Jet Substructure at the LHC Wouter Waalewijn LANL - January 8, 2015 - - PowerPoint PPT Presentation

SLIDE 1

Jet Substructure at the LHC

Wouter Waalewijn LANL - January 8, 2015

SLIDE 2

Outline

• Introduction
• Jet Charge
• Jet Mass
• Hadronization of Jets
• Quark/Gluon Discrimination
• Conclusions

SLIDE 3

Introduction

SLIDE 4

What is a Jet?

Produce jets of hadrons Energetic quarks and gluons radiate and hadronize

4

g g g g q q q q

q q ¯ q ¯ q g g g g

SLIDE 5

• Repeatedly cluster nearest “particles”
• Cut off by jet “radius”

Rapidity

y

Azimuthal angle

φ

Jet Algorithms

pi, pj → pi + pj

5

R pT

distance = (∆y)2 + (∆φ)2

15o 2o 90o

SLIDE 6

• Repeatedly cluster nearest “particles”
• Cut off by jet “radius”
• Default at LHC: anti-

Rapidity

y

Azimuthal angle

φ

Jet Algorithms

kT pi, pj → pi + pj

(Cacciari, Salam, Soyez)

(arXiv:0802.1189)

6

R

Rapidity

y

Azimuthal angle

φ

15o 2o 90o

pT pT

SLIDE 7

Jets at the LHC

• Most measurements involve jets as signal or background

7

SLIDE 8

• Bin by jet multiplicity to improve background rejection

• Large logarithms lead to large theory uncertainties

Jet Cross Sections

(Berger, Marcantonini, Stewart, Tackmann, WW; Banfi, Monni, Salam, Zanderighi, Becher, Neubert, Rothen; Stewart, Tackmann, Walsh, Zuberi; Liu, Petriello; Boughezal, Focke, Li, Liu; Jaiswal, Okui, …)

σ(H + 0 jets) ∝ 1 − 6αs π ln2 pcut

T

mH + . . .

(ATLAS-CONF-2013-030)

1 2 3 4 5 6 7

Events / bin

10 20 30 10 × µ e (b) All jets,

j

n stat ± Obs syst ± Exp DY Top Higgs VV Misid WW

ATLAS Prelim.

WW* → H

• 1

fb 20.3 = t d L

∫

TeV, 8 = s

Number of jets

H → WW

(ATLAS-CONF-2014-060)

no jets above this pT Events/bin

SLIDE 9

(ATLAS-CONF-2013-052)

• New heavy particles could produce boosted top, W, Higgs


decay products lie within one “fat” jet

• Distinguish from QCD jets using jet substructure
• Avoids combinatorial background

Jet Substructure for Boosted Objects

9

Hadronic decay of top quark

SLIDE 10

• One leptonic and one hadronic top
• Boosted analysis crucial for large

Top Tagging in

10

Z’ mass [TeV]

0.5 1 1.5 2 2.5 3

) [pb] t t → BR(Z’ ×

Z’

σ

• 2

10

• 1

10 1 10

2

10

3

10

• Obs. 95% CL upper limit
• Exp. 95% CL upper limit

uncertainty σ

• Exp. 1

uncertainty σ

• Exp. 2

Leptophobic Z’ (LO x 1.3)

• Obs. 95% CL upper limit
• Exp. 95% CL upper limit

uncertainty σ

• Exp. 1

uncertainty σ

• Exp. 2

Leptophobic Z’ (LO x 1.3)

ATLAS Preliminary

• 1

= 14.3 fb dt L

∫

= 8 TeV s

Z0 → t¯ t

[TeV]

t t

m Efficiency [%]

2 4 6 8 10 12 14 16 18 20 0.5 1 1.5 2 2.5 3 3.5 ATLAS Preliminary Simulation

=8 TeV s

+ jets, combined µ + jets, boosted µ e + jets, combined e + jets, boosted

mZ0

Z0 t b ¯ b ¯ ` ν ¯ u d

(ATLAS-CONF-2013-052)

SLIDE 11

Jet Substructure for Quark/Gluon Discrimination

• New physics often more quarks than QCD backgrounds
• Extensive Pythia study (Gallicchio, Schwartz)
• Charged track multiplicity and jet “girth” are good

• More variables only give


marginal improvement

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 10

2

10

3

10 charged mult R=0.5 subjet mult Rsub=0.1 mass/Pt R=0.3 girth R=0.5 |pull| R=0.3 planar flow R=0.3 group of 5 best pair charge * girth

• ptimal kernel

1st subjet R=0.5 avg kT of Rsub=0.1 decluster kT Rsub=0.1 jet shape Ψ(0.1)

Quark Jet Acceptance Gluon Rejection Gluon Rejection Gluon Rejection

Quark acceptance Gluon rejection

girth = X

i∈jet

pi

T

pJ

T

p (yi−yJ)2 + (φi−φJ)2

(arXiv:1106.3076)

11

SLIDE 12

Jet Mass and Charge

Motivation:

• Measured at the LHC
• Benchmark for our ability


to calculate substructure

• Test and improve Monte Carlo:


Herwig and Pythia differ

GeV 1 d m σ d σ 1 0.005 0.01 0.015 0.02 0.025

ATLAS

• 1

L = 35 pb

∫

2010 Data, Systematic unc. Total unc. Pythia Herwig++

= 1, |y| < 2

PV

N R=1.0

t

anti-k < 400 GeV

T

300 < p

20 40 60 80 100 120 140 160 180 200

0.2

Events/0.14e 100 200 300 400 500 ATLAS Preliminary

• 1

L dt = 5.8 fb

∫

= 8 TeV, s =0.3 κ

Data 2012

+

µ Data 2012

• µ

t MC@NLO t

+

µ t MC@NLO t

• µ

Background (MC)

