Exploring The (Metric) Space of Collider Events ATLAS-Theory Lunch - - PowerPoint PPT Presentation

Exploring The (Metric) Space of Collider Events

ATLAS-Theory Lunch Seminar

Eric M. Metodiev

Center for Theoretical Physics Massachusetts Institute of T echnology Joint work with Patrick Komiske and Jesse Thaler

[1902.02346]

April 17, 2019

1

Exploring the (Metric) Space of Collider Events

Outline

2

When are two events similar? The Energy Mover’s Distance Movie Time Applications

Eric M. Metodiev, MIT

Exploring the (Metric) Space of Collider Events

Outline

3

When are two events similar? The Energy Mover’s Distance Movie Time Applications

Eric M. Metodiev, MIT

Exploring the (Metric) Space of Collider Events

When are two events similar?

Eric M. Metodiev, MIT 4

Exploring the (Metric) Space of Collider Events

When are two collider events similar?

Eric M. Metodiev, MIT 5

Fragmentation

partons 𝑕 𝑣 𝑒 …

Collision Detection Hadronization

hadrons 𝜌± 𝐿± … 𝑞 𝑞

How an event gets its shape

Exploring the (Metric) Space of Collider Events

When are two collider events similar? Experimentally: very complicated

Eric M. Metodiev, MIT 6

Theoretically: very complicated

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

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

Exploring the (Metric) Space of Collider Events

When are two collider events similar?

Eric M. Metodiev, MIT 7

Fragmentation

partons 𝑕 𝑣 𝑒 …

Collision Detection Hadronization

hadrons 𝜌± 𝐿± … 𝑞 𝑞

Energy flow is robust information Treat events as distributions of energy: ෍

𝑗=1 𝑁

𝐹𝑗 𝜀(ො 𝑜 − Ƹ 𝑞𝑗)

energy direction Ignoring particle flavor, charge…

Exploring the (Metric) Space of Collider Events

Outline

8

When are two events similar? The Energy Mover’s Distance Movie Time Applications

Eric M. Metodiev, MIT

Exploring the (Metric) 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  their expectation values are close. Also known as the 1-Wasserstein metric.

[Y. Rubner, C. Tomasi, and L.J. Guibas] [S. Peleg, M. Werman, H. Rom]

Exploring the (Metric) Space of Collider Events

The Energy Mover’s Distance

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

Eric M. Metodiev, MIT 10

𝐹𝑗 𝐹

𝑘 ′

𝜄𝑗𝑘 𝑔

𝑗𝑘

From Earth to Energy

[P.T. Komiske, EMM, J. Thaler, 1902.02346]

EMD ℇ, ℇ′ = min

{𝑔} ෍ 𝑗=1 𝑁

෍

𝑘=1 𝑁′

𝑔

𝑗𝑘

𝜄𝑗𝑘 𝑆

Difference in radiation pattern

Exploring the (Metric) Space of Collider Events

The Energy Mover’s Distance

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

Eric M. Metodiev, MIT 11

𝐹𝑗 𝐹

𝑘 ′

𝜄𝑗𝑘 𝑔

𝑗𝑘

From Earth to Energy

[P.T. Komiske, EMM, J. Thaler, 1902.02346]

EMD ℇ, ℇ′ = min

{𝑔} ෍ 𝑗=1 𝑁

෍

𝑘=1 𝑁′

𝑔

𝑗𝑘

𝜄𝑗𝑘 𝑆 + ෍

𝑗=1 𝑁

𝐹𝑗 − ෍

𝑘=1 𝑁′

𝐹

𝑘 ′ Difference in radiation pattern Difference in total energy

Exploring the (Metric) Space of Collider Events

The Energy Mover’s Distance

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

Eric M. Metodiev, MIT 12

EMD ℇ, ℇ′ = min

{𝑔} ෍ 𝑗=1 𝑁

෍

𝑘=1 𝑁′

𝑔

𝑗𝑘

𝜄𝑗𝑘 𝑆 + ෍

𝑗=1 𝑁

𝐹𝑗 − ෍

𝑘=1 𝑁′

𝐹

𝑘 ′ Difference in radiation pattern Difference in total energy

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

1 2 𝜄max

Solvable via Optimal Transport problem.

