Exploring the (Metric) Space of Collider Events with CMS Open Data Monash University Virtual Seminar Eric M. Metodiev Center for Theoretical Physics Massachusetts Institute of Technology Joint work with Patrick Komiske and Jesse Thaler [1902.02346] CMS Open Data also with Radha Mastandrea and Preksha Naik [1908.08542] November 19, 2019 1
Outline The Metric Space of Collider Events When are two events similar? The Energy Mover’s Distance A Geometric Language for Observables Old Observables in a New Light Quantifying Hadronization Exploring the Space of Jets with CMS Open Data Most Representative and Anomalous Jets Visualizing the Space and its (fractal) dimension Eric M. Metodiev, MIT Exploring the Space of Collider Events 2
Outline The Metric Space of Collider Events When are two events similar? The Energy Mover’s Distance A Geometric Language for Observables Old Observables in a New Light Quantifying Hadronization Exploring the Space of Jets with CMS Open Data Most Representative and Anomalous Jets Visualizing the Space and its (fractal) dimension Eric M. Metodiev, MIT Exploring the Space of Collider Events 3
When are two events similar? Eric M. Metodiev, MIT Exploring the Space of Collider Events 4
When are two events similar? These two jets “look” similar, but have different numbers of particles, flavors, and locations. How do we quantify this? Jet 1 Jet 2 “Space of Jets” 400 GeV 𝑆 = 0.5 anti- 𝑙 𝑈 Jets from CMS Open Data Eric M. Metodiev, MIT Exploring the Space of Collider Events 5
When are two events similar? How a jet gets its shape Detection 𝑞 Hadronization hadrons 𝜌 ± 𝐿 ± … Fragmentation partons 𝑣 𝑒 … 𝑞 Collision Eric M. Metodiev, MIT Exploring the Space of Collider Events 6
When are two events similar? An 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 Space of Collider Events 7
When are two jets 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: ℇ(ො 𝑜) = 𝐹 𝑗 𝜀(ො 𝑜 − ො 𝑜 𝑗 ) 𝑗=1 Ignoring particle flavor, charge… energy direction Eric M. Metodiev, MIT Exploring the Space of Collider Events 8
Outline The Metric Space of Collider Events When are two collider events similar? When they have similar energy distributions The Energy Mover’s Distance A Geometric Language for Observables Old Observables in a New Light Quantifying Hadronization Exploring the Space of Jets with CMS Open Data Most Representative and Anomalous Jets Visualizing the Space and its (fractal) dimension Eric M. Metodiev, MIT Exploring the Space of Collider Events 9
Outline The Metric Space of Collider Events When are two collider events similar? When they have similar energy distributions The Energy Mover’s Distance A Geometric Language for Observables Old Observables in a New Light Quantifying Hadronization Exploring the Space of Jets with CMS Open Data Most Representative and Anomalous Jets Visualizing the Space and its (fractal) dimension Eric M. Metodiev, MIT Exploring the Space of Collider Events 10
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 their expectation values are close. Also known as the 1- Wasserstein metric. Eric M. Metodiev, MIT Exploring 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 jet (pile of energy) into another [Komiske, EMM , Thaler, 1902.02346] 𝑁 ′ 𝑁 ′ 𝑁 𝑁 𝐹 𝑗 𝜄 𝑗𝑘 𝜄 𝑗𝑘 EMD ℇ, ℇ ′ = min ′ 𝑔 𝑆 + 𝐹 𝑗 − 𝐹 {𝑔} ′ 𝐹 𝑗𝑘 𝑘 𝑘 𝑔 𝑗𝑘 𝑗=1 𝑘=1 𝑗=1 𝑘=1 Difference in Difference in radiation pattern total energy Eric M. Metodiev, MIT Exploring the 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 [Komiske, EMM , Thaler, 1902.02346] ℇ′ ℇ ′′ ℇ EMD(ℇ , ℇ′) + EMD ℇ ′ , ℇ ′′ ≥ EMD(ℇ , ℇ′′) 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. Eric M. Metodiev, MIT Exploring the Space of Collider Events 13
