Brookhaven National Laboratorysoyez/data/talks/2009-03-LHC_BNL.pdf · 2014. 5. 6. · Deﬁning...

Defining jets at the LHC

Gregory Soyez

Brookhaven National Laboratory

in collaboration with G. Salam, M. Cacciari and J. Rojo

arXiv:0704:0292, arXiv:0802:1189, arXiv:0810.1304

Gregory Soyez LHC@BNL, BNL, Upton, NY, USA, March 16 2009 Jets at the LHC – p. 1

Unavoidable theory

QCD probability for gluon emission (angle θ and ⊥-mom. kt):

dP ∝ αs

dθ

θ

dkt

kt

Two divergences:

θ ≈ 0

collinear

pt

kt ≪ pt

soft

Divergences cancelled by virtual corrections


Motivation: why QCD?

Lot of QCD in the final-state at the LHC

QCD studies: e.g. t → bqq

new physics:

H → bb

Z ′ → qq

SUSY → QCD

backgrounds: e.g. gg → bb, ...

⇒ Huge effort to compute multileg/NLO processes in pQCD (∼ 100 M$)

This talk: how to avoid wasting that effort, in the optimal way


Motivation: why jets

Collinear divergence ⇒ QCD produces “jetty” showers

Example: LEP (OPAL) events

2 jets 3 jets

“Jets” ≡ bunch of collimated particles ∼= hard partons


Motivation: why jets

Collinear divergence ⇒ QCD produces “jetty” showers

“Jets” ≡ bunch of collimated particles ∼= hard partons

BUT

a “parton” is an ambiguous concept (NLO)

“collinear” has some arbitraryness

2 jets 3 jets ? jets

⇒ Different jet definitions


20th century jet finders

Recombination: Cone:kt algorithm

Cambridge/Aachen alg.

a

CDF JetClu

CDF MidPoint

D0 (run II) Cone

PxCone

ATLAS Cone

CMS Iterative Cone

PyCell/CellJet

GetJet





a

CDF JetClu

CDF MidPoint

D0 (run II) Cone

PxCone

ATLAS Cone

CMS Iterative Cone

PyCell/CellJet

GetJet

Idea: undo the showering

Successivelyb find the closest pair of particlesb recombine them

Distance:kt:b di,j = min(k2

t,i, k2t,j)(∆φ2

i,j + ∆y2i,j)

Cam/Aachen:b di,j = ∆φ2

i,j + ∆y2i,j

stop at a distance R





a

CDF JetClu

CDF MidPoint

D0 (run II) Cone

PxCone

ATLAS Cone

CMS Iterative Cone

PyCell/CellJet

GetJet

Idea: dominant flow of energy

Stable cone (radius R):sum of particles in the cone pointstowards the cone centre

All these are iterative cones:b start from a seedb iterate until stable

seeds = {particles, midpoints}

blJet ≡ stable coneblmodulo overlapping





a

CDF JetClu

CDF MidPoint

D0 (run II) Cone

PxCone

ATLAS Cone

CMS Iterative Cone

PyCell/CellJet

GetJet

Cone with split-merge

Split/merge if the overlap issmaller/larger than a threshold f





a

CDF JetClu

CDF MidPoint

D0 (run II) Cone

PxCone

ATLAS Cone

CMS Iterative Cone

PyCell/CellJet

GetJet

Cone with progressive removal

Successivelyb iterate from hardest particleb call that a jet (remove particles)

Basic property:blhard circular jets


21st century: how does that picture change?