+

µ Background (MC)

• µ
• 2

2 Data/MC

Jet charge [e] Jet mass [GeV]

(ATLAS-CONF-2013-086) (arXiv:1203.4606)

SLIDE 13

Jet Charge

Krohn, Lin, Schwartz, WW (arXiv:1209.2421)
 WW (arXiv:1209.3091)

SLIDE 14

Defining Jet Charge

• If too small: sensitive to soft hadrons contamination
• If too large: only sensitive to most energetic hadron 


need more statistics Qκ = X

i∈jet

Qi ⇣pi

T

pJ

T

⌘κ

(Feynman, Field)

14

κ κ

Qκ [e] κ = 0.5 Pythia

(1/σ)dσ/dQκ [e−1]

→

SLIDE 15

Historical Applications

• Test parton model
• Jet charge at LEP:
• Forward-backward charge asymmetry (AMY (1990),…)
• mixing (ALEPH (1992), …)

B0 ↔ B0

15

m

24

• J. P. Berge et al. / Quark jets
• .8

O.2

• .o'

1.0

z~

"~'~ 0.8

• .6

0.4 G2

• .q

3

' i i i

(ai v~N

^ ~ r=0.2

d - quark ~,~,", / /

,,.?/~ u-quark

(b)

z~ u N

,',, Jl~ r=0.5

d-quark i '~'~1 , ~-~__.__~; I PI \ u-quorK

,~'i if/

:r '! /7

• 2
• I

I 2

Qw

• Fig. II. Weighted charge Q~ = ]~,(zi)rei for the neutrino charged current induced hadrons traveling

forward in the hadronic c.m.s. (a) for r = 0.2, and (b) for r = 0.5. The solid curves represent the Field and Feynman predictions for the 10 GeV/c u-quark jets and the dashed lines the corresponding predictions for the 10 GeV/c d-quark jets.

• events. To compare with the predictions which are calculated for 10 GeV quark jets,

we select c.m. energies above 6 GeV. Corresponding predictions by Field and Feynman are shown for the d- and u-quark jets with the two values of r, r = 0.2 and r = 0.5 [6]. It is important to recognize that even though the Field and Feynman approach involves a parametrization of (other) leptoproduction data it gives predic- tions for the weighted charge which differ according to the flavour of the fragment- ing quark. The average weighted charge values are given in table 1 with the

• predictions. Experimental results for the weighted charge for antineutrino (neutrino)

charged current events are consistent with the predictions for the d-quark (u-quark) jets but not with the predictions for the u-quark (d-quark) jets. We have considered possible effects caused by the use of a nuclear target in this

• experiment. Nuclear break-up products generally increase the visible net charge of

the observed final state hadrons. Our selection criteria for the current fragments usually removes the slow secondary particles arising from the nuclear break-up, but it is expected that a small contamination from the nuclear fragments remains in our sample of events. To study these effects, we have selected a sample of events in which the net visible charge of the final state hadrons, Qv, corresponds to the initial state charge within one unit, i.e., we select -2 < Qv < 1. Effects of this selection on the measured jet net charge and on the measured weighted charge are summarized in

J.P. Berge et al. / Quark jets

23

• experiments. From the K +/~r + ratio in high energy proton-proton experiments [23]

extrapolated to the Feynman x of one (to avoid resonance contributions), we estimate Ps/P ~0.50. Another estimate of Ps/P can be obtained from the cross section ratios (J/q~ ~ K + K*)/(Jfl~b ~ p~') corrected for phase-space factors [241. The result pJp = 0.49 __ 0.11 implies p = 6.40 __+ 0.02. An electroproduction experi- ment obtains for the ratio (K ° + K.°)/(~r + +~r-) a value of 0.13 _+ 0.03 which the

authors interpret as the ratio Ps/P (ref. [25]); this value would mean considerably stronger SU(3) symmetry violation in the quark jets. A jet net charge measurement in the same experiment, on the other hand, gives p~/p = 0.36 (ref. [261), which is again consistent with our measurements. Field and Feynman have proposed an alternative way of distinguishing quark jets

• f different flavour [6]. There, one weights each particle with a z-dependent weight

such that particles closer to the overlap region get a small weight and particles with large fractional energy z (further from the overlap region) get a large weight; i.e., the weighted charge is defined as Q~ = Y~(zi)re~, where r is a small number and e~ is the integer charge of the ith hadron in the final state. Resulting distributions from our experiment are shown in fig. 10 (fig. 11) for antineutrino (neutrino) charged current 0.81- r=0.2

[ d-quark ~,.

t

• ,

I

2"

0.01.~.,~-~.~ .... . • ~-~...-.~

'

. . . . . . . N

1.0 ~ r=0.5 d-quark ZO" 0.8 v~(/' ~ u-quark

• oho

~i,;

• .

