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

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

Outline When are two events similar? The Energy Mover’s Distance Movie Time Applications 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(ො 𝑜 − 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? The Energy Mover’s Distance Movie Time Applications Eric M. Metodiev, MIT Exploring the (Metric) 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 [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 9

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 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 ′ 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 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] 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. ℇ′′ 𝑁 ′ 𝑁 ′ 𝑁 𝑁 𝜄 𝑗𝑘 EMD ℇ, ℇ ′ = min ′ {𝑔} ෍ ෍ 𝑔 𝑆 + ෍ 𝐹 𝑗 − ෍ 𝐹 𝑗𝑘 𝑘 ℇ ′ 𝑗=1 𝑘=1 𝑗=1 𝑘=1 ℇ Difference in Difference in total energy radiation pattern Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 12

Outline When are two events similar? The Energy Mover’s Distance Movie Time Applications Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 13

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 14

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 15

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 16

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 17

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 18

Outline When are two events similar? The Energy Mover’s Distance Movie Time Applications Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 19

Old Observables in a New Language Thrust is the EMD between the event and two back-to-back particles. 𝑢 = 𝐹 − max ෍ | Ԧ 𝑞 𝑗 ⋅ ො 𝑜| 𝑢(ℇ) = min ℇ ′ =2 EMD(ℇ, ℇ′) 𝑜 ො 𝑗 with 𝜄 𝑗𝑘 = Ƹ 𝑞 𝑗 ⋅ Ƹ 𝑞 𝑘 , Ƹ 𝑞 = Ԧ 𝑞/𝐹 𝑶 -(sub)jettiness is the EMD between the event and the closest 𝑂 -particle event. 𝑁 𝛾 = min 𝛾 , 𝜄 2,𝑙 𝛾 , … , 𝜄 𝑂,𝑙 𝛾 } 𝜐 𝑂 (ℇ) = min ℇ ′ =𝑂 EMD ℇ, ℇ′ . 𝜐 𝑂 𝑂 axes ෍ 𝐹 𝑗 min 𝑙 {𝜄 1,𝑙 𝑗=1 𝜐 𝛾 ≠ 1 is p-Wasserstein distance with p = 𝛾 . Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 20

Ƹ EMD and IRC-Safe Observables Events close in EMD are close in any infrared and collinear safe observable 𝑁 Additive IRC-safe observables: 𝒫 ℇ = ෍ 𝐹 𝑗 Φ 𝑞 𝑗 𝑗=1 EMD ℇ, ℇ ′ ≥ 1 Earth Mover’s Difference in 𝑆𝑀 𝒫 ℇ − 𝒫 ℇ ′ Distance observable values “Lipschitz constant” of Φ i.e. bound on its derivative 𝒫 e.g. jet angularities: 𝑁 [C. Berger, T. Kucs, and G. Sterman, 0303051] 𝜇 (𝛾) = ෍ 𝛾 𝐹 𝑗 𝜄 𝑗 [A. Larkoski, J. Thaler, and W. Waalewijn, 1408.3122] For 𝛾 ≥ 1 jet angularities: 𝑗=1 𝜇 (𝛾) ℇ − 𝜇 (𝛾) ℇ ′ ≤ 𝛾 EMD ℇ, ℇ ′ Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 21

𝑁 Quantifying event modifications: Hadronization 𝜇 (𝛾=1) = ෍ 𝐹 𝑗 𝜄 𝑗 𝑗=1 partons hadrons 𝜇 (𝛾=1) = 111.1GeV 𝜇 (𝛾=1) = 111.6GeV ℇ = ℇ partons 𝜇 (𝛾=1) ℇ − 𝜇 (𝛾=1) ℇ ′ ≤ EMD ℇ, ℇ ′ ℇ ′ = ℇ hadrons Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 22

𝑁 Quantifying event modifications: Hadronization 𝜇 (𝛾=1) = ෍ 𝐹 𝑗 𝜄 𝑗 𝑗=1 partons hadrons 𝜇 (𝛾=1) = 111.1GeV 𝜇 (𝛾=1) = 111.6GeV ℇ = ℇ partons 𝜇 (𝛾=1) ℇ − 𝜇 (𝛾=1) ℇ ′ ≤ EMD ℇ, ℇ ′ ℇ ′ = ℇ hadrons Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 23

Exploring the Space of Events: W jets 𝑨 W 𝜄 1 −𝑨 Visualize the space of events with t-Distributed Stochastic Neighbor Embedding (t-SNE). [L. van der Maaten, G. Hinton] W jets are 2-pronged and constrained by W mass: Finds an embedding into a low-dimensional 2 2 𝑞 𝜈𝐾 2 = 𝑛 𝑋 manifold that respects distances. 𝑨 1 − 𝑨 𝜄 2 = 2 𝑞 𝑈 𝑞 𝑈 Hence we expect a two -dimensional space of W jets: 𝑨, 𝜒 After 𝜒 rotation, one -dimensional: 𝑨 Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 24

Exploring the Space of Events: W jets “top heavy” 𝑨 W 𝜄 1 −𝑨 W jets are 2-pronged and “one pronged” constrained by W mass: “balanced” 2 2 𝑞 𝜈𝐾 2 = 𝑛 𝑋 ? 𝑨 1 − 𝑨 𝜄 2 = 2 𝑞 𝑈 𝑞 𝑈 Hence we expect a two -dimensional space of W jets: 𝑨, 𝜒 After 𝜒 rotation, W jets, 𝑆 = 1.0 “bottom heavy” one -dimensional: 𝑨 𝑞 𝑈 ∈ 500,510 GeV 2x zoom Eric M. Metodiev, MIT Exploring the (Metric) Space of Collider Events 25