QCD divergences

Ingredient: QCD soft and collinear divergencies

LO NLO(virt) NLO(real)∞ ∞

∞ (from soft gluons) cancel


QCD divergences



Consider an extra (NLO) soft gluon

Assume LO gives 2 jets ⇒ NLO(virt) gives 2 jets


QCD divergences





NLO(real) gives 2 jets ⇒ ∞ cancel ⇒ finite jet cross-section


QCD divergences





NLO(real) gives 2 jets ⇒ ∞ cancel ⇒ finite jet cross-sectionNLO(real) gives 1 jets ⇒ ∞ do not cancel ⇒ infinite jet cross-section


QCD divergences



For pQCD to make sense, the (hard) jets should not change when

one has a soft emission i.e. adds a very soft gluon

one has a collinear splittingi.e. replaces one parton by two at the same place (η, φ)


IR (un)safety? JetClu and Atlas Cone

-1 0 1 2 30

100

200

300

400pt

φ -1 0 1 2 30

100

200

300

400pt

φ



-1 0 1 2 30

100

200

300

400pt

φ -1 0 1 2 30

100

200

300

400pt

φ

Stable cones found



-1 0 1 2 30

100

200

300

400pt

φ -1 0 1 2 30

100

200

300

400pt

φ

2 jets 1 jet

A soft gluon changed the number of jets⇒ IR unsafety of JetClu and the ATLAS Cone



-1 0 1 2 30

100

200

300

400pt

φ -1 0 1 2 30

100

200

300

400pt

φ

2 jets 1 jet

MidPointseed

A soft gluon changed the number of jets⇒ IR unsafety of JetClu and the ATLAS Cone

Fixed by MidPoint

[Blazey et al., 00]


IR (un)safety? MidPoint

-1 0 1 2 30

100

200

300

400pt

φ -1 0 1 2 30

100

200

300

400pt

φ



-1 0 1 2 30

100

200

300

400pt

φ -1 0 1 2 30

100

200

300

400pt

φ

Stable cones found



-1 0 1 2 30

100

200

300

400pt

φ -1 0 1 2 30

100

200

300

400pt

φ

2 jets 1 jet

A soft gluon changed the number of jets⇒ IR unsafety of MidPoint (1 order in αs later than JetClu)



-1 0 1 2 30

100

200

300

400pt

φ -1 0 1 2 30

100

200

300

400pt

φ

2 jets 1 jet

missed stable cone

Solution: be sure to find all stable cones

SISCone: Seedless Infrared-Safe Cone algorithmhttp://projects.hepforge.org/siscone

[G.Salam, G.S., 07]

Idea: enumerate enclosures by enumerating pairs of particles


http://projects.hepforge.org/siscone

Collinear (un)safety? the CMS iterative cone

-1 0 1 20

100

200

300

400pt

φ -1 0 1 20

100

200

300

400pt

φ


Collinear (un)safety? the CMS iterative cone

-1 0 1 20

100

200

300

400pt

φ

1st seed

-1 0 1 20

100

200

300

400pt

φ

1st seed 2nd seed

1 jet 2 jets

A colinear splitting changed the number of jets⇒ Collinear unsafety of the CMS iterative cone


Anti- kt

Come back to recombination-type algorithms:

dij = min(k2pt,i, k

2pt,j)

(

∆φ2ij + ∆η2

ij

)

p = 1: kt algorithm

p = 0: Aachen/Cambridge algorithm


Anti- kt

Come back to recombination-type algorithms:

dij = min(k2pt,i, k

2pt,j)

(

∆φ2ij + ∆η2

ij

)

p = 1: kt algorithm

p = 0: Aachen/Cambridge algorithm

p = −1: anti-kt algorithm [M.Cacciari, G.Salam, G.S., 08]

Why should that be related to the iterative cone ?!?

“large kt ⇒ small distance”i.e. hard partons “eat” everything up to a distance R

i.e. circular/regular jets, jet borders unmodified by soft radiation

infrared and collinear safe


21st century jet finders



anti-kt algorithm

a

CDF JetClu

CDF MidPoint

D0 (run II) Cone

PxCone

ATLAS Cone

CMS Iterative Cone

PyCell/CellJet

GetJet

SISCone

4 availablesafe algorithms

All accessible from FastJethttp://www.fastjet.fr [M.Cacciari, G.Salam, G.S.]


