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

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

Outline When are two jets similar? Energy Mover’s Distance Quantifying Jet Similarity ! Exploring the Space of Jets Eric M. Metodiev, MIT The Space of Collider Events 2

Outline When are two jets similar? Energy Mover’s Distance Quantifying Jet Similarity ! Exploring the Space of Jets Eric M. Metodiev, MIT The Space of Collider Events 3

When are two jets similar? These two jets “look” similar, but have different numbers of particles, flavors, and locations. How do we quantify this? Jet 1 Jet 2 PRELIMINARY PRELIMINARY 400 GeV AK5 Jets from CMS Open Data “Space of Jets” See Radha’s talk on Thursday for more! Eric M. Metodiev, MIT The Space of Collider Events 4

When are two jets similar? Rapidity ! A z i m u t h " Detection ) Hadronization hadrons & ± ( ± … Fragmentation ) partons # $ % … Collision The energy flow (distribution of energy) is the information that is robust to: [N.A. Sveshnikov, F.V. Tkachov, 9512370] fragmentation, hadronization, detector effects, … [F.V. Tkachov, 9601308] [P.S. Cherzor, N.A. Sveshnikov, 9710349] Energy flow ó Infrared and Collinear (IRC) Safe information Eric M. Metodiev, MIT The Space of Collider Events 5

When are two jets similar? PRELIMINARY Rapidity ! A z i m u t h " Detection ) Hadronization hadrons & ± ( ± … Fragmentation PRELIMINARY ) partons # $ % … Collision 4 Treat jets as distributions of energy: ℇ(, -) = 0 5 1 6(, - − , - 1 ) 123 Ignoring particle flavor, charge… energy direction Eric M. Metodiev, MIT The Space of Collider Events 6

Outline When are two jets similar? When they have similar distributions of energy Energy Mover’s Distance Quantifying Jet Similarity ! Exploring the Space of Jets Eric M. Metodiev, MIT The Space of Collider Events 7

Outline When are two jets similar? When they have similar distributions of energy Energy Mover’s Distance Quantifying Jet Similarity ! Exploring the Space of Jets Eric M. Metodiev, MIT The Space of Collider Events 8

The Energy Mover’s Distance Review: The Earth Mover’s Distance Earth Mover’s Distance : the minimum “work” (stuff x distance) to rearrange one pile of dirt into another [Peleg, Werman, Rom] [Rubner, Tomasi, Guibas] 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. Eric M. Metodiev, MIT The Space of Collider Events 9

The Energy Mover’s Distance From Earth to Energy Energy Mover’s Distance : the minimum “work” (energy x angle) to rearrange one jet (pile of energy) into another [Komiske, EMM, Thaler, 1902.02346] PRELIMINARY PRELIMINARY 2 4 2 4 2 2 9 / 6 /3 6 /3 EMD ℇ, ℇ & = min & {,} . . 5 7 + . 9 / − . 9 & 9 /3 3 3 5 /3 /01 301 /01 301 Difference in Difference in total energy radiation pattern Eric M. Metodiev, MIT The Space of Collider Events 10

The Energy Mover’s Distance From Earth to Energy Energy Mover’s Distance : the minimum “work” (energy x angle) to rearrange one event (pile of energy) into another [Komiske, EMM, Thaler, 1902.02346] PRELIMINARY ℇ′ ℇ ++ ℇ EMD(ℇ , ℇ′) + EMD ℇ + , ℇ ++ ≥ EMD(ℇ , ℇ′′) EMD has dimensions of energy # True metric as long as ! ≥ $ % &'( ! ≥ the jet radius, for conical jets Solvable via Optimal Transport problem. ~ 1 ms to compute EMD for two jets with 100 particles. Eric M. Metodiev, MIT The Space of Collider Events 11

The Energy Mover’s Distance From Earth to Energy Energy Mover’s Distance : the minimum “work” (energy x angle) to rearrange one event (pile of energy) into another [Komiske, EMM, Thaler, 1902.02346] ℇ′ ℇ ## ℇ 158.7 GeV 122.5 GeV EMD(ℇ , ℇ′) + EMD ℇ # , ℇ ## ≥ EMD(ℇ , ℇ′′) 205.8 GeV https://energyflow.network Eric M. Metodiev, MIT The Space of Collider Events 12

Outline When are two jets similar? When they have similar distributions of energy Energy Mover’s Distance The “work” to rearrange one jet into another Quantifying Jet Similarity ! Exploring the Space of Jets Eric M. Metodiev, MIT The Space of Collider Events 13

