Understanding Jet SubstructureJonathan Walsh, University of Washington

work with Steve Ellis, Chris Vermilion

1

Overview

Heavy particle searches and jet algorithms

Systematics in jet substructure

Reducing systematics

Results from studies on top reconstruction

Future Prospects

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Jets at the LHCJets will play a large role in understanding the physics at the LHC.

Heavy particles can be produced and decay hadronically into single jets.

Want to understand more innovative ways to use jets in analyses.

Many heavy QCD jets (mass > W/Z mass) at the LHC - forms a large background.

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Finding Heavy Particles with Jets

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ttbar QCD dijet

QCD multijet production overwhelms the production rate for heavy particles.

In the jet mass spectrum, production of non-QCD jets may appear as local excesses (bumps!) that must be identified and enhanced using analyses.

Want to find techniques that will help identify non-QCD jets.

Jet substructure is a prime candidate - comes from recombination algorithms.

σttbar ⋲ 10-3σj j

arb.

uni

ts

arb.

uni

tsfalling , no intrinsic

large mass scaleshaped by

the jet algorithm

Recombination Jet AlgorithmsRecombination algorithms (kT, CA) use metrics between 4-vectors to pairwise merge objects and form jets.

Metrics for kT:

Metrics for CA:

The metrics are based on the dominant physics in the QCD shower.

They will shape the substructure of the jet in predictable ways.

jet

ρkT(i, j) = min(pTi, pTj

)∆Rij

Dρb,kT(i) = pTi

ρCA(i, j) =∆Rij

Dρb,CA(i) = 1

5

Do the kinematics of the substructure match that of a

decaying heavy particle?

Using Jet Substructure

Can we use the substructure to help separate QCD jets from jets reconstructing heavy particle decays?

Want to map the kinematics at the vertices onto a decay.

Masses (jet and subjet) are key variables - strong discriminators between QCD and non-QCD jets.

How does the choice of algorithm affect the substructure we will observe?

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t

W

b

q

q’ ↔jet

Reconstruction in Jet SubstructureWant to identify a heavy particle reconstructed in a single jet.

Requires a correct ordering in the substructure and accurate reconstruction.

Must understand how decays and QCD differ in their expected substructure.

Makes reconstruction sensitive to systematics of the jet algorithm.

Jet substructure affected by the systematics of the algorithm.

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t

W

b

q

q’ ↔jet

uncorrelatedmerging

?

Systematics of the Jet Algorithm

The metrics of kT and CA will shape the jet substructure.

Consider generic recombination step: i,j ➜ p

Useful variables:

Merging metrics:

In terms of z, θ, the algorithms will give different kinematic distributions:

CA orders only in θ : z is unconstrained

kT orders in z·θ : z and θ are both regulated

z =min(pTi

, pTj)

pTp

θ = ∆Rij

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ρkT = pTpzθ/D ρCA = θ/D

Studying Systematics: QCD Jets

We compare the substructure of the kT and CA algorithm by looking at jets in QCD dijet events.

High pT jets: 300-500 GeV - these jets will be part of a background sample used in later studies on top reconstruction.

Use a large D jet algorithm: D = 1.0

Look at LAST recombinations in the jet - these are the parts of the substructure that will be tested to determine whether the jet is likely to come from a heavy particle decay.

Labeling for the last recombination: 1,2 ➜ J

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Systematics of Algorithm: θConsider θ on LAST recombination for CA and kT.

CA orders only in θ - means θ tends to be large (often close to D) at the last merging.

kT orders in z·θ, meaning θ can be small

Get a distribution in θ that is more weighted towards small θ than CA

CA kT

10D D

norm

aliz

ed

dist

ribu

tion

s

Consider z on LAST recombination for CA and kT.

Metric for CA is independent of z - distribution of z comes from the ordering in θ

Periphery of jet is dominated by soft protojets - these are merged early by kT, but can be merged late by CA

CA has many more low z, large θ recombinations than kT

CA kT

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Systematics of Algorithm: zno

rmal

ized

di

stri

buti

ons

Consider heavier subjet mass at LAST recombination, scaled by the jet mass

Last recombinations in CA dominated by small z and large θ

Subjet mass for CA is close to the jet mass - a1 near 1

kT has no very soft splittings - suppression of large a1 jets

CA kT

a1 = max(m1, m2)/mj

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Systematics of Algorithm: Subjet Massesno

rmal

ized

di

stri

buti

ons

Shaping in Heavy Particle ReconstructionSome kinematic regimes of heavy particle decay have a poor reconstruction rate.