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

From Earth to Energy

[P.T. Komiske, EMM, J. Thaler, 1902.02346]

ℇ ℇ′′ ℇ′

Exploring the (Metric) Space of Collider Events

Outline

13

When are two events similar? The Energy Mover’s Distance Movie Time Applications

Eric M. Metodiev, MIT

Exploring the (Metric) Space of Collider Events

Movie Time: Visualizing the EMD

Eric M. Metodiev, MIT 14

EMD is the cost of an optimal transport problem. We also get the shortest path between the events. Interpolate along path to visualize! Taking a walk in the space of events

Exploring the (Metric) Space of Collider Events

Movie Time: Visualizing Jet Formation

Eric M. Metodiev, MIT 15 𝑞 𝑞

QCD Jets W Jets T

• p Jets

Pythia 8, 𝑆 = 1.0 jets, 𝑞𝑈 ∈ 500,550 GeV

Fragmentation Collision Hadronization

Exploring the (Metric) Space of Collider Events

Movie Time: Visualizing QCD Jet Formation

Eric M. Metodiev, MIT 16

Quark Fragmentation Hadronization

EMD: 111.6 GeV

fragmentation

EMD: 18.1 GeV

hadronization

Exploring the (Metric) Space of Collider Events

Movie Time: Visualizing W Jet Formation

Eric M. Metodiev, MIT 17

Decay Quarks Fragmentation Hadronization W

EMD: 78.3 GeV

decay

EMD: 26.3 GeV

fragmentation

EMD: 12.9 GeV

hadronization

Exploring the (Metric) Space of Collider Events

Movie Time: Visualizing Top Jet Formation

Eric M. Metodiev, MIT 18

EMD: 161.1 GeV

decay

EMD: 47.1 GeV

fragmentation

EMD: 27.0 GeV

hadronization Decay Quarks Fragmentation Hadronization Top

Exploring the (Metric) Space of Collider Events

Outline

19

When are two events similar? The Energy Mover’s Distance Movie Time Applications

Eric M. Metodiev, MIT

Exploring the (Metric) Space of Collider Events

𝜐

Old Observables in a New Language

Eric M. Metodiev, MIT 20

𝑶-(sub)jettiness is the EMD between the event and the closest 𝑂-particle event.

𝜐𝑂(ℇ) = min

ℇ′ =𝑂 EMD ℇ, ℇ′ .

𝜐𝑂

𝛾 = min 𝑂 axes ෍ 𝑗=1 𝑁

𝐹𝑗 min

𝑙 {𝜄1,𝑙 𝛾 , 𝜄2,𝑙 𝛾 , … , 𝜄𝑂,𝑙 𝛾 }

𝛾 ≠ 1 is p-Wasserstein distance with p = 𝛾.

𝑢 = 𝐹 − max

ො 𝑜

෍

𝑗

| Ԧ 𝑞𝑗 ⋅ ො 𝑜| 𝑢(ℇ) = min

ℇ′ =2 EMD(ℇ, ℇ′)

with 𝜄𝑗𝑘 = Ƹ 𝑞𝑗 ⋅ Ƹ 𝑞𝑘, Ƹ 𝑞 = Ԧ 𝑞/𝐹

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

Exploring the (Metric) Space of Collider Events

EMD and IRC-Safe Observables

Eric M. Metodiev, MIT 21

EMD ℇ, ℇ′ ≥ 1 𝑆𝑀 𝒫 ℇ − 𝒫 ℇ′ 𝒫 ℇ = ෍

𝑗=1 𝑁

𝐹𝑗 Φ Ƹ 𝑞𝑗

Additive IRC-safe observables:

Difference in

• bservable values

Earth Mover’s Distance

𝜇(𝛾) = ෍

𝑗=1 𝑁

𝐹𝑗 𝜄𝑗

𝛾

e.g. jet angularities:

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

For 𝛾 ≥ 1 jet angularities:

𝜇(𝛾) ℇ − 𝜇(𝛾) ℇ′ ≤ 𝛾 EMD ℇ, ℇ′

Events close in EMD are close in any infrared and collinear safe observable

[C. Berger, T. Kucs, and G. Sterman, 0303051] [A. Larkoski, J. Thaler, and W. Waalewijn, 1408.3122]

