

Cambridge/Aachen

☺☺☺ ☂ ☂ ☁☁ ☺☺☺

anti-kt ☺☺☺ ☺☺ ☁/☺ ☺☺ ✘

SISCone ☺ ☁ ☺☺ ☁ ✘

(other algorithms not listed here: e.g. variable-R, …)


UE characterisation

41

ρ≡median[{

p jettArea jet

}]

(over a single event)

Jet algorithms like kt or Cambridge/Aachen allow one to determine on an event-by-event basis

the “typical” level of transverse momentum density of a roughly uniform background noise:

This ρ value can, in turn, be used to characterise the UE

Since this measurement is done with the jets, it is alternative/complementary to the usual analyses done using charged tracks (à la R. Field)

MC, Salam, 2007


UE characterisation

42

UE level Its fluctuations

Potential discriminating power between

different Pythia tunes, Herwig, etc

Useful for tuning MCs

MC, Salam, Sapeta, 2009Correlations at

different rapidities

ρ distribution

(See also CMS analysis)


Background subtraction

43

phard jet, correctedT = phard jet, rawT −ρ×Areahard jet

Once measured, the background density can be used to correct the transverse momentum of the hard jets:

ρ being calculated on an event-by-event basis, and each jet subtracted individually, this procedure will remove many fluctuations and generally

improve the resolution of, say, a mass peak

NB. Also be(a)ware of backreaction (immersing a hard jet in a soft background may cause some particles belonging to the

hard event to be lost from (backreaction loss) or added to (backreaction gain) the jet).Small effect for UE, larger for pileup, can be very important for heavy ions.Analytical understanding of this effect available (MC, Salam, Soyez, arXiv:0802:1188)

∆pt = ρA± (σ√

A + σρA + ρ√〈A2〉 − 〈A〉2) + ∆pBR

t


Analytical investigations

44

‣Mass of a jet

‣Dijet mass

‣Filtering

S. Sapeta, Qi Cheng Zhang, 1009.1143

G. Soyez, 1006.3634

M. Rubin, 1002.4557

‣ Jet areas MC, G. Salam, G. Soyez, 0802.1188definition of ‘jet area’, susceptibility to jet pt contamination,anomalous dimensions, back-reaction

optimization of filtering parameters

analytical calculation of Rbest

definition of ‘mass area’, susceptibility to jet-mass contamination

‣ Pert. and non-pert. R dependenceM. Dasgupta, L. Magnea, G. Salam, 0712.3014

Put everything together

Jet reconstruction in heavy ions collisions


Hard jets and background in HI

46

Hard jets(pp collisions)

Hard jets + background(AA collisions)

Can we ‘reconstruct’ the hard jet?MC, Rojo, Salam, Soyez, (forever) in preparation

The background adds on average 50 (150) GeV at RHIC (LHC)


Goal

47

Reconstruct the momentum the hard

jet would have without the background: (subtracts background,

fluctuations and back-reaction remain)

MC, Salam, arXiv:0707.1378

psubµ,jet ≡ pµ,jet − ρAµ,jet


Goal

47

Reconstruct the momentum the hard

jet would have without the background: (subtracts background,

fluctuations and back-reaction remain)

MC, Salam, arXiv:0707.1378

psubµ,jet ≡ pµ,jet − ρAµ,jet

Quality measures

Offset

Dispersion σ∆pt ≡√〈∆p2

t 〉 − 〈∆pt〉2

Small offset and dispersion will indicate a good reconstruction

〈∆pt〉 ≡ 〈pAA,subt − ppp,sub

t 〉


smaller effective area

Δpt distributions in AuAu at RHIC

48

0

0.02

0.04

0.06

0.08

0.1

-30 -20 -10 0 10 20 30

1/N

dN

/d!

pt [G

eV

-1]

!pt [GeV]

"!pt# = -3.4 GeV

$!pt = 7.0 GeV

RHIC, 0-10% central|y|<1, 30<pt,hard<35 GeV

Doughnut(R,3R)

R=0.4

kt

0

0.02

0.04

0.06

0.08

0.1

-30 -20 -10 0 10 20 30

1/N

dN

/d!

pt [G

eV

-1]

!pt [GeV]

"!pt# = -1.4 GeV

$!pt = 6.8 GeV

C/A

0

0.02

0.04

0.06

0.08

0.1

-30 -20 -10 0 10 20 30

1/N

dN

/d!

pt [G

eV

-1]

!pt [GeV]

"!pt# = 0.5 GeV

$!pt = 7.5 GeV

anti-kt

0

0.02

0.04

0.06

0.08

0.1

-30 -20 -10 0 10 20 30

1/N

dN

/d!

pt [G

eV

-1]

!pt [GeV]

"!pt# = 0.5 GeV

$!pt = 4.7 GeV

C/A(filt)back-reaction


Back-reaction contribution to <Δpt>

-5

-4

-3

-2

-1

0

1

2

3

4

10 15 20 25 30 35 40 45 50

Ba

ck-r

ea

ctio

n [

Ge

V]

pt,hard [GeV]

RHIC, 0-10% central

|y|<1, R=0.4, unquenched

ktC/A

anti-ktC/A(filt)

!"p

t# [

Ge

V]

pt,hard [GeV]

RHIC, 0-10% central

|y|<1, R=0.4, unquenched

Doughnut(R,3R) range

ktC/A

anti-ktC/A(filt)

-5

-4

-3

-2

-1

0

1

2

3

4

10 15 20 25 30 35 40 45 50

RHIC

LHC

<Δpt> Back-reaction

Back-reaction explains the residual offset, with the exception of C/A(filt) (accidental compensation of back-reaction and positive offset)

!"p

t# [

Ge

V]

pt,hard [GeV]

LHC, unquenched

|y|<2.4, R=0.4


ktC/A

anti-ktC/A(filt)

-12

-9

-6

-3

0

3

6

9

40 60 100 200 500

Ba

ck-r

ea

ctio

n [

Ge

V]

pt,hard [GeV]

LHC, unquenched

|y|<2.4, R=0.4

ktC/A

anti-ktC/A(filt)

-12

-9

-6

-3

0

3

6

9

40 60 100 200 500


Dispersion of Δpt

50

4

5

6

7

8

10 15 20 25 30 35 40 45 50

!"

pt [

Ge

V]

pt,hard [GeV]

RHIC, 0-10% central

unquenched, |y|<1, R=0.4


ktC/A

anti-ktC/A(filt)

‣ C/A(filt) markedly better, as a consequence of its smaller effective area

‣ Dispersions increase at large pt, as a consequence of a larger dispersion of back-reaction

‣ anti-kt remains fairly constant (‘resiliency’), and eventually becomes better at large pt

0

5

10

15

20

25

30

35

40 60 100 200 500

!"

pt [

Ge

V]

pt,hard [GeV]

LHC, unquenched

|y|<2.4, R=0.4


ktC/Aanti-ktC/A(filt)


Conclusions

51

‣ Robust and public code standardizes the offer of an extensive set of fast, IRC safe jet algorithms, offering replacements for the IRC unsafe ones. It offers ample flexibility in choosing the most effective jet definition for any given analysis

‣ Analytical understanding of many characteristics available. Possibility to optimize the analyses without running MonteCarlos, and/or to understand the results

‣ ‘Third-generation’ algorithms exploiting jet substructure look very promising

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Standard Candles: Jets

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