Outline When are two jets similar? When they have similar distributions of energy Energy Mover’s Distance The “work” to rearrange one jet into another Quantifying Jet Similarity ! Exploring the Space of Jets Eric M. Metodiev, MIT The Space of Collider Events 14

Energy Moving and IRC Safety Events close in EMD are close in any infrared and collinear safe observable! Additive IRC-safe observables: EMD ℇ, ℇ & ≥ 1 Difference in Energy Mover’s )* + ℇ − + ℇ & observable values Distance “Lipschitz constant” of Φ i.e. bound on its derivative + 2 + ℇ = . 3 / Φ 5 6 / /01 e.g. 7 ≥ 1 jet angularities: [Berger, Kucs, Sterman, 0303051] [Larkoski, Thaler, Waalewijn, 1408.3122] 8 (:) ℇ − 8 (:) ℇ & ≤ 7 EMD ℇ, ℇ & Eric M. Metodiev, MIT The Space of Collider Events 15

Old Observables in a New Language " -subjettiness is the EMD between the event and the closest # -particle event. < 4 (ℇ) = min 4 , ? @,: 4 , … , ? $,: 4 } ! $ (ℇ) = min ℇ , -$ EMD ℇ, ℇ′ . ! $ $ 5678 9 = : min{? ;,: C ≥ 1 is p-Wasserstein :-; distance with p = C . # = 3 # = 1 # = 2 PRELIMINARY PRELIMINARY PRELIMINARY ! Geometry in the space of events Thrust is the EMD between the event and two back-to-back particles. G(ℇ) = min ℇ , -@ EMD(ℇ, ℇ′) G(ℇ) = = − max 9 | ⃗ O : ⋅ K Q| K L with ? :R = K Q : ⋅ K Q R , K Q = ⃗ O/= : Eric M. Metodiev, MIT The Space of Collider Events 16

Quantifying Pileup and Detector Effects with EMD EMD universally quantifies pileup and detector effects. Gen./Sim. EMD: 44.4 GeV Gen./Sim. EMD: 33.7 GeV Gen./Sim. EMD: 6.7 GeV PRELIMINARY PRELIMINARY PRELIMINARY #$% > 1 GeV cut + charged hadron subtraction + Tracks only, ! " See extra slides for histograms. Can also quantify hadronization effects this way. Eric M. Metodiev, MIT The Space of Collider Events 17

Outline When are two jets similar? When they have similar distributions of energy Energy Mover’s Distance The “work” to rearrange one jet into another Quantifying Jet Similarity ! Geometry of the space of jets. Bounds for pileup, detector effects Exploring the Space of Jets Eric M. Metodiev, MIT The Space of Collider Events 18

Outline When are two jets similar? When they have similar distributions of energy Energy Mover’s Distance The “work” to rearrange one jet into another Quantifying Jet Similarity ! Geometry of the space of jets. Bounds for pileup, detector effects Exploring the Space of Jets Eric M. Metodiev, MIT The Space of Collider Events 19

Most Representative Jets: K-medoids Jet Mass PRELIMINARY Eric M. Metodiev, MIT The Space of Collider Events 20

Most Representative Jets: K-medoids Jet Mass PRELIMINARY Eric M. Metodiev, MIT The Space of Collider Events 21

Towards Anomaly Detection More Typical More Anomalous Mean EMD to Dataset PRELIMINARY PRELIMINARY 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] Eric M. Metodiev, MIT The Space of Collider Events 22

Towards Anomaly Detection More Typical More Anomalous Mean EMD to Dataset PRELIMINARY PRELIMINARY 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] Eric M. Metodiev, MIT The Space of Collider Events 23

Exploring the Space of Jets: Visualizing the Manifold Visualize the space of events with t-Distributed Stochastic Neighbor Embedding (t-SNE). [L. van der Maaten, G. Hinton] Finds an embedding into a low-dimensional manifold that respects distances. What does the space of jets look like? Eric M. Metodiev, MIT The Space of Collider Events 24

Exploring the Space of Jets: Visualizing the Manifold one-prong What does the space of jets look like? two-prong Eric M. Metodiev, MIT The Space of Collider Events 25

Exploring the Space of Jets: Correlation Dimension Correlation dimension: ; ; dim ( = ( 6 6( ln 7 7 Θ[EMD ℇ 8 , ℇ < < (] 89: <9: Energy scale ( Count neighbors in dependence ball of radius ( Quark jets Gluon jets Dimension blows up at dim $/& (() = − 8- . / $/& ( low energies. At LL: ln 0 3 4 /2 Jets are “more than fractal” Eric M. Metodiev, MIT The Space of Collider Events 26