Example: Higgs decay H ➜ bb with a very backwards going b in the Higgs rest frame.

The backwards-going b will be soft in the lab frame - difficult to accurately reconstruct.

When the Higgs is reconstructed in the jet, the mass distribution is broadened by the likely poor mass resolution.

b

b

H

H rest frame

➙

13

_b

b

H

lab frame

_

_

Shaping in Heavy Particle ReconstructionIn multi-step decays, kinematic constraints are more severe.

Example: hadronic top decay with a backwards going W in the top rest frame

In the lab frame, the decay angle of the W will typically be larger than the top quark.

This geometry makes it difficult to reconstruct the W as a subjet - even at the parton level!

One of the quarks from the W will be soft - can mispair the one of the quarks from the W with the b, giving inaccurate substructure

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b

W

tt rest frame

➙ b

tlab frame

W

q’

q

Kinematics of Reconstructed Heavy Particles

Decays resulting in soft partons are less likely to be accurately reconstructed

Soft partons can be recombined early in the jet algorithm - inaccurate substructure

When the heavy particle mass is reconstructed, the resolution may be poor - leads to broaded jet mass distributions

Small z recombinations are not indicative of a correctly reconstructed heavy particle

Can the jet substructure be modified to reduce the effect of soft recombinations?

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Pruning the Jet SubstructureWe have characterized systematics of jet substructure in QCD jets

CA: small z, large θ in the final recombinations

kT: small z; θ need not be large

Heavy particle decays have a poor reconstruction rate when the decay has a small z

This is a generic problem - try to come up with a generic solution

Try to modify the jet substructure to improve signal (heavy particle production) - background (QCD) separation

We call this procedure pruning

others have tried similar ideas - Salam/Butterworth (Higgs),

Kaplan (tops), Thaler/Wang (tops)16

Pruning ProcedurePrune the substructure of found jets to improve signal-background separation, do it in a generic way

Procedure:

Start with the objects (e.g. towers) forming a jet found with a recombination algorithm

Rerun the algorithm, but at each recombination test whether:

z < zcut and ΔRij > Dcut

If it is, prune the softer branch by NOT doing the recombination and throwing the softer branch away

The found jet is the pruned jet, and can be compared to the original jet

CA: zcut = 0.1 and Dcut = θ/2

kT: zcut = 0.15 and Dcut = θ/2

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Testing PruningStudy on top reconstruction:

Hadronic top decay serves as a good surrogate for a massive particle produced at the LHC

Use a QCD multijet background - separate (unmatched) samples from 2, 3, and 4 hard parton MEs

ME from MadGraph, showered and hadronized in Pythia, jets found with homemade code

Look at several effects before/after pruning:

Mass resolution of reconstructed tops

Improvements in pruning

pT dependence on separation of reconstructed tops

Choice of jet algorithm angular parameter D

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Defining Reconstructed TopsA jet reconstructing a top will have a mass within the top mass window, and a primary subjet mass within the W mass window - call these jets top jets

Defining the top, W mass windows:

Fit the top mass and W mass distributions with Breit-Wigners and a continuum background, find the widths of the peaks

The top and W windows are defined separately for pruning and not pruning - allows us to test whether pruning is narrowing the mass distribution

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140 150 160 170 180 190 200 2100

500

1000

1500

2000

2500

3000

3500

jet mass, pruned

prunedunpruned

sample mass fit

Statistical Measures

Count top jets in signal and background samples

Compare pruned and unpruned samples with 3 measures:

3 measures: ε, R, S - efficiency, S/B, and S/B1/2

ε =NS(pA)

NS(A)R =

NS(pA)/NB(pA)

NS(A)/NB(A)S =

NS(pA)/√

NB(pA)

NS(A)/√

NB(A)

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NB : number of top jets in background sample

NS : number of top jets in signal sample

A : unpruned algorithm pA : pruned algorithm

Mass Windows and Pruning

Fit the top and W mass peaks, look at window widths for pruning and not pruning

Pruning windows much narrower, meaning better top resolution - better heavy particle ID

Pruning window widths fairly consistent between algorithms, over a range in pT

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200 400 600 800 1000 1200pT

5

10

15

20

25

30

35

width !GeV" Top mass window width

200 400 600 800 1000 1200pT

5

10

15

20

25width !GeV" Wmass window width

not pruned, kT

pruned, kT

not pruned, CA

pruned, CA

Improvements in PruningFirst pass: use constant D = 1.0 over a range of pT bins - 200 GeV wide pT bins between 200 and 1200 GeV

