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Gavin Salam (CERN) Jets and jet substructure (3) TASI, June 2013 2 / 19

Small v. large jet radius (R)

Small jet radius Large jet radius

single parton @ LO: jet radius irrelevant



Small jet radius

θ

Large jet radius

θ

perturbative fragmentation: large jet radius better(it captures more)



Small jet radius

KL

π−π+

π0

K+

non−perturbativehadronisation

θ

Large jet radius

KL

π−π+

π0

K+


θ

non-perturbative fragmentation: large jet radius better(it captures more)



Small jet radius

UE

KL

π−π+

π0

K+


θ

Large jet radius

UE

KL

π−π+

π0

K+


θ

underlying ev. & pileup “noise”: small jet radius better(it captures less)



Small jet radius Large jet radius

multi-hard-parton events: small jet radius better(it resolves partons more effectively)


Jet pt v. parton pt : perturbatively?

The question’s dangerous: a “parton” is an ambiguous concept

Three limits can help you:

◮ Threshold limit e.g. de Florian & Vogelsang ’07

◮ Parton from color-neutral object decay (Z ′)

◮ Small-R (radius) limit for jet

One simple result (small-R limit)

〈pt,jet − pt,parton〉

pt=

αs

πlnR ×

{

1.01CF quarks0.94CA + 0.07nf gluons

+O (αs)

only O (αs) depends on algorithm & process

cf. Dasgupta, Magnea & GPS ’07Gavin Salam (CERN) Jets and jet substructure (3) TASI, June 2013 4 / 19

Jet pt v. parton pt : hadronisation?

Hadronisation: the “parton-shower” → hadrons transition

Method:

◮ “infrared finite αs” / infrared renormalons a la Dokshitzer & Webber ’95

Korchemsky & Sterman ’94

Seymour ’97

Main result

〈pt,jet − pt,parton−shower 〉 ≃ −0.4 GeV

R×

{

CF quarksCA gluons

cf. Dasgupta, Magnea & GPS ’07

coefficient holds for anti-kt; see Dasgupta & Delenda ’09 for kt alg.


Underlying Event (UE)

“Naive” prediction (UE ≃ colour dipole between pp):

∆pt ≃ 0.4 GeV ×R2

2×

{

CF qq dipoleCA gluon dipole

Perugia 2011 Pythia tune:

∆pt ≃ 5 − 10 GeV ×R2

2

This big coefficient motivates special effort to understand interplaybetween jet algorithm and UE: “jet areas”

How does coefficient depend on algorithm?

How does it depend on jet pt? How does it fluctuate?


What R is best for an isolated jet?

PT radiation:

q : 〈∆pt〉 ≃αsCF

πpt lnR

Hadronisation:

q : 〈∆pt〉 ≃ −CF

R· 0.4 GeV

Underlying event:

q, g : 〈∆pt〉 ≃R2

2·2.5−15 GeV

Minimise fluctuations in ptptpt

Use crude approximation:

〈∆p2t 〉 ≃ 〈∆pt〉2

E.g. to reconstruct mX ∼ (ptq + ptq)

Xpp

q

q

q

q

in small-R limit (!)

NB: full calc, correct fluct: Soyez ’10


PT radiation:


πpt lnR

Hadronisation:

q : 〈∆pt〉 ≃ −CF

R· 0.4 GeV

Underlying event:

q, g : 〈∆pt〉 ≃R2

2·2.5−15 GeV



〈∆p2t 〉 ≃ 〈∆pt〉2

50 GeV quark jet

⟨δp t

⟩2 pert +

⟨δp t

⟩2 h +

⟨δp t

⟩2 UE [G

eV2 ]

R

LHCquark jetspt = 50 GeV

0

5

10

15

20

25

30

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

⟨δpt⟩2pert

⟨δpt⟩2h

⟨δpt⟩2UE




PT radiation:


πpt lnR

Hadronisation:

q : 〈∆pt〉 ≃ −CF

R· 0.4 GeV

Underlying event:

q, g : 〈∆pt〉 ≃R2

2·2.5−15 GeV



〈∆p2t 〉 ≃ 〈∆pt〉2

1 TeV quark jet

⟨δp t

⟩2 pert +

⟨δp t

⟩2 h +

⟨δp t

⟩2 UE [G

eV2 ]