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 Exploring the Space of Collider Events 14
Outline The Metric Space of Collider Events When are two collider events similar? When they have similar energy distributions The Energy Mover’s Distance The “work” to rearrange one event into another A Geometric Language for Observables Old Observables in a New Light Quantifying Hadronization Exploring the Space of Jets with CMS Open Data Most Representative and Anomalous Jets Visualizing the Space and its (fractal) dimension Eric M. Metodiev, MIT Exploring the Space of Collider Events 15
Outline The Metric Space of Collider Events When are two collider events similar? When they have similar energy distributions The Energy Mover’s Distance The “work” to rearrange one event into another A Geometric Language for Observables Old Observables in a New Light Quantifying Hadronization Exploring the Space of Jets with CMS Open Data Most Representative and Anomalous Jets Visualizing the Space and its (fractal) dimension Eric M. Metodiev, MIT Exploring the Space of Collider Events 16
A Geometric Language for Observables 𝑶 -(sub)jettiness is a ubiquitous “N - prong” observable used at the LHC 𝑁 [Thaler, Van Tilburg, 1011.2268] 𝛾 , 𝜄 2,𝑗 𝛾 , … , 𝜄 𝑂,𝑗 𝛾 } 𝜐 𝑂 (ℇ) = min 𝑂 axes 𝐹 𝑗 min{𝜄 1,𝑗 𝑗=1 Eric M. Metodiev, MIT Exploring the Space of Collider Events 17
A Geometric Language for Observables 𝑶 -(sub)jettiness is a ubiquitous “N - prong” observable used at the LHC 𝑁 [Thaler, Van Tilburg, 1011.2268] 𝛾 , 𝜄 2,𝑗 𝛾 , … , 𝜄 𝑂,𝑗 𝛾 } 𝜐 𝑂 (ℇ) = min 𝑂 axes 𝐹 𝑗 min{𝜄 1,𝑗 𝑗=1 𝑂 = 1, 𝜐 1 ∼ 1 Eric M. Metodiev, MIT Exploring the Space of Collider Events 18
A Geometric Language for Observables 𝑶 -(sub)jettiness is a ubiquitous “N - prong” observable used at the LHC 𝑁 [Thaler, Van Tilburg, 1011.2268] 𝛾 , 𝜄 2,𝑗 𝛾 , … , 𝜄 𝑂,𝑗 𝛾 } 𝜐 𝑂 (ℇ) = min 𝑂 axes 𝐹 𝑗 min{𝜄 1,𝑗 𝑗=1 𝑂 = 2, 𝜐 2 ∼ 1 Eric M. Metodiev, MIT Exploring the Space of Collider Events 19
A Geometric Language for Observables 𝑶 -(sub)jettiness is a ubiquitous “N - prong” observable used at the LHC 𝑁 [Thaler, Van Tilburg, 1011.2268] 𝛾 , 𝜄 2,𝑗 𝛾 , … , 𝜄 𝑂,𝑗 𝛾 } 𝜐 𝑂 (ℇ) = min 𝑂 axes 𝐹 𝑗 min{𝜄 1,𝑗 𝑗=1 𝑂 = 3, 𝜐 3 ≪ 1 Eric M. Metodiev, MIT Exploring the Space of Collider Events 20
A Geometric Language for Observables 𝑶 -(sub)jettiness is the EMD between the event and the closest 𝑂 -particle event. 𝑁 𝛾 , 𝜄 2,𝑗 𝛾 , … , 𝜄 𝑂,𝑗 𝛾 } 𝜐 𝑂 (ℇ) = min ℇ ′ =𝑂 EMD ℇ, ℇ′ . 𝜐 𝑂 (ℇ) = min 𝑂 axes 𝐹 𝑗 min{𝜄 1,𝑗 𝛾 -Wasserstein distance 𝑗=1 𝑂 = 3, 𝜐 3 ≪ 1 𝜐 1 two particle jet submanifold 𝜐 2 three particle jet manifold 𝜐 3 Geometry in the space of events Eric M. Metodiev, MIT Exploring the Space of Collider Events 21
A Geometric Language for Observables Thrust is a classic event shape that measures how “pencil - like” an event is. [Farhi, PRL 1977] 𝑢(ℇ) = 𝐹 − max | Ԧ 𝑞 𝑗 ⋅ ො 𝑜| ො 𝑜 𝑗 Eric M. Metodiev, MIT Exploring the Space of Collider Events 22
A Geometric Language for Observables Thrust is a classic event shape that measures how “pencil - like” an event is. [Farhi, PRL 1977] 𝑢(ℇ) = 𝐹 − max | Ԧ 𝑞 𝑗 ⋅ ො 𝑜| ො 𝑜 𝑗 𝑢 ≪ 1 Eric M. Metodiev, MIT Exploring the Space of Collider Events 23
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