[PPT] - The Space of Collider Events BOOST 2019 Eric M. Metodiev Center PowerPoint Presentation

SLIDE 1

The Space of Collider Events

BOOST 2019

Eric M. Metodiev

Center for Theoretical Physics Massachusetts Institute of T echnology Joint work with Patrick Komiske, Radha Mastandrea, Preksha Naik, and Jesse Thaler

[1902.02346], to appear in PRL [19xx.xxxxx]

July 22, 2019

1

SLIDE 2

The Space of Collider Events

Outline

When are two jets similar? Energy Mover’s Distance Quantifying Jet Similarity Exploring the Space of Jets

Eric M. Metodiev, MIT 2

!

SLIDE 3

The Space of Collider Events

Outline

When are two jets similar? Energy Mover’s Distance Quantifying Jet Similarity Exploring the Space of Jets

Eric M. Metodiev, MIT 3

!

SLIDE 4

The Space of Collider Events

When are two jets similar?

These two jets “look” similar, but have different numbers of particles, flavors, and locations.

Eric M. Metodiev, MIT 4

Jet 1 Jet 2

How do we quantify this?

PRELIMINARY PRELIMINARY

“Space of Jets”

400 GeV AK5 Jets from CMS Open Data See Radha’s talk on Thursday for more!

SLIDE 5

The Space of Collider Events

When are two jets similar?

Eric M. Metodiev, MIT 5

Rapidity ! A z i m u t h "

Fragmentation

partons # $ % …

Collision Detection Hadronization

hadrons &± (± … ) )

The energy flow (distribution of energy) is the information that is robust to: fragmentation, hadronization, detector effects, … Energy flow ó Infrared and Collinear (IRC) Safe information

[F.V. Tkachov, 9601308] [N.A. Sveshnikov, F.V. Tkachov, 9512370] [P.S. Cherzor, N.A. Sveshnikov, 9710349]

SLIDE 6

The Space of Collider Events

When are two jets similar?

Eric M. Metodiev, MIT 6

Rapidity ! A z i m u t h "

Fragmentation

partons # $ % …

Collision Detection Hadronization

hadrons &± (± … ) )

Treat jets as distributions of energy: ℇ(,

) = 0

123 4

51 6(,

− ,
1)

energy direction Ignoring particle flavor, charge…

PRELIMINARY PRELIMINARY

SLIDE 7

The Space of Collider Events

Outline

When are two jets similar? Energy Mover’s Distance Quantifying Jet Similarity Exploring the Space of Jets

Eric M. Metodiev, MIT 7

When they have similar distributions of energy !

SLIDE 8

The Space of Collider Events

Outline

When are two jets similar? Energy Mover’s Distance Quantifying Jet Similarity Exploring the Space of Jets

Eric M. Metodiev, MIT 8

When they have similar distributions of energy !

SLIDE 9

The Space of Collider Events

The Energy Mover’s Distance

Earth Mover’s Distance: the minimum “work” (stuff x distance) to rearrange one pile of dirt into another

Eric M. Metodiev, MIT 9

Review: The Earth Mover’s Distance Metric on the space of (normalized) distributions: symmetric, non-negative, triangle inequality Distributions are close in EMD ó their expectation values are close. Also known as the 1-Wasserstein metric.

[Rubner, Tomasi, Guibas] [Peleg, Werman, Rom]

SLIDE 10

The Space of Collider Events

PRELIMINARY PRELIMINARY

The Energy Mover’s Distance

Energy Mover’s Distance: the minimum “work” (energy x angle) to rearrange one jet (pile of energy) into another

Eric M. Metodiev, MIT 10

EMD ℇ, ℇ& = min

{,} . /01 2

.

301 24

5

/3

6/3 7 + .

/01 2

9/ − .

301 24

9

3 &

9/ 9

3 &

6/3 5

/3

Difference in radiation pattern Difference in total energy

From Earth to Energy

[Komiske, EMM, Thaler, 1902.02346]

SLIDE 11

The Space of Collider Events

The Energy Mover’s Distance

Eric M. Metodiev, MIT 11

EMD has dimensions of energy True metric as long as ! ≥

# $ %&'(

Solvable via Optimal Transport problem.