R

0

10

20

30

40

50

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

⟨δpt⟩2pert ⟨δpt⟩

2UE

LHCquark jetspt = 1 TeV




PT radiation:


πpt lnR

Hadronisation:

q : 〈∆pt〉 ≃ −CF

R· 0.4 GeV

Underlying event:

q, g : 〈∆pt〉 ≃R2

2·2.5−15 GeV



〈∆p2t 〉 ≃ 〈∆pt〉2

1 TeV quark jet

⟨δp t

⟩2 pert +

⟨δp t

⟩2 h +

⟨δp t

⟩2 UE [G

eV2 ]

R

0

10

20

30

40

50

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

⟨δpt⟩2pert ⟨δpt⟩

2UE

LHCquark jetspt = 1 TeV



At low pt, small RRR limits relative impact of UE

At high pt, perturbative effects dominate overnon-perturbative → RbestRbestRbest ∼ 1.

Dijet mass: scan over R [Pythia 6.4]

R = 0.31/

N d

n/db

in /

2

dijet mass [GeV]

qq, M = 100 GeV

arXiv:0810.1304

0

0.02

0.04

0.06

0.08

60 80 100 120 140

SISCone, R=0.3, f=0.75Qw

f=0.24 = 24.0 GeV

Resonance X → dijets

Xpp

q

q

q

q



R = 0.31/

N d

n/db

in /

2

dijet mass [GeV]

qq, M = 100 GeV

arXiv:0810.1304

0

0.02

0.04

0.06

0.08

60 80 100 120 140


f=0.24 = 24.0 GeV


Xpp

q

q

q

q

jet

jet



R = 0.41/

N d

n/db

in /

2

dijet mass [GeV]

qq, M = 100 GeV

arXiv:0810.1304

0

0.02

0.04

0.06

0.08

60 80 100 120 140


f=0.24 = 22.5 GeV


Xpp

q

q

q

q

jet

jet



R = 0.51/

N d

n/db

in /

2

dijet mass [GeV]

qq, M = 100 GeV

arXiv:0810.1304

0

0.02

0.04

0.06

0.08

60 80 100 120 140


f=0.24 = 22.6 GeV


Xpp

q

q

q

q

jet

jet



R = 0.61/

N d

n/db

in /

2

dijet mass [GeV]

qq, M = 100 GeV

arXiv:0810.1304

0

0.02

0.04

0.06

0.08

60 80 100 120 140


f=0.24 = 23.8 GeV


Xpp

q

q

q

q

jet

jet



R = 0.71/

N d

n/db

in /

2

dijet mass [GeV]

qq, M = 100 GeV

arXiv:0810.1304

0

0.02

0.04

0.06

0.08

60 80 100 120 140


f=0.24 = 25.1 GeV


Xpp

q

q

q

q

jet

jet



R = 0.81/

N d

n/db

in /

2

dijet mass [GeV]

qq, M = 100 GeV

arXiv:0810.1304

0

0.02

0.04

0.06

0.08

60 80 100 120 140


f=0.24 = 26.8 GeV


Xpp

q

q

q

q

jet

jet



R = 0.91/

N d

n/db

in /

2

dijet mass [GeV]

qq, M = 100 GeV

arXiv:0810.1304

0

0.02

0.04

0.06

0.08

60 80 100 120 140


f=0.24 = 28.8 GeV


Xpp

q

q

q

q

jet

jet



R = 1.01/

N d

n/db

in /

2

dijet mass [GeV]

qq, M = 100 GeV

arXiv:0810.1304

0

0.02

0.04

0.06

0.08

60 80 100 120 140


f=0.24 = 31.9 GeV


Xpp

q

q

q

q

jet

jet



R = 1.11/

N d

n/db

in /

2

dijet mass [GeV]

qq, M = 100 GeV

arXiv:0810.1304

0

0.02

0.04

0.06

0.08

60 80 100 120 140


f=0.24 = 34.7 GeV


Xpp

q

q

q

q

jet

jet



R = 1.21/

N d

n/db

in /

2

dijet mass [GeV]

qq, M = 100 GeV

arXiv:0810.1304

0

0.02

0.04

0.06

0.08

60 80 100 120 140


f=0.24 = 37.9 GeV


Xpp

q

q

q

q

jet

jet



R = 1.31/

N d

n/db

in /

2

dijet mass [GeV]