Physical impact

MidPoint/CMS iterative cone unsafe at O(α4s) (or O(αewα3

s))

IRC-safe until

Physical observable JetClu/ATLAS cone MidPoint/CMS it. cone SISCone/recomb.

Inclusive jet cross section LO NLO any3-jet cross section none LO anyW/Z/H + 2 jet cross sect. none LO anyjet masses in 3 jets none none any

Example: (Midpoint-SISCone)/SISCone

0.00

0.05

0.10

0.15

50 100 150 200

dσm

idpo

int(

1)/d

p t /

dσS

ISC

one/

dpt −

1

pt [GeV]

pp √s = 14 TeV

R=0.7, f=0.5, |y|<0.7Pythia 6.4

(b) hadron-level (with UE)

hadron-level (no UE)

parton-level

Incl. cross-section: a few %

Masses in 3-jet events: ∼ 45%

0 10 20 30 40 50 60 70 80 90 100M (GeV)

0

0.1

0.2

0.3

0.4

0.5

rel.

diff.

for

dσ/d

M2 Mass spectrum of jet 2

midpoint(0) -- SISConeSISCone

NLOJetR=0.7, f=0.5∆ R23 < 1.4


Physical impact

MidPoint/CMS iterative cone unsafe at O(α4s) (or O(αewα3

s))

IRC-safe until

Physical observable JetClu/ATLAS cone MidPoint/CMS it. cone SISCone/recomb.

Inclusive jet cross section LO NLO any3-jet cross section none LO anyW/Z/H + 2 jet cross sect. none LO anyjet masses in 3 jets none none any

Huge theoretical effort to compute multileg/NLO processesThat can be wasted by using unappropriate tools.

Note: arXiv:0903.0814: W + 2 jets vs. LO QCD using CDF JetClu

arXiv:0903.1748: Z + 2 jets vs. NLO QCD using the D0runII cone

arXiv:0903.1801: Z + 2 jets vs. NLO QCD using the CMS iterative cone


Filtering using jet substructure

More refined clustering (“3rd generation of algorithms”)

Cambridge+Filtering algorithm:

Cluster with Aachen/Cambridge and radius R

For each jet, recluster it with Aachen/Cambridge and radius Rsub

keep only nsub hardest sub-jets of the initial jet


Filtering using jet substructure

More refined clustering (“3rd generation of algorithms”)

Cambridge+Filtering algorithm:

Cluster with Aachen/Cambridge and radius R

For each jet, recluster it with Aachen/Cambridge and radius Rsub

keep only nsub hardest sub-jets of the initial jet

Aim: remove the soft background

Properties:

Proven to improve jet reconstruction, in H → bb

[J.Butterworth, A.Davison, M.Rubin, G.Salam, 08]

Additional parameters that deserve appropriate studies

We will use the simplest choice: Rsub = R/2, nsub = 2


jet definitions = algorithm + parameters

Algorithm: kt, Aachen/Cam., anti- kt, SISCone, filtering?+ parameters: mainly R a

Which one to choose?


Underlying idea

Competition between

catching perturbative radiation

Out-of-cone radiation:

b 〈δpt〉 ∝ −∫

R

dθ

θ∼ − log(1/R)

not catching soft background radiation (underlying event)

〈δpt〉 ∼ Soft contents ∝ jet area ∼ R2

the coefficients depend on the algorithm


Jet optimisation study

We analyse 3 processes typical of kinematic reconstructions:

Z ′ → qq →2 jets and H → gg →2 jets:simple environment: identify 2 jets and reconstruct MZ′,H

source of monochromatic quark/gluon jetsscale dependence: mass of the Z′/H varied between 100 GeV and 4 TeVficticious narrow Z′, H

tt → W+bW−b → qqbqqb →6 jets:complex environment: identify 6 jets and reconstruct 2 topbalance between reconstruction efficiency and identification

with

the 5 IRC-safe algorithms: kt, Cambridge, anti-kt, SISCone, Cam+filtering

jet radius varied between 0.1 and 1.5


Reconstruction quality (1)

Measure of the jet reconstruction efficiency:

Forget about measures related to parton-jet matching

Forget about fits depending on the shape of the peak

⇒ maximise the signal over background ratio (S/√

B)a narrower peak is better.