O.C

' -'"

• 3
• 2
• I

I 2

• Fig. 10. Weighted charge Q~; = Yi(z,)re, for the antineutrino charged current induced hadrons traveling

forward in the hadronic'c.m.s. (a) for r= 0.2, and (b) for r = 0.5. The solid curves represent the Field and Feynman predictions for the hadrons arising from the fragmentation of a u-quark with 10 GeV/c incident momentum and the dashed lines the corresponding predictions for the 10 GeV/c d-quark jets.

ro

24

• J. P. Berge et al. / Quark jets
• .8

O.2

• .o'

1.0

z~

"~'~ 0.8

• .6

0.4 G2

• .q

3

' i i i

(ai v~N

^ ~ r=0.2

d - quark ~,~,", / /

,,.?/~ u-quark

(b)

z~ u N

,',, Jl~ r=0.5

d-quark i '~'~1 , ~-~__.__~; I PI \ u-quorK

,~'i if/

:r '! /7

• 2
• I

I 2

Qw

• Fig. II. Weighted charge Q~ = ]~,(zi)rei for the neutrino charged current induced hadrons traveling

forward in the hadronic c.m.s. (a) for r = 0.2, and (b) for r = 0.5. The solid curves represent the Field and Feynman predictions for the 10 GeV/c u-quark jets and the dashed lines the corresponding predictions for the 10 GeV/c d-quark jets.

• events. To compare with the predictions which are calculated for 10 GeV quark jets,

we select c.m. energies above 6 GeV. Corresponding predictions by Field and Feynman are shown for the d- and u-quark jets with the two values of r, r = 0.2 and r = 0.5 [6]. It is important to recognize that even though the Field and Feynman approach involves a parametrization of (other) leptoproduction data it gives predic- tions for the weighted charge which differ according to the flavour of the fragment- ing quark. The average weighted charge values are given in table 1 with the

• predictions. Experimental results for the weighted charge for antineutrino (neutrino)

charged current events are consistent with the predictions for the d-quark (u-quark) jets but not with the predictions for the u-quark (d-quark) jets. We have considered possible effects caused by the use of a nuclear target in this

• experiment. Nuclear break-up products generally increase the visible net charge of

the observed final state hadrons. Our selection criteria for the current fragments usually removes the slow secondary particles arising from the nuclear break-up, but it is expected that a small contamination from the nuclear fragments remains in our sample of events. To study these effects, we have selected a sample of events in which the net visible charge of the final state hadrons, Qv, corresponds to the initial state charge within one unit, i.e., we select -2 < Qv < 1. Effects of this selection on the measured jet net charge and on the measured weighted charge are summarized in

J.P. Berge et al. / Quark jets

23

• experiments. From the K +/~r + ratio in high energy proton-proton experiments [23]

extrapolated to the Feynman x of one (to avoid resonance contributions), we estimate Ps/P ~0.50. Another estimate of Ps/P can be obtained from the cross section ratios (J/q~ ~ K + K*)/(Jfl~b ~ p~') corrected for phase-space factors [241. The result pJp = 0.49 __ 0.11 implies p = 6.40 __+ 0.02. An electroproduction experi- ment obtains for the ratio (K ° + K.°)/(~r + +~r-) a value of 0.13 _+ 0.03 which the

authors interpret as the ratio Ps/P (ref. [25]); this value would mean considerably stronger SU(3) symmetry violation in the quark jets. A jet net charge measurement in the same experiment, on the other hand, gives p~/p = 0.36 (ref. [261), which is again consistent with our measurements. Field and Feynman have proposed an alternative way of distinguishing quark jets

• f different flavour [6]. There, one weights each particle with a z-dependent weight

such that particles closer to the overlap region get a small weight and particles with large fractional energy z (further from the overlap region) get a large weight; i.e., the weighted charge is defined as Q~ = Y~(zi)re~, where r is a small number and e~ is the integer charge of the ith hadron in the final state. Resulting distributions from our experiment are shown in fig. 10 (fig. 11) for antineutrino (neutrino) charged current 0.81- r=0.2

[ d-quark ~,.

t

• ,

I

2"

0.01.~.,~-~.~ .... . • ~-~...-.~

'

. . . . . . . N

1.0 ~ r=0.5 d-quark ZO" 0.8 v~(/' ~ u-quark

• oho

~i,;

• .

O.C

' -'"

• 3
• 2
• I

I 2

• Fig. 10. Weighted charge Q~; = Yi(z,)re, for the antineutrino charged current induced hadrons traveling

forward in the hadronic'c.m.s. (a) for r= 0.2, and (b) for r = 0.5. The solid curves represent the Field and Feynman predictions for the hadrons arising from the fragmentation of a u-quark with 10 GeV/c incident momentum and the dashed lines the corresponding predictions for the 10 GeV/c d-quark jets.

b )

d d u u u d νµp → µ−uX ¯ νµp → µ+dX

κ = 0.5 κ = 0.5 Q0.5 [e] Q0.5 [e]

(1/σ)dσ/dQ0.5 [e−1] (1/σ)dσ/dQ0.5 [e−1]

(Nucl. Phys. B184, 13 (1981))

SLIDE 16

Possible LHC application: vs.