~1ms to compute EMD for two jets with 100 particles. ! ≥ the jet radius, for conical jets

From Earth to Energy

[Komiske, EMM, Thaler, 1902.02346]

Energy Mover’s Distance: the minimum “work” (energy x angle) to rearrange one event (pile of energy) into another

ℇ ℇ′ ℇ++

EMD(ℇ, ℇ′) + EMD ℇ+, ℇ++ ≥ EMD(ℇ, ℇ′′) PRELIMINARY

SLIDE 12

The Space of Collider Events

The Energy Mover’s Distance

Eric M. Metodiev, MIT 12

From Earth to Energy

[Komiske, EMM, Thaler, 1902.02346]

ℇ ℇ′ ℇ##

EMD(ℇ, ℇ′) + EMD ℇ#, ℇ## ≥ EMD(ℇ, ℇ′′)

Energy Mover’s Distance: the minimum “work” (energy x angle) to rearrange one event (pile of energy) into another

205.8 GeV 158.7 GeV 122.5 GeV https://energyflow.network

SLIDE 13

The Space of Collider Events

Outline

When are two jets similar? Energy Mover’s Distance Quantifying Jet Similarity Exploring the Space of Jets

Eric M. Metodiev, MIT 13

When they have similar distributions of energy The “work” to rearrange one jet into another !

SLIDE 14

The Space of Collider Events

Outline

When are two jets similar? Energy Mover’s Distance Quantifying Jet Similarity Exploring the Space of Jets

Eric M. Metodiev, MIT 14

When they have similar distributions of energy The “work” to rearrange one jet into another !

SLIDE 15

The Space of Collider Events

Energy Moving and IRC Safety

Eric M. Metodiev, MIT 15

EMD ℇ, ℇ& ≥ 1 )* + ℇ − + ℇ&

+ ℇ = .

/01 2

3/ Φ 5 6/ Additive IRC-safe observables:

Difference in

bservable values

Energy Mover’s Distance

e.g. 7 ≥ 1 jet angularities:

“Lipschitz constant” of Φ i.e. bound on its derivative

8(:) ℇ − 8(:) ℇ& ≤ 7 EMD ℇ, ℇ& Events close in EMD are close in any infrared and collinear safe observable!

[Berger, Kucs, Sterman, 0303051] [Larkoski, Thaler, Waalewijn, 1408.3122]

+

SLIDE 16

The Space of Collider Events

!

Old Observables in a New Language

Eric M. Metodiev, MIT 16

"-subjettiness is the EMD between the event and the closest #-particle event.

!$(ℇ) = min

ℇ, -$ EMD ℇ, ℇ′ .

!$

4 (ℇ) = min $ 5678 9 :-; <

=: min{?;,:

4 , ?@,: 4 , … , ?$,: 4 }

C ≥ 1 is p-Wasserstein distance with p = C.

G(ℇ) = = − max

K L

9

:

| ⃗ O: ⋅ K Q| G(ℇ) = min

ℇ, -@ EMD(ℇ, ℇ′)

with ?:R = K Q: ⋅ K QR, K Q = ⃗ O/=

Thrust is the EMD between the event and two back-to-back particles.

# = 1 # = 2 # = 3

PRELIMINARY PRELIMINARY PRELIMINARY

Geometry in the space of events

SLIDE 17

The Space of Collider Events

Quantifying Pileup and Detector Effects with EMD

Eric M. Metodiev, MIT 17

+ charged hadron subtraction + Tracks only, !"

#$% > 1 GeV cut

Gen./Sim. EMD: 33.7 GeV Gen./Sim. EMD: 6.7 GeV

EMD universally quantifies pileup and detector effects.

See extra slides for histograms.

PRELIMINARY PRELIMINARY PRELIMINARY

Can also quantify hadronization effects this way.

Gen./Sim. EMD: 44.4 GeV

SLIDE 18

The Space of Collider Events

Outline

When are two jets similar? Energy Mover’s Distance Quantifying Jet Similarity Exploring the Space of Jets

Eric M. Metodiev, MIT 18

When they have similar distributions of energy The “work” to rearrange one jet into another ! Geometry of the space of jets. Bounds for pileup, detector effects

SLIDE 19

The Space of Collider Events

Outline

When are two jets similar? Energy Mover’s Distance Quantifying Jet Similarity Exploring the Space of Jets

Eric M. Metodiev, MIT 19

When they have similar distributions of energy The “work” to rearrange one jet into another ! Geometry of the space of jets. Bounds for pileup, detector effects

SLIDE 20

The Space of Collider Events

Most Representative Jets: K-medoids

Eric M. Metodiev, MIT 20

Jet Mass

PRELIMINARY

SLIDE 21

The Space of Collider Events

Most Representative Jets: K-medoids

Eric M. Metodiev, MIT 21

Jet Mass

PRELIMINARY

SLIDE 22

The Space of Collider Events

Towards Anomaly Detection

Eric M. Metodiev, MIT 22

PRELIMINARY More Typical More Anomalous Complements recent developments in anomaly detection for collider physics.

[Collins, Howe, Nachman, 1805.02664] [Heimel, Kasieczka, Plehn, Thompson, 1808.08979] [Farina, Nakai, Shih, 1808.08992] [Cerri, Nguyen, Pierini, Spiropulu, Vlimant, 1811.10276]

Mean EMD to Dataset

PRELIMINARY

SLIDE 23

The Space of Collider Events

Towards Anomaly Detection

Eric M. Metodiev, MIT 23

PRELIMINARY More Typical More Anomalous Complements recent developments in anomaly detection for collider physics.