1/N

dN

/dbi

n

dijet mass [GeV]

0

0.01

0.02

0.03

0.04

0.05

80 100 120

kt, R=1.0

Qwf=0.12 = 13.0 GeV

dijet mass [GeV]

80 100 120

kt, R=0.5

Qwf=0.12 = 8.3 GeV

qq 100 GeV

dijet mass [GeV]

80 100 120

SISCone, R=0.5, f=0.75Qw

f=0.12 = 7.4 GeV


Reconstruction quality (2)

Assuming a constant background,

quality measure −→ effective luminosity ratio

ρL(JD2/JD1) =L needed with JD2

L needed with JD1

=Qw

f=z(JD2)

Qwf=z(JD1)

e.g. ρL(JD2/JD1) = 2

⇔ JD2 requires 2 times the integrated luminosity of JD1

⇔ to achieve the same discriminative power.

Note: results cross-checked with 2 different definitions of the quality measure


Best choices

5

10

15

20

25

30

35

100

150 200

300

500 700

1000

2000

4000

Bes

t Qw f=

0.12

(G

eV)

M (GeV)

qq

ktCam/Aa

anti-ktSISCone

C/A-filt

0.4

0.6

0.8

1

1.2

1.4

100

150 200

300

500 700 1000

2000

4000

Bes

t R (

from

Qw f=

0.12

)

M (GeV)

qq

ktCam/Aa

anti-ktSISCone

C/A-filt

SISCone and Cam+filtering perform better

Rbest strongly depends on the mass


Quarks vs. gluons

5

10

15

20

25

30

35

100

150 200

300

500 700

1000

2000

4000

Bes

t Qw f=

0.12

(G

eV)

M (GeV)

qq

ktCam/Aa

anti-ktSISCone

C/A-filt

0.4

0.6

0.8

1

1.2

1.4

100

150 200

300

500 700 1000

2000

4000

Bes

t R (

from

Qw f=

0.12

)

M (GeV)

qq

ktCam/Aa

anti-ktSISCone

C/A-filt

10 20 30 40 50 60 70 80 90

100 110

100

150 200

300

500 700 1000

2000

4000

Bes

t Qw f=

0.13

(G

eV)

M (GeV)

gg

ktCam/Aa

anti-ktSISCone

C/A-filt

0.4

0.6

0.8

1

1.2

1.4

100

150 200

300

500 700 1000

2000

4000

Bes

t R (

from

Qw f=

0.13

)

M (GeV)

gg

ktCam/Aa

anti-ktSISCone

C/A-filt

Same conclusions for gluon jets with slightly larger R


Luminosity ratios

1

1.2

1.4

1.6

1.8

2

2.2

0.4 0.6 0.8 1 1.2 1.4

ρL

R

gg, 2 TeV

(kt,R) vs. (SISCone,Rbest)

Mandatory at the LHC:Not choosing the best alg.AND R can be very costlyfor new discoveries

Note: typical choice, R ∼ 0.5

1

1.2

1.4

1.6

1.8

2

2.2

0.4 0.6 0.8 1 1.2 1.4

ρL

R

gg, 2 TeV

(SISCone,R) vs. Best

best

100 GeVbest

1

1.2

1.4

1.6

1.8

2

2.2

0.4 0.6 0.8 1 1.2 1.4

ρL

R

qq, 100 GeV

(SISCone,R) vs. Best

best 2 TeVbest


Conclusions

New jet algorithms available

JetCluATLAS Cone

MidPointIterative Cone

SISCone

Anti-kt

X as fastX IRC safe

X regularX IRC safe

important for precision at the LHC!