𝒫

Exploring the (Metric) Space of Collider Events

Quantifying event modifications: Hadronization

Eric M. Metodiev, MIT 22

𝜇(𝛾=1) ℇ − 𝜇(𝛾=1) ℇ′ ≤ EMD ℇ, ℇ′ ℇ = ℇpartons ℇ′ = ℇhadrons

partons hadrons

𝜇(𝛾=1) = 111.1GeV 𝜇(𝛾=1) = 111.6GeV

𝜇(𝛾=1) = ෍

𝑗=1 𝑁

𝐹𝑗 𝜄𝑗

Exploring the (Metric) Space of Collider Events

Quantifying event modifications: Hadronization

Eric M. Metodiev, MIT 23

ℇ = ℇpartons ℇ′ = ℇhadrons

partons hadrons

𝜇(𝛾=1) = 111.1GeV 𝜇(𝛾=1) = 111.6GeV

𝜇(𝛾=1) = ෍

𝑗=1 𝑁

𝐹𝑗 𝜄𝑗

𝜇(𝛾=1) ℇ − 𝜇(𝛾=1) ℇ′ ≤ EMD ℇ, ℇ′

Exploring the (Metric) Space of Collider Events

Exploring the Space of Events: W jets

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]

W 𝑨

1−𝑨

𝜄 𝑨 1 − 𝑨 𝜄2 = 𝑞𝜈𝐾

2

𝑞𝑈

2 = 𝑛𝑋 2

𝑞𝑈

2

W jets are 2-pronged and constrained by W mass: Hence we expect a two-dimensional space of W jets: 𝑨, 𝜒 After 𝜒 rotation,

• ne-dimensional: 𝑨

Exploring the (Metric) Space of Collider Events

Exploring the Space of Events: W jets

Eric M. Metodiev, MIT 25

W 𝑨

1−𝑨

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

W jets, 𝑆 = 1.0 𝑞𝑈 ∈ 500,510 GeV

𝑨 1 − 𝑨 𝜄2 = 𝑞𝜈𝐾

2

𝑞𝑈

2 = 𝑛𝑋 2

𝑞𝑈

2

W jets are 2-pronged and constrained by W mass: Hence we expect a two-dimensional space of W jets: 𝑨, 𝜒 After 𝜒 rotation,

• ne-dimensional: 𝑨

Exploring the (Metric) Space of Collider Events

Exploring the Space of Jets: Correlation Dimension

Eric M. Metodiev, MIT 26

dim 𝑅 = 𝑅 𝜖 𝜖𝑅 ln ෍

𝑗=1 𝑂

෍

𝑘=1 𝑂

Θ[EMD ℇ𝑗, ℇ𝑘 < 𝑅]

Energy scale 𝑅 dependence Count neighbors in ball of radius 𝑅

𝑂neighboring

points

𝑠 ∝ 𝑠dim dim(𝑠) = r 𝜖 𝜖𝑠 ln 𝑂neighbors 𝑠 Intuition: Correlation dimension:

Exploring the (Metric) Space of Collider Events

Exploring the Space of Jets: Correlation Dimension

Eric M. Metodiev, MIT 27

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

• p jets are most complex.

“Decays” have ~constant dimension.

Exploring the (Metric) Space of Collider Events

Exploring the Space of Jets: Correlation Dimension

Eric M. Metodiev, MIT 28

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.

Exploring the (Metric) Space of Collider Events

Exploring the Space of Jets: Correlation Dimension

Eric M. Metodiev, MIT 29

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.

Exploring the (Metric) Space of Collider Events

Exploring the Space of Jets: Correlation Dimension

Eric M. Metodiev, MIT 30

dim𝑟/𝑕(𝑅) = − 8𝛽𝑡𝐷𝑟/𝑕 𝜌 ln 𝑅 𝑞𝑈/2 𝐷𝑟 = 𝐷𝐺 = 4 3 𝐷𝑕 = 𝐷𝐵 = 3 At LL:

+ 1-loop running of 𝛽𝑡 Quark jets Gluon jets

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

Exploring the (Metric) Space of Collider Events

Exploring the Space of Events: Jet Classification

Eric M. Metodiev, MIT 31

Classify W jets vs. QCD jets Look at a jet’s nearest neighbors (kNN) to predict its class. Nearing performance of ML.

vs. better N-subjettiness

EMD kNN ML

Exploring the (Metric) Space of Collider Events

Going Beyond

Quantifying pileup mitigation New histogram and data visualizations Clustering sets of events New observables through EMD geometry EMD for density estimation (& unfolding?) “Event” mover’s distance between ensembles? Model (in)dependent anomaly detection? Train ML models to optimize EMD directly? Include flavor information?