• Hadronically decaying or with 1 TeV mass
• 2-dim. likelihood discriminant based on both jet charges


W 0

Z0

W 0 Z0

16

ln L(W 0) − ln L(Z0) Pythia 50 events

W 0 Z0

Z0 → u¯ u Z0 → d ¯ d vs. W 0 → u ¯ d W 0 → d¯ u

SLIDE 17

LHC Challenges

• Trade off between soft contamination and statistics
• We did not include: backgrounds, detector effects, …

17

0.0 0.5 1.0 1.5 2.0 κ 1 2 3 4 5 6 Significance

Wprime vs. Zprime, 50 events FSR only FSR+MI+ISR FSR+MI+ISR+trim Npileup=10 Npileup=10 +trim

κ

Significance [σ]

W 0 vs. Z0

Pythia 50 events

SLIDE 18

LHC Challenges

• Trade off between soft contamination and statistics
• We did not include: backgrounds, detector effects, …
• Various sources of contamination:
• Initial-State Radiation
• Multiparton Interactions
• Pile-up (overestimated)
• All soft increase

18

0.0 0.5 1.0 1.5 2.0 κ 1 2 3 4 5 6 Significance

Wprime vs. Zprime, 50 events FSR only FSR+MI+ISR FSR+MI+ISR+trim Npileup=10 Npileup=10 +trim

κ

Significance [σ]

W 0 vs. Z0 κ

Pythia 50 events

SLIDE 19

Jet Charge Not IR Safe

• Consider in collinear limit
• divergences don’t cancel between real/virtual

19

q → qg q q q(z) g g(1−z) Qqzκ 6= Qq

SLIDE 20

Jet Charge Not IR Safe

• Consider in collinear limit
• divergences don’t cancel between real/virtual
• Jet charge only defined for hadrons

20

q → qg q q q(z) g g(1−z)

• 1.0
• 0.5

0.0 0.5 1.0 1 2 3 4 5 6

d 0.5

0.5

hadronic partonic

d-quark (1/σ)dσ/dQ0.5 [e−1] Q0.5[e]

Qqzκ 6= Qq

Pythia

SLIDE 21

Average Jet Charge Calculation

• At LO, weight = fragmentation function

21

hQκi = X

h

Z dz | {z }

hadron h

Qhzκ | {z }

charge

1 σjet dσh∈jet dz | {z }

weight

Dh

q (z, µ ∼ pJ T R)

Jet scale

SLIDE 22

Average Jet Charge Calculation

• At LO, weight = fragmentation function
• Calculate dependence from evolution to
• describes hadronization

22

hQκi = X

h

Z dz | {z }

hadron h

Qhzκ | {z }

charge

1 σjet dσh∈jet dz | {z }

weight

µ ∼ ΛQCD µ ∼ pJ

T R

µ ∼ ΛQCD Dh

q (z, µ ∼ pJ T R)

Dh

q (z, µ ∼ ΛQCD)

pJ

T , R

Jet scale

SLIDE 23

100 200 300 400 500 600 0.75 0.80 0.85 0.90 0.95 1.00

E @GeVD edD

u and d quark, anti-kT, R=0.5

k=0.5 k=1 k=2

100 200 300 400 500 600 0.8 0.9 1.0 1.1

E @GeVD XQ1

q\ @normalizedD

u and d quark, anti-kT, k=1

R=0.3 R=0.5 R=1

RG Evolution vs. Pythia’s Parton Shower

23

hQκi [normalized] hQκi [normalized]

perturbative splitting + evolution

}

hQκ(pJ

T R, flavor)i = perturbative(κ, pJ T R) ⇥ hadronization(κ, flavor)

hQκ(pJ

T R)i

hQκ(50 GeV)i pJ

T [GeV]

pJ

T [GeV]

R = 0.5 κ = 1

• Normalize average jet charge:





Hadronization (and flavor dependence) drops out


• ✓ Good agreement

SLIDE 24

• Average jet charge at 



 


• ✓ Pythia consistent with fragmentation functions
• Large uncertainties as we need





Most fragmentation data is giving

Fragmentation Functions vs. Pythia’s Hadronization

24

u-quark d-quark κ PYTHIA DSS AKK08 PYTHIA DSS AKK08 0.5 0.271 0.237 0.221

• 0.162
• 0.184
• 0.062

1 0.144 0.122 0.134

• 0.078
• 0.088
• 0.046

2 0.055 0.046 0.064

• 0.027
• 0.030
• 0.027

(DSS = De Florian, Sassot, Stratmann, AKK08 = Albino, Kniehl, Kramer)

Dh+

q −Dh− q

= Dh+

q −Dh+ ¯ q

e+e− Dh+

q +Dh+ ¯ q

pJ

T = 100 GeV, R = 0.5

SLIDE 25

• Depends on proton structure

and scattering process

• Pure QCD measurement of

valence structure of proton!

• Study of scale violation

effect is ongoing

Average Dijet Charge at the LHC

25

Dijet Mass [GeV] Dijet Charge [e]

• 0.05

0.05 0.1 0.15 0.2 0.25 0.3 ATLAS Preliminary

• 1

L dt = 5.8 fb

∫

= 8 TeV, s =1.0 κ =0.3 κ Pythia Dijets Data

Dijet Mass [GeV] 500 1000 1500

Data/MC

1 2

Dijet mass [GeV] Dijet charge [e]

(ATLAS-CONF-2013-086)

SLIDE 26

e splitting Parton shower Hadronization

Full Jet Charge Distribution

• Perturbative splitting reduces -dependence (Jain, Procura, WW)
• Hadronization depends on full charge distribution
• Related to multi-hadron fragmentation functions

26

Perturbative splitting Shower evolution Hadronization

µ ∼ ΛQCD µ ∼ pJ

T R

µ Di(Qκ, µ)

SLIDE 27

Full Jet Charge Distribution

• RGE:

27

µ d dµ Di(Qκ, µ) =

Splitting probability

z }| { X

j

Z dz αs 2π Pji(z)

