Exploring The (Metric) Space of Collider Events CERN Particle and - PowerPoint PPT Presentation

Exploring The (Metric) Space of Collider Events CERN Particle and Astro-Particle Physics Seminar Eric M. Metodiev Center for Theoretical Physics Massachusetts Institute of T echnology Joint work with Patrick Komiske and Jesse Thaler [1902.02346] February 22, 2019 1

Outline When are two events similar? Part I The Energy Mover’s Distance Introduction Movie Time Observables Quantifying event modifications Part II Applications Exploring the Space of Events Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 2

Outline When are two events similar? Part I The Energy Mover’s Distance Introduction Movie Time Observables Quantifying event modifications Part II Applications Exploring the Space of Events Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 3

When are two events similar? Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 4

When are two collider events similar? How an event gets its shape Detection 𝑞 Hadronization hadrons 𝜌 ± 𝐿 ± … Fragmentation partons 𝑕 𝑣 𝑒 … 𝑞 Collision Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 5

When are two collider events similar? A collider event is… Theoretically: very complicated Experimentally: very complicated However: The energy flow (distribution of energy) is the information that is robust to: fragmentation, hadronization, detector effects, … [N.A. Sveshnikov, F.V. Tkachov, 9512370] [F.V. Tkachov, 9601308] [P.S. Cherzor, N.A. Sveshnikov, 9710349] Energy flow  Infrared and Collinear (IRC) Safe information Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 6

When are two collider events similar? Energy flow is robust information Detection 𝑞 Hadronization hadrons 𝜌 ± 𝐿 ± … Fragmentation partons 𝑕 𝑣 𝑒 … 𝑞 Collision 𝑁 Treat events as distributions of energy: ෍ 𝐹 𝑗 𝜀( Ƹ 𝑞 𝑗 ) 𝑗=1 Ignoring particle flavor, charge… energy direction Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 7

Outline When are two events similar? When they have similar distributions of energy Part I The Energy Mover’s Distance Introduction Movie Time Observables Quantifying event modifications Part II Applications Exploring the Space of Events Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 8

Outline When are two events similar? When they have similar distributions of energy Part I The Energy Mover’s Distance Introduction Movie Time Observables Quantifying event modifications Part II Applications Exploring the Space of Events Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 9

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 [S. Peleg, M. Werman, H. Rom] [Y. Rubner, C. Tomasi, and L.J. Guibas] 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. Eric M. Metodiev, MIT Exploring the (Metric) 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 [P.T. Komiske, EMM, J. Thaler, 1902.02346] 𝑁 ′ 𝑁 𝜄 𝑗𝑘 𝐹 𝑗 EMD ℇ, ℇ ′ = min 𝜄 𝑗𝑘 {𝑔} ෍ ෍ 𝑔 𝑗𝑘 ′ 𝐹 𝑆 𝑘 𝑔 𝑗=1 𝑘=1 𝑗𝑘 Difference in radiation pattern Eric M. Metodiev, MIT Exploring the (Metric) 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 [P.T. Komiske, EMM, J. Thaler, 1902.02346] 𝑁 ′ 𝑁 ′ 𝑁 𝑁 𝜄 𝑗𝑘 𝐹 𝑗 EMD ℇ, ℇ ′ = min 𝜄 𝑗𝑘 ′ {𝑔} ෍ ෍ 𝑔 𝑆 + ෍ 𝐹 𝑗 − ෍ 𝐹 𝑗𝑘 𝑘 ′ 𝐹 𝑘 𝑔 𝑗=1 𝑘=1 𝑗=1 𝑘=1 𝑗𝑘 Difference in Difference in total energy radiation pattern Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 12

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 [P.T. Komiske, EMM, J. Thaler, 1902.02346] EMD has dimensions of energy 1 True metric as long as 𝑆 ≥ 2 𝜄 max 𝑆 ≥ the jet radius, for conical jets Solvable via Optimal Transport problem. ~ 1 ms to compute EMD for two jets with 100 particles. 𝑁 ′ 𝑁 ′ 𝑁 𝑁 𝜄 𝑗𝑘 𝐹 𝑗 EMD ℇ, ℇ ′ = min 𝜄 𝑗𝑘 ′ {𝑔} ෍ ෍ 𝑔 𝑆 + ෍ 𝐹 𝑗 − ෍ 𝐹 𝑗𝑘 𝑘 ′ 𝐹 𝑘 𝑔 𝑗=1 𝑘=1 𝑗=1 𝑘=1 𝑗𝑘 Difference in Difference in total energy radiation pattern Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 13