Eric M. Metodiev, MIT 32

Exploring the (Metric) Space of Collider Events

The End

Thank you!

Eric M. Metodiev, MIT 33

Exploring the (Metric) Space of Collider Events

Extra Slides

Eric M. Metodiev, MIT 34

Exploring the (Metric) Space of Collider Events

Exploring the Space of Events: k-medoids

Eric M. Metodiev, MIT 35

Exploring the (Metric) Space of Collider Events

Observables

Eric M. Metodiev, MIT 36

𝑂-(sub)jettiness: 𝜐𝑂

𝛾 = ෍ 𝑗=1 𝑁

𝐹𝑗 min

𝑂 axes{𝜄1,𝑙 𝛾 , 𝜄2,𝑙 𝛾 , … , 𝜄𝑂,𝑙 𝛾 }

𝜐1/𝐹 ≫ 0 𝜐1/𝐹 > 𝜐2/𝐹 ≫ 0 𝜐3/𝐹 ≃ 0 measures how well jet energy is aligned into N (sub)jets

[J. Thaler, K. Van Tilburg, 1011.2268] [J. Thaler, K. Van Tilburg, 1108.2701] [I. Stewart, F. Tackmann, W. Waalewijn, 1004.2489]

Exploring the (Metric) Space of Collider Events

Observables

Eric M. Metodiev, MIT 37

𝑂-subjettiness: 𝜐𝑂

𝛾 = ෍ 𝑗=1 𝑁

𝐹𝑗 min

𝑂 axes{𝜄1,𝑙 𝛾 , 𝜄2,𝑙 𝛾 , … , 𝜄𝑂,𝑙 𝛾 }

𝜐1/𝐹 ≫ 0 𝜐1/𝐹 > 𝜐2/𝐹 ≫ 0 𝜐3/𝐹 ≃ 0 measures how well jet energy is aligned into N subjets

𝑂-subjettiness is the EMD between the event and the closest 𝑂-particle event.

𝛾 ≠ 1 corresponds to other p-Wasserstein distances with p = 𝛾.

𝜐𝑂(ℇ) = min

ℇ′ =𝑂 EMD ℇ, ℇ′ .

[J. Thaler, K. Van Tilburg, 1011.2268] [J. Thaler, K. Van Tilburg, 1108.2701]

Exploring the (Metric) Space of Collider Events

Observables

Eric M. Metodiev, MIT 38

𝒫 ℇ = ෍

𝑗=1 𝑁

𝐹𝑗 Φ Ƹ 𝑞𝑗

Take any additive IRC-safe observable: 𝜇(𝛾) = ෍

𝑗=1 𝑁

𝐹𝑗 𝜄𝑗

𝛾

e.g. jet angularities: 𝜄𝑗 𝐹𝑗 Getting quantitative

[C. Berger, T. Kucs, and G. Sterman, 0303051] [A. Larkoski, J. Thaler, and W. Waalewijn, 1408.3122]

Exploring the (Metric) Space of Collider Events

Observables

Via the Kantorovich-Rubinstein dual formulation of EMD:

Eric M. Metodiev, MIT 39

EMD ℇ, ℇ′ ≥ 1 𝑆𝑀 ෍

𝑗=1 𝑁

𝐹𝑗Φ Ƹ 𝑞𝑗 − ෍

𝑘=1 𝑁′

𝐹

𝑘 ′ Φ

Ƹ 𝑞𝑘′ = 1 𝑆𝑀 𝒫 ℇ − 𝒫 ℇ′ 𝒫 ℇ = ෍

𝑗=1 𝑁

𝐹𝑗 Φ Ƹ 𝑞𝑗

Take any additive IRC-safe observable:

Difference in

• bservable values

Earth Mover’s Distance

𝜇(𝛾) = ෍

𝑗=1 𝑁

𝐹𝑗 𝜄𝑗

𝛾

e.g. jet angularities:

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

𝜄𝑗 𝐹𝑗

[C. Berger, T. Kucs, and G. Sterman, 0303051] [A. Larkoski, J. Thaler, and W. Waalewijn, 1408.3122]