[Collins, Howe, Nachman, 1805.02664] [Heimel, Kasieczka, Plehn, Thompson, 1808.08979] [Farina, Nakai, Shih, 1808.08992] [Cerri, Nguyen, Pierini, Spiropulu, Vlimant, 1811.10276]

Mean EMD to Dataset

PRELIMINARY

SLIDE 24

The Space of Collider Events

Exploring the Space of Jets: Visualizing the Manifold

Eric M. Metodiev, MIT 24

Visualize the space of events with t-Distributed Stochastic Neighbor Embedding (t-SNE). Finds an embedding into a low-dimensional manifold that respects distances.

[L. van der Maaten, G. Hinton]

What does the space

f jets look like?

SLIDE 25

The Space of Collider Events

Exploring the Space of Jets: Visualizing the Manifold

Eric M. Metodiev, MIT 25

ne-prong

two-prong What does the space

f jets look like?

SLIDE 26

The Space of Collider Events

Exploring the Space of Jets: Correlation Dimension

Eric M. Metodiev, MIT 26

dim$/&(() = − 8-./$/& ln ( 34/2 At LL:

Quark jets Gluon jets

Dimension blows up at low energies. Jets are “more than fractal”

dim ( = ( 6 6( ln 7

89: ;

7

<9: ;

Θ[EMD ℇ8, ℇ< < (]

Energy scale ( dependence Count neighbors in ball of radius (

Correlation dimension:

SLIDE 27

The Space of Collider Events

Outline

When are two jets similar? Energy Mover’s Distance Quantifying Jet Similarity Exploring the Space of Jets

Eric M. Metodiev, MIT 27

When they have similar distributions of energy The “work” to rearrange one jet into another ! Geometry of the space of jets. Bounds for pileup, detector effects New ways to visualize and probe jet data

SLIDE 28

The Space of Collider Events

Going Beyond

Classification with EMD Clustering sets of events New observables through EMD geometry? “Event” mover’s distance between ensembles? Include flavor information?

Eric M. Metodiev, MIT 28

SLIDE 29

The Space of Collider Events

The End

Thank you!

Eric M. Metodiev, MIT 29

SLIDE 30

The Space of Collider Events

Extra Slides

Eric M. Metodiev, MIT 30

SLIDE 31

The Space of Collider Events

EnergyFlow

Eric M. Metodiev, MIT 31

https://energyflow.network

pip install energyflow

SLIDE 32

The Space of Collider Events Eric M. Metodiev, MIT 32

CMS Open Data

pendata.cern.ch

An amazing resource for physics exploration and proof-of-principle studies.

SLIDE 33

The Space of Collider Events

CMS Open Data

Many exciting physics applications with the CMS Open Data already. Exposing the QCD splitting function Looking for parity violation in jets Searching for dimuon resonances Analyzing collision data with deep learning techniques

Eric M. Metodiev, MIT 33

[Andrews, et al., 1902.08276] [Andrews, Paulini, Gleyzer, Poczos, 1807.11916] [Madrazo, Cacha, Iglesias, de Lucas, 1708.07034] [Lester, Schott, 1904.11195] [Cesarotti, Soreq, Strassler, Thaler, Xue, 1902.04222] [Tripathee, Xue, Larkoski, Marzani, Thaler, 1704.05842] [Larkoski, Marzani, Thaler, Tripathee, Xue, 1704.05066]

SLIDE 34

The Space of Collider Events

Exploring the Space of Jets: Correlation Dimension

Eric M. Metodiev, MIT 34

dim $ = $ & &$ ln )

*+,

)

.+,

Θ[EMD ℇ*, ℇ. < $]

Energy scale $ dependence Count neighbors in ball of radius $

89:;<=>?@;9<

A?;9BC

D ∝ DF;G dim(D) = r & &D ln 89:;<=>?@C D Intuition: Correlation dimension:

SLIDE 35

The Space of Collider Events

Quantifying Pileup and Detector Effects with EMD

Eric M. Metodiev, MIT 35

better better Gen./Sim. EMD universally quantifies pileup mitigation and detector effects.

SLIDE 36

The Space of Collider Events

CMS 2011A Jet Primary Dataset (+ Simulation)

2.3 $b&' of 7 TeV proton-proton collision data. ~1 million 3 = 0.5 jets with 78 ∈ 375,425 GeV, = < 1.9

Eric M. Metodiev, MIT 36

[link]

PRELIMINARY

[Komiske, Mastandrea, EMM, Naik, Thaler, to appear]

SLIDE 37

The Space of Collider Events

Jet Substructure Observables

Eric M. Metodiev, MIT 37

PRELIMINARY PRELIMINARY PRELIMINARY

!" = $

%∈'()

*%

+ "

, = $

%∈'()

1 *.