Outline When are two events similar? When they have similar distributions of energy Part I The Energy Mover’s Distance Introduction Work to rearrange one event into another. Movie Time Observables Quantifying event modifications Part II Applications Exploring the Space of Events Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 14

Outline When are two events similar? When they have similar distributions of energy Part I The Energy Mover’s Distance Introduction Work to rearrange one event into another. Movie Time Observables Quantifying event modifications Part II Applications Exploring the Space of Events Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 15

Movie Time: Visualizing the EMD Taking a walk in the space of events EMD is the cost of an optimal transport problem. We also get the shortest path between the events. Interpolate along path to visualize! Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 16

Movie Time: Visualizing Jet Formation Hadronization Fragmentation Collision QCD Jets W Jets 𝑞 T op Jets 𝑞 Pythia 8, 𝑆 = 1.0 jets, 𝑞 𝑈 ∈ 500,550 GeV Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 17

Movie Time: Visualizing QCD Jet Formation Quark Fragmentation Hadronization fragmentation hadronization EMD: 111.6 GeV EMD: 18.1 GeV Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 18

Movie Time: Visualizing W Jet Formation W Decay Quarks Fragmentation Hadronization decay fragmentation hadronization EMD: 78.3 GeV EMD: 26.3 GeV EMD: 12.9 GeV Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 19

Movie Time: Visualizing Top Jet Formation Top Decay Quarks Fragmentation Hadronization decay fragmentation hadronization EMD: 161.1 GeV EMD: 47.1 GeV EMD: 27.0 GeV Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 20

Outline When are two events similar? When they have similar distributions of energy Part I The Energy Mover’s Distance Introduction Work to rearrange one event into another. Movie Time Visualize energy movement and jet formation. Observables Quantifying event modifications Part II Applications Exploring the Space of Events Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 21

Outline When are two events similar? When they have similar distributions of energy Part I The Energy Mover’s Distance Introduction Work to rearrange one event into another. Movie Time Visualize energy movement and jet formation. Observables Quantifying event modifications Part II Applications Exploring the Space of Events Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 22

Observables 𝑁 𝑂 -subjettiness: 𝛾 = ෍ 𝛾 , 𝜄 2,𝑙 𝛾 , … , 𝜄 𝑂,𝑙 𝛾 } 𝜐 𝑂 𝐹 𝑗 min 𝑂 axes {𝜄 1,𝑙 [J. Thaler, K. Van Tilburg, 1011.2268] 𝑗=1 [J. Thaler, K. Van Tilburg, 1108.2701] measures how well jet energy is aligned into N subjets 𝜐 1 /𝐹 ≫ 0 𝜐 1 /𝐹 > 𝜐 2 /𝐹 ≫ 0 𝜐 3 /𝐹 ≃ 0 Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 23

Observables 𝑁 𝑂 -subjettiness: 𝛾 = ෍ 𝛾 , 𝜄 2,𝑙 𝛾 , … , 𝜄 𝑂,𝑙 𝛾 } 𝜐 𝑂 𝐹 𝑗 min 𝑂 axes {𝜄 1,𝑙 [J. Thaler, K. Van Tilburg, 1011.2268] 𝑗=1 [J. Thaler, K. Van Tilburg, 1108.2701] measures how well jet energy is aligned into N subjets 𝜐 1 /𝐹 ≫ 0 𝜐 1 /𝐹 > 𝜐 2 /𝐹 ≫ 0 𝜐 3 /𝐹 ≃ 0 𝑂 -subjettiness is the EMD between the event and the closest 𝑂 -particle event. 𝜐 𝑂 (ℇ) = min ℇ ′ =𝑂 EMD ℇ, ℇ′ . 𝛾 ≠ 1 corresponds to other p-Wasserstein distances with p = 𝛾 . Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 24

Ƹ Observables 𝑁 Getting quantitative Take any additive IRC-safe observable: 𝒫 ℇ = ෍ 𝐹 𝑗 Φ 𝑞 𝑗 𝑗=1 𝐹 𝑗 𝑁 𝜄 𝑗 𝜇 (𝛾) = ෍ 𝛾 e.g. jet angularities: 𝐹 𝑗 𝜄 𝑗 [C. Berger, T. Kucs, and G. Sterman, 0303051] 𝑗=1 [A. Larkoski, J. Thaler, and W. Waalewijn, 1408.3122] Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 25