Sample over distributions of branches

z }| { Z dQa

κ Dj(Qa κ, µ)

Z dQb

κ Dk(Qb κ, µ)

× δ[Qκ − zκQa

κ − (1 − z)κQb κ]

| {z }

Charge is (weighted) sum of branches

Perturbative splitting Shower evolution Hadronization i j(z) k(1−z)

µ ∼ ΛQCD µ ∼ pJ

T R

SLIDE 28

RG Evolution vs. Pythia’s Parton Shower

✓ Use Pythia as input and evolve good agreement

• Distribution changes more slowly than single hadron

distributions (e.g. fragmentation functions)

28

• 1.0
• 0.5

0.0 0.5 1.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0

@eD @ D

Pythia at pTR=40 Evolve to pTR=400 Pythia at pTR=400

flavor=d

• 1.0
• 0.5

0.0 0.5 1.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

@eD @ D

Pythia at pTR=40 Evolve to pTR=400 Pythia at pTR=400

flavor=g

(1/σ)dσ/dQ1 [e−1] (1/σ)dσ/dQ1 [e−1] Q1 [e] Q1 [e] d-quark, κ = 1 gluon, κ = 1

SLIDE 29

Jet Mass

Jouttenus, Tackmann, Stewart, WW (arXiv:1302.0846)

SLIDE 30

30

Jet Mass Resummation

LL NLL NNLL

• Jet mass is defined as 

• Cross section contains logarithms of
• Need to resum dominant higher-order effects for
• Nonsingular is suppressed by

ni m2

J =

✓ X

i∈jet

pµ

i

◆2

Z mcut

J

dmJ dσ dmJ = σ0

• 1 + αs[c12L2+c11L+c10+n1(mcut

J )]

+ α2

s[c24L4+c23L3+c22L2+c21L + c20 + n2(mcut J )]

+ α3

s[c36L6+c35L5+c34L4+c33L3 + c32L2 + . . . ]

+ . . . + . . . + . . . + . . . + ...

L = ln(mcut

J /pJ T )

(mcut

J /pJ T )2

mcut

J

⌧ pJ

T

SLIDE 31

Jet Mass and Jet Definition

• Clustering algorithms theoretically complicated
• Jet mass spectrum is fairly independent of jet definition


use -jettiness (with correct )

31

Geometric R1 CA R1 antikT R1 antikT R1.2

Pythia, ggHg, cut25 GeV, ΗJ0.2, 280pT J 320 GeV

50 100 150 200 0.000 0.005 0.010 0.015

mJ [GeV] (1/σ)dσ/dmJ [GeV−1]

→ N R

SLIDE 32

• Jettiness Event Shape

32

N

• Reference vectors: ,
• for narrow jets, large for jets
• Used as substructure (Thaler, van Tilburg), 1-jettiness in DIS 


(Kang, Liu, Mantry, Qiu; Kang, Lee, Stewart) beams jets

W/Z qb qa q1 q2

T a

N

T b

N

T 1

N

T 2

N

• TN → 0

TN N > N TN = X

i

min{ˆ qa · pi, ˆ qb · pi, ˆ q1 · pi, . . . } = T a

N + T b N + T 1 N + . . .

ˆ qa,b = (1, 0, 0, ±1)

(Stewart, Tackmann, WW) jet size parameter

ˆ qJ = (1, ˆ nJ)/ρJ

jet axis

SLIDE 33

• Jettiness Event Shape

33

N

• Reference vectors: ,
• for narrow jets, large for jets
• Used as substructure (Thaler, van Tilburg), 1-jettiness in DIS 


(Kang, Liu, Mantry, Qiu; Kang, Lee, Stewart)

• splits into contributions 


from each beam/jet region

• Related to jet mass:

beams jets

W/Z qb qa q1 q2

T a

N

T b

N

T 1

N

T 2

N

• TN → 0

TN > N TN TN = X

i

min{ˆ qa · pi, ˆ qb · pi, ˆ q1 · pi, . . . } = T a

N + T b N + T 1 N + . . .

ˆ qa,b = (1, 0, 0, ±1)

(Stewart, Tackmann, WW)

ˆ qJ = (1, ˆ nJ)/ρJ m2

J = 2ρJEJT J N

N

SLIDE 34

• Jettiness Parameters

34

N

• Reference vectors: ,
• by minimizing or from jet alg. (same for )
• Choose to match jet area of anti-

beams jets

TN = X

i

min{ˆ qa · pi, ˆ qb · pi, ˆ q1 · pi, . . . } = T a

N + T b N + T 1 N + . . .

ˆ qa,b = (1, 0, 0, ±1) TN → 0 TN kT

• 0.0

0.5 1.0 1.5 0.0 0.5 1.0 1.5

R ΡR,ΗJ0 R R2 R3

• 4

3 2 1 1 2 3 4 3 2 1 1 2 3

Η Φ

geometric R1 antikT

y φ

ρJ = ρ(R, ηJ) ˆ qJ = (1, ˆ nJ)/ρJ ˆ nJ

SLIDE 35

35

f

H

I I

J

f

1 2 3

s

soft or Glauber − +

J J

• Hard scattering
• Initial state radiation (+PDFs)
• Final state radiation
• Soft radiation
• Jettiness Factorization

N

dσ(N jets) dT a

N dT b N · · · dT N N

= Z dxa dxb d(phase space) X

κ

Z dta Bκa(ta, xa, µ) × Z dtb Bκb(tb, xb, µ)

N

Y

J=1

Z dsJ JκJ(sJ, µ) tr  Hκ

N({qµ i }, µ)

× Sκ

N

✓ T a

N − ta

Qa , T b

N − tb

Qb , . . . , T N

N − sN

QN ,

• ˆ

qi , µ ◆

SLIDE 36

• Jettiness Factorization

N

• Separating physics at different scales enables resummation
• At NNLL order need one-loop

• Three-loop cusp and two-loop non-cusp anomalous dim.