/ =

∑%∈'() *.,%

"

∑%∈'() *.,%

"

Jet Mass Constituent Multiplicity Momentum Dispersion

Study jet substructure at truth and detector level.

[Larkoski, Marzani, Thaler, Tripathee, Xue, 1704.05066]

Similar to:

SLIDE 38

The Space of Collider Events

Exploring the Space of Jets: Correlation Dimension

Eric M. Metodiev, MIT 38

QCD jets are simplest. W jets are more complicated. T

p jets are most complex.

“Decays” have ~constant dimension. MC

SLIDE 39

The Space of Collider Events

Exploring the Space of Jets: Correlation Dimension

Eric M. Metodiev, MIT 39

QCD jets are simplest. W jets are more complicated. T

p jets are most complex.

“Decays” have ~constant dimension. Fragmentation becomes more complex at lower energy scales. MC

SLIDE 40

The Space of Collider Events

Exploring the Space of Jets: Correlation Dimension

Eric M. Metodiev, MIT 40

QCD jets are simplest. W jets are more complicated. T

p jets are most complex.

“Decays” have ~constant dimension. Fragmentation becomes more complex at lower energy scales. Hadronization becomes relevant at scales around 20 GeV. MC

SLIDE 41

The Space of Collider Events

Exploring the Space of Jets: Correlation Dimension

Eric M. Metodiev, MIT 41

Pileup & Detector Effects

Can we understand this analytically?

PRELIMINARY

Dimension blows up at low energies. Jets are “more than fractal”

SLIDE 42

The Space of Collider Events

Jet Kinematic Distributions

Eric M. Metodiev, MIT 42

SLIDE 43

The Space of Collider Events

Quantifying event modifications: Hadronization

Eric M. Metodiev, MIT 43

ℇ = ℇ#$%&'() ℇ* = ℇ+$,%'()

partons hadrons

(/01) = 111.1GeV
(/01) = 111.6GeV
(/01) = 9

:01 ;

<: =:

(/01) ℇ − -(/01) ℇ*

≤ EMD ℇ, ℇ*

SLIDE 44

The Space of Collider Events

Exploring the Space of Events: Jet Classification

Eric M. Metodiev, MIT 44

Classify W jets vs. QCD jets Look at a jet’s nearest neighbors (kNN) to predict its class. Optimal IRC-safe classifier with enough data. Nearing performance of ML.

vs. better N-subjettiness

EMD kNN ML

SLIDE 45

The Space of Collider Events

Exploring the Space of Events

Eric M. Metodiev, MIT 45

Use EMD as a measure of event similarity Unsupervised clustering algorithms can be used to cluster events Jets are clusters of particles ???? are clusters of jets VP Tree: O(log(N)) neighbor query time Much more to explore. Vantage Point (VP) Tree

SLIDE 46

The Space of Collider Events

Exploring the Space of Events: W jets

Eric M. Metodiev, MIT 46

W !

1−!

# 2x zoom “bottom heavy” “top heavy” “one pronged” “balanced” ?

W jets, $ = 1.0 )* ∈ 500,510 GeV

! 1 − ! #1 = )23

1

)*

1 = 45 1

)*

1

W jets are 2-pronged: !: Energy Sharing of Prongs #: Angle between Prongs 8: Azimuthal orientation Constrained by W mass: Hence we expect a two-dimensional space of W jets. After 8 rotation: one-dimensional

SLIDE 47

The Space of Collider Events

Exploring the Space of Jets: Correlation Dimension

Eric M. Metodiev, MIT 47

= − 8$%&'/) * ln

.//2

&' = &1 = 4 3 &) = &4 = 3

+ 1-loop running of $%

dim'/) - = - 8 8- ln 9

:;< =

9

>;< =

Θ[EMD ℇ:, ℇ> < -] = - 8 8- ln Pr [EMD < -] = - 8 8- ln exp − 4$M&'/) * lnN

.//2

= - 8 8- ln Pr [O P;< < -; &'/) → 2 &'/)]

[A. Larkoski, 1709.06195]

Sketch of leading log (one emission) calculation:

SLIDE 48

The Space of Collider Events

What is a collision event?

Eric M. Metodiev, MIT 48

! "± $± %± &± &'

(

)/ ̅ ) ,/- ,

photon electron muon pion kaon K-long proton neutron

tracker ECAL HCAL

When are two collider events similar?

How an event gets its shape: Experiment

SLIDE 49

The Space of Collider Events

Pileup Mitigation with PUMML

Eric M. Metodiev, MIT 49