qq, M = 100 GeV

arXiv:0810.1304

0

0.02

0.04

0.06

0.08

60 80 100 120 140


f=0.24 = 42.3 GeV


Xpp

q

q

q

q

jet

jet



R = 1.31/

N d

n/db

in /

2

dijet mass [GeV]

qq, M = 100 GeV

arXiv:0810.1304

0

0.02

0.04

0.06

0.08

60 80 100 120 140


f=0.24 = 42.3 GeV

1

1.5

2

2.5

3

0.5 1 1.5ρ L

from

Qw f=

0.24

R

qq, M = 100 GeV

arXiv:0810.1304

SISCone, f=0.75

After scanning, summarise “quality” v. RRR. Minimum ≡ BESTpicture not so different from crude analytical estimate


Scan through qq mass values

mqq = 100 GeV

1

1.5

2

2.5

3

0.5 1 1.5

ρ L fr

om Q

w f=0.

24

R

qq, M = 100 GeV

arXiv:0810.1304

SISCone, f=0.75

Best R is at minimum of curve

◮ Best R depends strongly onmass of system

◮ Increases with mass, just likecrude analytical prediction

NB: current analytics too crude

NB: 100,000 plots for various jet algorithms, narrow qq and gg resonancesfrom http://quality.fastjet.fr Cacciari, Rojo, GPS & Soyez ’08

Other related work: Krohn, Thaler & Wang ’09; Soyez ’10


http://quality.fastjet.fr


mqq = 150 GeV

1

1.5

2

2.5

3

0.5 1 1.5

ρ L fr

om Q

w f=0.

24

R

qq, M = 150 GeV

arXiv:0810.1304

SISCone, f=0.75










mqq = 200 GeV

1

1.5

2

2.5

3

0.5 1 1.5

ρ L fr

om Q

w f=0.

24

R

qq, M = 200 GeV

arXiv:0810.1304

SISCone, f=0.75










mqq = 300 GeV

1

1.5

2

2.5

3

0.5 1 1.5

ρ L fr

om Q

w f=0.

24

R

qq, M = 300 GeV

arXiv:0810.1304

SISCone, f=0.75










mqq = 500 GeV

1

1.5

2

2.5

3

0.5 1 1.5

ρ L fr

om Q

w f=0.

24

R

qq, M = 500 GeV

arXiv:0810.1304

SISCone, f=0.75










mqq = 700 GeV

1

1.5

2

2.5

3

0.5 1 1.5

ρ L fr

om Q

w f=0.

24

R

qq, M = 700 GeV

arXiv:0810.1304

SISCone, f=0.75










mqq = 1000 GeV

1

1.5

2

2.5

3

0.5 1 1.5

ρ L fr

om Q

w f=0.

24

R

qq, M = 1000 GeV

arXiv:0810.1304

SISCone, f=0.75










mqq = 2000 GeV

1

1.5

2

2.5

3

0.5 1 1.5

ρ L fr

om Q

w f=0.

24

R

qq, M = 2000 GeV

arXiv:0810.1304

SISCone, f=0.75










mqq = 4000 GeV

1

1.5

2

2.5

3

0.5 1 1.5

ρ L fr

om Q

w f=0.

24

R

qq, M = 4000 GeV

arXiv:0810.1304

SISCone, f=0.75









http://quality.fastjet.fr/




Experimental results

ATLAS dijet mass

2000 3000 4000

1

10

210

310

410

510 DataBackground

[GeV]jjReconstructed m2000 3000 4000

Eve

nts

Sig

nific

ance

-2

0

2

ATLAS Preliminary

-1 = 13.0 fbdt L ∫ = 8 TeVs

CMS dijet mass

(pb/G

eV

)jj

/dm

!d

-810

-710

-610

-510

-410

-310

-210

-110

1

10

Data

Fit

QCD MC

JES Uncertainty

CMS Preliminary-1 = 8 TeV , L= 19.6 fbs

| < 1.3jj"#| < 2.5 , |"|

> 890 GeV , Wide Jetsjjm

A / C (3.6 TeV)

W’ (1.9 TeV)

Dijet Mass (GeV)

1000 1500 2000 2500 3000 3500 4000 4500 5000 5500

Da

ta!

(Data

-Fit)/

-4-3-2-101234


Highest mass central dijet event atthe LHC: 5.15 TeV!