Pruning shows large improvements at high pT: in bins where D is not well matched to the decay of the top

Error bars show statistical errors

200 400 600 800 1000 1200pT

1.5

2.0

Ε

jjjjjjjjj

200 400 600 800 1000 1200pT

0

2

4

6

8

10

12R

jjjjjjjjj

200 400 600 800 1000 1200pT

2

3

4

5

S

CA

200 400 600 800 1000 1200pT

0.6

0.7

0.8

0.9

Ε

jjjjjjjjj

200 400 600 800 1000 1200pT0

5

10

15

20

R

jjjjjjjjj

200 400 600 800 1000 1200pT

1.5

2.0

2.5

3.0

3.5

S

kT

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Heavy Particle Decays and D

Heavy particle ID with the unpruned algorithm is improved when D is matched to the expected average decay angle

Good rule of thumb: D = 2m/pT

Two cases:

θD

D > θ lets in extra radiationQCD jet masses larger

θ D

D < θparticle will not be

reconstructed23

Improvements in PruningOptimize D for each pT bin: D = min(2m/pT, 1.0)

Pruning still shows improvements

Natural question: how does pruning compare between fixed D = 1.0 and D optimized for each pT bin?

200 400 600 800 1000 1200pT

0.80

0.85

0.90

0.95

1.05

Ε

200 400 600 800 1000 1200pT

1.5

2.0

2.5

3.0

3.5

4.0

Rjjjjjjjjj

200 400 600 800 1000 1200pT

1.2

1.4

1.6

1.8

2.0S

CA

200 400 600 800 1000 1200pT

0.65

0.70

0.75

0.80

0.85

0.90

0.95

Εjjjjjjjjj

200 400 600 800 1000 1200pT

1.5

2.0

2.5

3.0

3.5

4.0

4.5R

jjjjjjjjj

200 400 600 800 1000 1200pT

1.2

1.4

1.6

1.8

2.0S

kT

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Pruning and D Dependence

The improvements of pruning are relatively independent of D - error bars include region of no improvement for R and S

Pruning has removed much of the dependence on D in heavy particle ID - allows for a broader search

200 400 600 800 1000 1200pT

0.70

0.75

0.80

0.85

0.90

0.95

Εjjjjjjjjj

200 400 600 800 1000 1200pT

1.2

1.4

1.6

1.8

2.0

2.2

2.4

Rjjjjjjjjj

200 400 600 800 1000 1200pT

0.9

1.1

1.2

1.3

1.4S

200 400 600 800 1000 1200pT

0.86

0.88

0.90

0.92

0.94

0.96

0.98

Εjjjjjjjjj

200 400 600 800 1000 1200pT

1.2

1.4

1.6

1.8R

jjjjjjjjj

200 400 600 800 1000 1200pT

0.9

1.1

1.2

1.3S

CA

kT

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Results form Pruning StudyPruning narrows jet and subjet mass distributions of reconstructed top quarks

Pruning improves both signal purity (R) and signal-to-noise (S) in top quark reconstruction using a QCD multijet background

The D dependence of the jet algorithm is somewhat removed by pruning - the improvements in R and S using an optimized D are only marginal over using a constant D = 1.0

Has potential to reduce work in heavy particle searches

Evidence that pruning is removing systematics of the jet algorithm

Look for our paper on pruning - arriving on the arXiv soon

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Future ProspectsMany questions remain about using jet substructure:

How does the detector affect jet substructure and the systematics of the algorithm? How does it affect techniques like pruning?

Which kinematic variables best discriminate between QCD and non-QCD jets? How powerful are these variables?

How can jet substructure fit into an analysis? How orthogonal is the information provided by jet substructure to other data from the event?

How can theory calculations link up with experimental observations about jet substructure?

Jet substructure shows promise to learn about the physics behind jets, but there is still much to discover

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ConclusionsSystematics of the jet algorithm are important in studying jet substructure

The jet substructure we expect from the kT and CA algorithms are very different

Shaping can make it difficult to determine the physics of a jet

Generic techniques can help:

Reduce systematics from the algorithm

Narrow mass distributions of reconstructed heavy particles

Improve the power of heavy particle searches

Many questions to be answered to determine the usefulness of jet substructure

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