Getting quantitative

Exploring the (Metric) Space of Collider Events

Observables

Via the Kantorovich-Rubinstein dual formulation of EMD:

Eric M. Metodiev, MIT 40

EMD ℇ, ℇ′ ≥ 1 𝑆𝑀 ෍

𝑗=1 𝑁

𝐹𝑗Φ Ƹ 𝑞𝑗 − ෍

𝑘=1 𝑁′

𝐹

𝑘 ′ Φ

Ƹ 𝑞𝑘′ = 1 𝑆𝑀 𝒫 ℇ − 𝒫 ℇ′ 𝒫 ℇ = ෍

𝑗=1 𝑁

𝐹𝑗 Φ Ƹ 𝑞𝑗

Take any additive IRC-safe observable:

Difference in

• bservable values

Earth Mover’s Distance

𝜇(𝛾) = ෍

𝑗=1 𝑁

𝐹𝑗 𝜄𝑗

𝛾

e.g. jet angularities:

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

For 𝛾 ≥ 1 jet angularities, 𝑀 = 𝛾/𝑆 over the jet cone, so:

𝜇(𝛾) ℇ − 𝜇(𝛾) ℇ′ ≤ 𝛾 EMD ℇ, ℇ′

The EMD provides a robust upper bound to any modifications of these observables. 𝜄𝑗 𝐹𝑗

[C. Berger, T. Kucs, and G. Sterman, 0303051] [A. Larkoski, J. Thaler, and W. Waalewijn, 1408.3122]

Getting quantitative

Exploring the (Metric) Space of Collider Events

Observables

Eric M. Metodiev, MIT 41

Theorem: Any infrared and collinear safe observable 𝒫 can be approximated arbitrarily well as: 𝒫 𝑞1, … , 𝑞𝑁 = 𝐺 ෍

𝑗=1 𝑁

𝐹𝑗 Φ Ƹ 𝑞𝑗 for some Φ: ℝ2 → ℝℓ and F: ℝℓ → ℝ and sufficiently large ℓ. Key idea: Energy-weighted angular structures contain all the IRC-safe information.

1 𝑆𝑀 ෍

𝑗=1 𝑁

𝐹𝑗Φ Ƹ 𝑞𝑗 − ෍

𝑘=1 𝑁′

𝐹

𝑘 ′ Φ

Ƹ 𝑞𝑘′ ≤ EMD ℇ, ℇ′

Events close in EMD are close in all infrared and collinear safe information!

[M. Zaheer, et al., 1703.06114] [P.T. Komiske, EMM, J. Thaler, 1810.05165]

Exploring the (Metric) Space of Collider Events

Quantifying event modifications: Hadronization

Eric M. Metodiev, MIT 42

Exploring the (Metric) Space of Collider Events

Quantifying event modifications: Pileup

Eric M. Metodiev, MIT 43

Exploring the (Metric) Space of Collider Events

Quantifying event modifications: Pileup

Eric M. Metodiev, MIT 44

Leading Vertex Jet + Pileup How can we quantify pileup mitigation?

[M. Cacciari, G.P. Salam, G. Soyez, 1407.0408] [D. Bertolini, P. Harris, M. Low, N. Tran, 1407.6013] [P.T. Komiske, EMM, B. Nachman, M.D. Schwartz, 1707.08600]

Exploring the (Metric) Space of Collider Events

Quantifying event modifications: Pileup

Eric M. Metodiev, MIT 45

Discontinuous under physically-sensible single-pixel perturbations. Undesirable behavior with increasing resolution. Compare calorimeter images pixel by pixel? Requires ad hoc choices of observables. Compare on a collection of observables?

Exploring the (Metric) Space of Collider Events

Quantifying event modifications: Pileup

Eric M. Metodiev, MIT 46

+ Pileup CHS PUPPI SoftKiller Measure pileup mitigation performance with EMD! PUMML Leading Vertex Jet Guarantees performance on IRC safe observables. Stable under physically-sensible perturbations. Train to optimize EMD with machine learning?