Dijet Mass (GeV)1000 2000 3000 4000 5000 6000

No

rmalized

yie

ld/G

eV

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

0.0045 QuarkQuark

QuarkGluon

GluonGluon

CMS Simulation Preliminary

= 8 TeV, WideJetss

| < 1.3jj

η∆| < 2.5 & |η|

Expected resonance limits [TeV]7 TeV, 5 fb−1, published

ATLAS CMSX → (R = 0.6) (wide)

q∗ qg 2.94 3.05string qg 4.29 3.47octet scalar gg 1.97 2.24W ′ qq 1.74 1.78


http://arxiv.org/abs/1210.1718


Expected resonance limits [TeV]7 TeV, 5 fb−1, published

ATLAS CMSX → (R = 0.6) (wide)

q∗ qg 2.94 3.05string qg 4.29 3.47octet scalar gg 1.97 2.24W ′ qq 1.74 1.78

CMS “wide jets”:

We [...] select the two AK5 jets with the highest pT in the event (leading AK5 jets).

Then we add the Lorentz vectors of all other AK5 jets with pT > 10 GeV and |η| < 2.5 to

the closest AK5 leading jet, if within ∆R =< 1.1, to obtain the two leading wide jets.

The parameter ∆R sets the maximum size of the wide jet.




Why do the experiments have a |∆ηjj | < 1.3 cut?

see blackboard!


Why do the experiments have a |∆ηjj | < 1.3 cut?

see blackboard!

Bottom line: if you’re looking for a hadronically decaying

resonance, never use jets far in rapidity the CoM systemof the resonance


pp → ttpp → ttpp → ttsimulated with Pythia, displayed with Delphes


6 partons v. 6 jets?

Alpgen pp → tt → 6q

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5

R

fraction of pp→tt→6q events with all Rqq > R

pp, 7 TeV

Alpgen partons

no pt cut on quarks




0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5

R


pp, 7 TeV

Alpgen partons

require all ptq > 10 GeV




0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5

R


pp, 7 TeV

Alpgen partons





0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5

R


pp, 7 TeV

Alpgen partons


Herwig pp → tt → hadronsDistribution of number of jets

0

1

2

3

4

0 2 4 6 8 10 12

dσ/d

nje

ts [a

rb. u

nits

]

number of jets

pp, 7 TeVHerwig 6.5 (no UE)

anti-kt R=0.5

pt,jet > 20 GeV


Take-home messages

◮ We can (sort of) calculate the relation between jet pt and parton pt

◮ That guides us in how to “focus” jets◮ generally want small R and low pt , because UE is large◮ larger R at high pt ’s◮ smaller R helps resolve multi jets, as in tt, SUSY, black holes, etc.

ATLAS mostly uses R = 0.4; also R = 0.6

CMS mostly uses R = 0.5; also R = 0.7 & “wide” jets

◮ Large di/multi-jet mass is not enough when looking for signals — QCDvery enhanced at small angles, signals aren’t

◮ Relation between number of partons & number is non-trivial at highmultiplicities


EXTRAS


Robustness: Mtop varies with R?

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

150 160 170 180 190 200

1/n

dn/d

m

reconstructed mt [GeV/c2]

kt

Pythia 6.325, mt = 175 GeV/c2

R=0.4tt -> bqq+bµνµ

no UE

with UE

Mtop

Game: measure top mass to 1 GeVexample for Tevatron

mt = 175 GeV

◮ Small R : lose 6 GeV to PTradiation and hadronisation, UEand pileup irrelevant

◮ Large R : hadronisation and PTradiation leave mass at∼ 175 GeV, UE adds 2− 4 GeV.

Is the final top mass (after W jet-energy-scale and Monte Carlo unfolding)independent of R used to measure jets?

Flexibility in jet finding gives powerful cross-check of systematic effects

cf. Seymour & Tevlin ’06



0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

150 160 170 180 190 200

1/n

dn/d

m


kt



no UE

with UE

Mtop

Game: measure top mass to 1 GeVexample for Tevatron

mt = 175 GeV








0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

150 160 170 180 190 200

1/n

dn/d

m


kt



no UE

with UE Game: measure top mass to 1 GeVexample for Tevatron

mt = 175 GeV








0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

150 160 170 180 190 200

1/n

dn/d

m


kt



no UE


mt = 175 GeV







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