B, J, H, S

B: Stewart, Tackmann, WW; Mantry, Petriello, J: Bauer, Manohar; Fleming, Leibovich, Mehen; Becher, Schwartz One-loop H for H+1-jet: Schmidt, One-loop S for N-jettiness: Jouttenus, Stewart, Tackmann, WW Three-loop cusp: Korchemsky, Radyushkin; Moch, Vermaseren, Vogt, Two-loop non-cusp known from: Kramer, Lampe; Harlander; Aybat, Dixon, Sterman; Becher, Neubert; Becher, Schwartz; Stewart, Tackmann, WW

dσ(N jets) dT a

N dT b N · · · dT N N

= Z dxa dxb d(phase space) X

κ

Z dta Bκa(ta, xa, µ) × Z dtb Bκb(tb, xb, µ)

N

Y

J=1

Z dsJ JκJ(sJ, µ) tr  Hκ

N({qµ i }, µ)

× Sκ

N

✓ T a

N − ta

Qa , T b

N − tb

Qb , . . . , T N

N − sN

QN ,

• ˆ

qi , µ ◆

H µH µSB µSJ µB µJ J B

SLIDE 37

Normalization

• We are required to veto additional jets through
• Normalizing the spectrum removes this dependence:








• Experimental results are also normalized

σ(T a

1 , T b 1 ≤ T cut, mJ, pJ T , yJ, Y )

R dmJ σ(T a

1 , T b 1 ≤ T cut, mJ, pJ T , yJ, Y )

T a

1 , T b 1

cut10 GeV cut25 GeV No jet veto

ggHg, ΗJ0.2, 280pT J 320 GeV

Pythia, Geometric R1 50 100 150 200 0.000 0.005 0.010 0.015

mJ [GeV] (1/σ)dσ/dmJ [GeV−1]

37

SLIDE 38

Perturbative Convergence

• We consider and


(proxies for gluon and quark jets)

✓ Good agreement between LL, NLL, NNLL

50 100 150 200 0.000 0.005 0.010 0.015

m @GeVD ê

J @normalizedD

NNLL NLL LL

Y=0, hJ=0, pT

J =300 GeV, T cut= 25 GeV

ggÆHg, Geometric R=1

mJ [GeV] (1/σ)dσ/dmJ [GeV−1]

50 100 150 200 0.000 0.005 0.010 0.015 0.020

eVD ê

J @

D NNLL NLL LL

Y=0, hJ=0, pT

J =300 GeV, T cut= 25 GeV

gqÆHq, Geometric R=1

mJ [GeV] (1/σ)dσ/dmJ [GeV−1]

gg → Hg gq → Hq

38

Gluon Quark

SLIDE 39

Dependence on Kinematics and Jet Radius

• Calculable dependence on kinematics
• Strong dependence on jet radius since


(Nonsingular important!)

39

mJ [GeV]

50 100 150 200 250 300 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016

eVD D pT

J = 325 GeV

pT

J = 425 GeV

pT

J = 525 GeV

ppÆH+1 j, R=1, NNLL

hJ = 0, Y = 0, Tcut=25 GeV

(1/σ)dσ/dmJ [GeV−1] mJ [GeV] (1/σ)dσ/dmJ [GeV−1]

25 50 75 100 125 150 175 200 0.000 0.005 0.010 0.015 0.020

eVD D R=0.5 R=0.8 R=1.2 ppÆH+1 j, pT

J = 325 GeV, NNLL

hJ = 0, Y = 0, Tcut=25 GeV

pJ

T , yJ, Y

mJ . pJ

T R/

√ 2

SLIDE 40

Comparison to Pythia and Herwig

✓ Reasonable agreement over a range of kinematics and

• No clear favorite between Pythia or Herwig
• Big differences for

40

25 50 75 100 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035

eVD D NNLL Herwig Pythia qg Æ Zq, partonic, R = 0.5

NNLL: pT

J = 325 GeV, hJ = 0, Y = 0

MC: 300 £ pT

J £ 350 GeV, »hJ» £ 0.2

mJ [GeV] (1/σ)dσ/dmJ [GeV−1]

50 100 150 200 250 300 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014

eVD D NNLL Herwig Pythia qg Æ Zq, partonic, R = 1.2

NNLL: pT

J = 325 GeV, hJ = 0, Y = 0

MC: 300 £ pT

J £ 350 GeV, »hJ» £ 0.2

mJ [GeV] (1/σ)dσ/dmJ [GeV−1]

Quark, R = 0.5 Quark, R = 1.0

R < 0.5 R

SLIDE 41

Comparison to Pythia and Herwig

• Reasonable agreement over a range of kinematics and
• No clear favorite between Pythia or Herwig
• Big differences for

41

R

50 100 150 200 250 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014

eVD H ê L ê

J @

D NNLL Herwig Pythia qq Æ Zg, partonic, R = 1

NNLL: pT

J = 325 GeV, hJ = 0, Y = 0

MC: 300 £ pT

J £ 350 GeV, »hJ» £ 0.2

mJ [GeV] (1/σ)dσ/dmJ [GeV−1]