Early discovery may rely on an optimal choice of a jet definition

SISCone and Camb/Aachen+filtering slightly preferred

Strong dependence on R: larger scales ↔ larger R

Available from FastJet (or SpartyJet)Check http://quality.fastjet.fr for interactive plots


Backup slides


Speed

0.001

0.01

0.1

1

10

100 1000 10000

run

time

(s)

N

CDF midpoint (s=0 GeV)

CDF midpoint (s=1 GeV)

KtJet

SISConekt (FastJet)

anti-kt (FastJet)

Recombination algorithms very fast [M. Cacciari, G. Salam, 06]

SISCone not slower than Midpoint (even with a 1 GeV seed threshold)


Optimisation - more results

1.0

1.5

2.0

ρ L

kt

ρ L fr

om Q

w f=z

C/A anti-kt SISCone

qq 100 GeV

C/A-filt

1.0

1.5

2.0

ρ L

qq 2 TeV

1.0

1.5

2.0

ρ L

gg 100 GeV

1.0

1.5

2.0

ρ L

gg 2 TeV

1.0

1.5

2.0

0.5 1.0 1.5

ρ 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

top in tt

RGregory Soyez LHC@BNL, BNL, Upton, NY, USA, March 16 2009 Jets at the LHC – p. 26

Need for subtraction

Pileup ≈ uniform soft background that shifts jets to higher pt

0

0.005

0.01

0.015

0.02

60 80 100 120 140

1/N

dN

/dm

(G

eV-1

)

reconstructed Z’ mass (GeV)

MZ’=100 GeV

kt, R=Rbest

no PUlow-lumi PU

high-lumi PU

... that needs to be subtracted!

⇒ Using jet areas!


Pileup subtraction

Basic idea: [M.Cacciari, G.Salam, 08]

pt,subtracted = pt,jet − ρpileup × Areajet


Pileup subtraction



Jet area: [M.Cacciari, G.Salam, G.S., 08]

region where the jet catches infinitely soft particles (active/passive)

tractable analytically in pQCDExample: area corrections from QCD radiation

〈A(pt,1, R)〉 = A1 parton(R) +CF,A

πb0

log

(

αs(Q0)

αs(Rpt)

)

πR2 d

area 6= πR2

area scaling violations

d passive active

kt 0.5638 0.519

Cam 0.07918 0.0865

SISCone -0.06378 0.1246

anti-kt 0 0

just a shift


Pileup subtraction



Jet area: [M.Cacciari, G.Salam, G.S., 08]

region where the jet catches infinitely soft particles (active/passive)

tractable analytically in pQCD

Pileup density per unit area: ρpileup

e.g. estimated from the mediane.g. of pt,jet/Areajet

0

5

10

15

20

25

30

35

-4 -2 0 2 4

Pt,j

et /

Are

a jet

η

median

implemented in FastJeton an event-by-event basis


Subtraction at work

0

0.005

0.01

0.015

0.02

60 80 100 120 140

1/N

dN

/dm

(G

eV-1

)


MZ’=100 GeV

kt, R=Rbest

no PUlow-lumi PU

high-lumi PU

0

0.005

0.01

0.015

0.02

60 80 100 120 140

1/N

dN

/dm

(G

eV-1

)


MZ’=100 GeV

kt, R=0.5

no PUlow-lumi PU

high-lumi PU

subtractionblablablablabla


Optimisation - pileup

1.0

1.5

2.0

2.5

ρ L

kt

PU(0.25

)

PU-s

ubno

PU

C/A anti-kt SISConeqq 2 T

eVC/A-filt

1.0

1.5

2.0

2.5

ρ L

gg 100 GeV

1.0

1.5

2.0

2.5

0.5 1.0 1.5

ρ 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

top in tt

R


Brookhaven National Laboratorysoyez/data/talks/2009-03-LHC_BNL.pdf · 2014. 5. 6. · Deﬁning...

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