Exploring the (Metric) Space of Collider Events

Exploring the Space of Events: W jets

Eric M. Metodiev, MIT 47

W 𝑨

1−𝑨

𝜄 Visualize the space of events with t-Distributed Stochastic Neighbor Embedding (t-SNE). Finds an embedding into a low-dimensional manifold that respects distances. 𝑨 1 − 𝑨 𝜄2 = 𝑞𝜈𝐾

2

𝑞𝑈

2 = 𝑛𝑋 2

𝑞𝑈

2

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

[L. van der Maaten, G. Hinton]

Exploring the (Metric) Space of Collider Events

Exploring the Space of Events: W jets

Eric M. Metodiev, MIT 48

W 𝑨

1−𝑨

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

W jets, 𝑆 = 1.0 𝑞𝑈 ∈ 500,510 GeV

𝑨 1 − 𝑨 𝜄2 = 𝑞𝜈𝐾

2

𝑞𝑈

2 = 𝑛𝑋 2

𝑞𝑈

2

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

Exploring the (Metric) Space of Collider Events

Exploring the Space of Jets: Correlation Dimension

Eric M. Metodiev, MIT 49

dim 𝑅 = 𝑅 𝜖 𝜖𝑅 ln ෍

𝑗=1 𝑂

෍

𝑘=1 𝑂

Θ[EMD ℇ𝑗, ℇ𝑘 < 𝑅]

Energy scale 𝑅 dependence Count neighbors in ball of radius 𝑅

𝑂neighboring

points

𝑠 ∝ 𝑠dim dim(𝑠) = r 𝜖 𝜖𝑠 ln 𝑂neighbors 𝑠 Intuition: Correlation dimension:

Exploring the (Metric) Space of Collider Events

Exploring the Space of Jets: Correlation Dimension

Eric M. Metodiev, MIT 50

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. Can we understand this analytically?

Exploring the (Metric) Space of Collider Events

Exploring the Space of Jets: Correlation Dimension

Eric M. Metodiev, MIT 51

dim𝑟/𝑕(𝑅) = − 8𝛽𝑡𝐷𝑟/𝑕 𝜌 ln 𝑅 𝑞𝑈/2 𝐷𝑟 = 𝐷𝐺 = 4 3 𝐷𝑕 = 𝐷𝐵 = 3 At LL:

+ 1-loop running of 𝛽𝑡 Quark jets Gluon jets

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

Exploring the (Metric) Space of Collider Events

Exploring the Space of Events: k-medoids

Eric M. Metodiev, MIT 52

Exploring the (Metric) Space of Collider Events

Exploring the Space of Events: Jet Classification

Eric M. Metodiev, MIT 53

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

Exploring the (Metric) Space of Collider Events

Exploring the Space of Events

Eric M. Metodiev, MIT 54

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

Exploring the (Metric) Space of Collider Events

Exploring the Space of Events: QCD Jets

Eric M. Metodiev, MIT 55

Exploring the (Metric) Space of Collider Events

Exploring the Space of Jets: Correlation Dimension

Eric M. Metodiev, MIT 56

= − 8𝛽𝑡𝐷𝑟/𝑕 𝜌 ln 𝑅 𝑞𝑈/2 𝐷𝑟 = 𝐷𝐺 = 4 3 𝐷𝑕 = 𝐷𝐵 = 3

+ 1-loop running of 𝛽𝑡

dim𝑟/𝑕 𝑅 = 𝑅 𝜖 𝜖𝑅 ln ෍

𝑗=1 𝑂

෍

𝑘=1 𝑂

Θ[EMD ℇ𝑗, ℇ𝑘 < 𝑅] = 𝑅 𝜖 𝜖𝑅 ln Pr [EMD < 𝑅] = 𝑅 𝜖 𝜖𝑅 ln exp − 4𝛽𝑇𝐷𝑟/𝑕 𝜌 ln2 𝑅 𝑞𝑈/2 = 𝑅 𝜖 𝜖𝑅 ln Pr [𝜇 𝛾=1 < 𝑅; 𝐷𝑟/𝑕 → 2 𝐷𝑟/𝑕]

[A. Larkoski, 1709.06195]

Sketch of leading log (one emission) calculation:

Exploring the (Metric) Space of Collider Events

What is a collision event?

Eric M. Metodiev, MIT 57

𝛿 𝑓± 𝜈± 𝜌± 𝐿± 𝐿𝑀 𝑞/ ҧ 𝑞 𝑜/ത 𝑜

photon electron muon pion kaon K-long proton neutron

When are two collider events similar?

How an event gets its shape: Experiment

Exploring the (Metric) Space of Collider Events

Pileup Mitigation with PUMML

Eric M. Metodiev, MIT 58