50 100 150 200 250 300 350 400 450 0.000 0.002 0.004 0.006 0.008

eVD D NNLL Herwig Pythia qq Æ Zg, partonic, R = 1

NNLL: pT

J = 575 GeV, hJ = 0, Y = 0

MC: 550 £ pT

J £ 600 GeV, »hJ» £ 0.2

mJ [GeV] (1/σ)dσ/dmJ [GeV−1]

R < 0.5

Gluon, 300 ≤ pJ

T ≤ 350 GeV

Gluon, 550 ≤ pJ

T ≤ 600 GeV

SLIDE 42

Other Jet Mass Calculations

• +jet and dijets
• NLL+NLO
• Key differences:
• +jet
• NNLL threshold resum.

γ Z

2 4 6 8 10 12 14 0.05 0.1 0.15 0.2 0.25 0.3 1/σ d σ/ d ζ ζ= mJ/pTJ Z+jet, R=0.6, pTJ > 200 GeV NLL+LO Sherpa PS Pythia 8 PS Herwig++ PS

LO refactorization refactorization refactorization

0.5

20 40 60 80 100 120 140 0.000 0.001 0.002 0.003 0.004 0.005

PYTHIA with hadronization PYTHIA wo hadronization

pT 500 GeV, R 0.5 NLL NNLLP

50 100 150 0.000 0.001 0.002 0.003 0.004 0.005 0.006

mR GeV dΣ dmR fb

Dasgupta et al. (arXiv:1207.1640) Chien et al. (arXiv:1208.0010)

• jet algorithm
• no jet veto large nonglobal logarithms

SLIDE 43

Hadronization of Jets

Tackmann, Stewart, WW (arXiv:1405.6722)

SLIDE 44

(Korchemsky, Sterman; Hoang, Stewart; Ligeti, Stewart, Tackmann)

• Soft function describes soft radiation:





• Color indices on Wilson lines are not written out
• Perturbative and nonperturbative contribution:

measurement

Factorization for Jet Mass

f

H

I I

J

f

1 2 3

s

soft or Glauber − +

J J

dσ dm2

J

= ff I I H Z dks J(m2

J − 2pJ T ks) S(ks)

S(ks) = h0|Y †

J (yJ)Y † ¯ nY † n δ(ks cosh yJ nJ ·ˆ

pJ) YnY¯

nYJ(yJ)|0i

Jet function Soft function

S(ks) = Z dk0

s Spert(ks − k0 s)FNP(k0 s)

eikonal Wilson lines

k0

s ∼ ΛQCD

SLIDE 45

• Expanding




• Shifts jet mass spectrum


(valid in tail of distribution)

• is universal for event shapes. 


(Dokshitzer, Webber; Akhoury, Zakharov; Lee, Sterman; Mateu, Stewart, Thaler)





How is this affected by jets? Ω = h0|Y †

J (yJ, φJ)Y † ¯ nY † n cosh yJ nJ ·ˆ

pJ YnY¯

nYJ(yJ, φJ)|0i

Leading Nonperturbative Effect

45

Yn Y¯

n

YJ(yJ, φJ) FNP(ks) = δ(ks) − Ω δ0(ks) + . . .

Ω

m2

J → m2 J + 2pJ T Ω

Ω e+e−

SLIDE 46

• is independent of by definition
• ’s and thus depend on color configuration


Ω = h0|Y †

J (yJ, φJ)Y † ¯ nY † n cosh yJ nJ ·ˆ

pJ YnY¯

nYJ(yJ, φJ)|0i

Properties of

46

Y Ω Ω pJ

T

Ω

Yn Y¯

n

YJ(yJ, φJ)

SLIDE 47

• is independent of by definition
• ’s and thus depend on color configuration
• Rotating + boosting shows that is independent of
 yJ, φJ

Ω = h0|Y †

J (yJ, φJ)Y † ¯ nY † n cosh yJ nJ ·ˆ

pJ YnY¯

nYJ(yJ, φJ)|0i

Properties of

47

Y

Ω

Ω Ω pJ

T

Boost+Rotation

Yn Y¯

n

Y¯

n

Yn YJ(yJ, φJ) YJ(0, 0)

Ω

SLIDE 48

Yn(ln R

2 , 0)

Y¯

n(ln R 2 , π)

Boost Y¯

n(0, π)

Yn(0, 0) YJ YJ

48

Rotate
 coordinate
 system

jet boundary

nJ ·ˆ pJ → R 2 nJ ·ˆ pJ

Dependence of on Jet Radius R

48

Ω

• For , the beam Wilson lines fuse and
• only depends on quark vs. gluon, equal to (for q)
• Only odd powers of arise

R ⌧ 1 R Ω = R

2 Ω0 + . . .

Ω0 ΩDIS

( : Dasgupta, Salam; Kang, Liu, Mantry, Qiu; Kang, Lee, Stewart) ΩDIS

SLIDE 49

Hadronization captured by

49

PYTHIA8 AU2 qg Æ Zq H7 TeVL partonic hadronic partonic + W

300 < pT

J < 400 GeV

»yJ» < 2, R = 1

50 100 150 200 0.000 0.005 0.010 0.015 0.020 0.025

mJ @GeVD H1êsL dsêdmJ @GeV-1D

mJ [GeV] (1/σ)dσ/dmJ [GeV−1]

Agrees with factorization predictions:

✓ Hadronization in the tail satisfies m2

J → m2 J + 2pJ T Ω

Ω

SLIDE 50

Hadronization captured by

50

Peak at ∼ Ω

1 2 3 4 5 0.0 0.2 0.4 0.6 0.8 1.0

ks @GeVD FNPHksL @GeV-2D

PYTHIA8 AU2 qg Æ Zq H7 TeVL partonic hadronic partonic + W partonic ƒ F

300 < pT

J < 400 GeV

»yJ» < 2, R = 1

50 100 150 200 0.000 0.005 0.010 0.015 0.020 0.025

mJ @GeVD H1êsL dsêdmJ @GeV-1D

Ω = Z dks ks FNP(ks)

mJ [GeV] (1/σ)dσ/dmJ [GeV−1]

Agrees with factorization predictions:

✓ Hadronization in the tail satisfies ✓ More general:

m2

J → m2 J + 2pJ T Ω

dσ dm2

J

→ Z ∞ dks dσ dm2

J

(m2

J − 2pJ T ks) FNP(ks)

Ω

SLIDE 51

Hadronization dependence on

✓ Agrees with factorization predictions


51

qg Zq qq Zg gg Hg PYTHIA8 AU2 part had

Ecm 7 TeV, R 1 yJ 1

150 200 250 300 350 400 450 500 0.0 0.5 1.0 1.5 2.0 2.5 3.0 pT

J GeV

hadR R2 GeV qg Zq qq Zg gg Hg HERWIG part had

Ecm 7 TeV, R 1 yJ 1

150 200 250 300 350 400 450 500 0.0 0.5 1.0 1.5 2.0 2.5 3.0 pT

J GeV

hadR R2 GeV

pJ

T

pJ

T

pJ

T

SLIDE 52

Hadronization dependence on

✓ Agrees with factorization predictions


52

qg Zq qq Zg gg Hg HERWIG part had

Ecm 7 TeV, R 0.8 300 pT

J 400 GeV

0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 yJ hadR R2 GeV qg Zq qq Zg gg Hg PYTHIA8 AU2 part had

Ecm 7 TeV, R 0.8 300 pT

J 400 GeV

0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 hadR R2 GeV

yJ

|yJ| |yJ|

SLIDE 53

Hadronization dependence on

✓ Linear coefficient only depends on quark vs. gluon

? Quark and gluon jets much more similar in Herwig

• Better fit to odd powers of in Pythia

53

qg Æ Zq qq Æ Zg gg Æ Hg PYTHIA8 AU2 Hpart Æ hadL ~ R H+ R3 + R5L

Ecm = 7 TeV, »yJ» < 2 300 < pT

J < 400 GeV

0.0 0.5 1.0 1.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 R WhadHRL @GeVD qg Æ Zq qq Æ Zg gg Æ Hg HERWIG++ Hpart Æ hadL ~ R H+ R3 + R5L

Ecm = 7 TeV, »yJ» < 2 300 < pT

J < 400 GeV

0.0 0.5 1.0 1.5 0.0 0.5 1.0 1.5 2.0 R WhadHRL @GeVD

Ω0 R R R R

R

SLIDE 54

Quark/Gluon Discrimination

Larkoski, Thaler, WW (arXiv:1408.3122)

SLIDE 55

I(A; B) = Z da db p(a, b) log2 p(a, b) p(a)p(b)

Mutual Information

55

• Can directly be calculated from double diff. cross section

• Quark/gluon discrimination is one bit of information

A B

I(A;B)

Number of bits of shared information

p(a, b) = 1 σ d2σ da db

SLIDE 56

T A B T A B

Discrimination Power

56

• same correlations
• and same individual discrimination power
• different joint discrimination power

Redundant variables: Complementary variables:

Quark/gluon discrimination

I(A; B): I(T; B): I(T; A, B): I(T; A)

SLIDE 57

Generalized Angularities

57

• IR safe, angularities (Berger, Kucs, Sterman)
• very IR unsafe, similar to jet charge
• blue: a bit IR unsafe, one nonpert. parameter at NLL

1 2 λκ

β

κ β 1 2 pD

T

eβ

width multiplicity

λκ

β =

X

i∈jet

zκ

i

✓θi R ◆β

zi = piT /pjet

T

θi

β = 0: κ = 1:

jet axis

SLIDE 58

Quark/Gluon Discrimination with

58

• (

)

> =

• (

)

> =

• (N)LL valid in

grey bounds

• LL is constant
• Significant

differences

λκ

β

Calculation uses arXiv:1306.6630 (Chang, Procura, Thaler, WW)

• ++

(

)

> =

• (

)

> =

SLIDE 59

• (N)LL valid in

grey bounds

• LL not const.
• Significant

differences

Quark/Gluon Discrimination with

59

= = = = = = = = ++ (

• )

> =

• =

= = = = = = = (

• )

> =

• =

= = = = = = =

• - (
• )

> =

• =

= = = = = = = (

• )

> =

• λρ

α, λκ β

Calculation uses arXiv:1401.4458 (Larkoski, Moult, Neill)

SLIDE 60

Conclusions

• Many LHC searches involves jets as signal or background
• Jet substructure provides a new set of tools for e.g.:
• Boosted objects Quark vs. gluon
• Much theoretical work remains to be done
• Gain insight Improve predictions/Monte Carlo
• Factorization is key: separating physics at different scales

Calculate jet mass and charge Universality of hadronization for jets with

• R ⌧ 1