Analyzing Jet Substructure with Energy Flow Elementary Particle - PowerPoint PPT Presentation

Analyzing Jet Substructure with Energy Flow Elementary Particle Physics Journal Club Eric M. Metodiev Center for Theoretical Physics Massachusetts Institute of T echnology Joint work with Patrick Komiske and Jesse Thaler [1712.07124] [1810.05165] [19xx.xxxxx] April 26, 2019 1

Patrick T. Komiske III (MIT) Analyzing Jet Substructure via Energy Flow Analyzing Jet Substructure with Energy Flow 2

Slide by Jesse Thaler Patrick T. Komiske III (MIT) Analyzing Jet Substructure via Energy Flow Analyzing Jet Substructure with Energy Flow 3

IRC Safety Jet Mass N-(sub)jettiness … Angularities ECFs Thrust C, D Planar Flow ECFGs Infrared (IR) safety – observable is unchanged under addition of a soft particle: 𝜁 𝑇 = 𝑇( ) Collinear (C) safety – observable is unchanged under collinear splitting of a particle: 𝑇 = 𝑇 ∀𝜇 ∈ [0,1] 𝜇 IRC safety guarantees that the soft and collinear divergences of a QFT cancel at each order in perturbation theory (KLN theorem) Divergences in QCD splitting function: 𝐷 𝑟 = 𝐷 𝐺 = 4/3 𝑒𝑄 𝑗→𝑗𝑕 ≃ 2𝛽 𝑡 𝑒𝜄 𝑒𝑨 𝜌 𝐷 𝑗 𝜄 𝑨 𝐷 𝑕 = 𝐷 𝐵 = 3 IRC-safe observables probe hard structure while being insensitive to low energy or small angle modifications Eric M. Metodiev, MIT Analyzing Jet Substructure with Energy Flow 4

Outline Energy Flow Polynomials A basis of jet substructure observables Energy Flow Moments Tensor moments of the radiation pattern Energy Flow Networks ML architecture designed to learn from events Eric M. Metodiev, MIT Analyzing Jet Substructure with Energy Flow 5

Outline Energy Flow Polynomials A basis of jet substructure observables Energy Flow Moments Tensor moments of the radiation pattern Energy Flow Networks ML architecture designed to learn from events Eric M. Metodiev, MIT Analyzing Jet Substructure with Energy Flow 6

Expanding an Arbitrary IRC-safe Observable 𝜈 ) 𝜈 , … , 𝑞 𝑁 Arbitrary IRC-safe observable: S(𝑞 1 [1712.07124] • Energy expansion: Approximate 𝑇 with polynomials of 𝑨 𝑗 𝑘 𝑨 𝑗 𝜄 𝑗𝑘 • IR safety: 𝑇 is unchanged under addition of soft particle 𝑨 𝑘 • C safety: 𝑇 is unchanged under collinear splitting of a particle • Relabeling symmetry: Particle index is arbitrary 𝑁 𝑁 Energy correlator parametrized ෍ … ෍ 𝑨 𝑗 1 … 𝑨 𝑗 𝑂 𝑔( Ƹ 𝑞 𝑗 1 , … , Ƹ 𝑞 𝑗 𝑂 ) by angular function f [F. Tkachov, hep-ph/9601308] 𝑗 1 =1 𝑗 𝑂 =1 Energy correlators linearly span IRC-safe observables • Angular expansion: Approximate 𝑔 with polynomials in 𝜄 𝑗𝑘 • Simplify: Identify unique analytic structure that emerge • Linear spanning basis in terms of “EFPs” has been found! • 𝑁 𝑁 𝑇 ≃ ෍ 𝑡 𝐻 EFP 𝐻 , EFP 𝐻 ≡ ෍ … ෍ 𝑨 𝑗 1 … 𝑨 𝑗 𝑂 ෑ 𝜄 𝑗 𝑙 𝑗 ℓ 𝑕∈𝐻 𝑗 1 =1 𝑗 𝑂 =1 𝑙,ℓ ∈𝐻 Eric M. Metodiev, MIT Analyzing Jet Substructure with Energy Flow 7

• IRC Safe Jet Observables Expanding an Arbitrary IRC-safe Observable 𝜈 ) 𝜈 , … , 𝑞 𝑁 Arbitrary IRC-safe observable: S(𝑞 1 • Energy expansion: Approximate 𝑇 with polynomials of 𝑨 𝑗 𝑘 𝑨 𝑗 𝜄 𝑗𝑘 • IR safety: 𝑇 is unchanged under addition of soft particle 𝑨 𝑘 • C safety: 𝑇 is unchanged under collinear splitting of a particle • Relabeling symmetry: Particle index is arbitrary 𝑁 𝑁 Energy correlator parametrized ෍ … ෍ 𝑨 𝑗 1 … 𝑨 𝑗 𝑂 𝑔( Ƹ 𝑞 𝑗 1 , … , Ƹ 𝑞 𝑗 𝑂 ) by angular function f [F. Tkachov, hep-ph/9601308] 𝑗 1 =1 𝑗 𝑂 =1 Energy correlators linearly span IRC-safe observables • Angular expansion: Approximate 𝑔 with polynomials in 𝜄 𝑗𝑘 • Simplify: Identify unique analytic structure that emerge • Linear spanning basis in terms of “EFPs” has been found! • 𝑁 𝑁 𝑇 ≃ ෍ 𝑡 𝐻 EFP 𝐻 , EFP 𝐻 ≡ ෍ … ෍ 𝑨 𝑗 1 … 𝑨 𝑗 𝑂 ෑ 𝜄 𝑗 𝑙 𝑗 ℓ 𝑕∈𝐻 𝑗 1 =1 𝑗 𝑂 =1 𝑙,ℓ ∈𝐻 Eric M. Metodiev, MIT Analyzing Jet Substructure with Energy Flow 8

Expanding an Arbitrary IRC-safe Observable 𝜈 ) 𝜈 , … , 𝑞 𝑁 Arbitrary IRC-safe observable: S(𝑞 1 • Energy expansion: Approximate 𝑇 with polynomials of 𝑨 𝑗 𝑘 𝑨 𝑗 𝜄 𝑗𝑘 • IR safety: 𝑇 is unchanged under addition of soft particle 𝑨 𝑘 • C safety: 𝑇 is unchanged under collinear splitting of a particle • Relabeling symmetry: Particle index is arbitrary 𝑁 𝑁 Energy correlator parametrized ෍ … ෍ 𝑨 𝑗 1 … 𝑨 𝑗 𝑂 𝑔( Ƹ 𝑞 𝑗 1 , … , Ƹ 𝑞 𝑗 𝑂 ) by angular function f [F. Tkachov, hep-ph/9601308] 𝑗 1 =1 𝑗 𝑂 =1 Energy correlators linearly span IRC-safe observables • Angular expansion: Approximate 𝑔 with polynomials in 𝜄 𝑗𝑘 • Simplify: Identify unique analytic structure that emerge • Obtain linear spanning basis of Energy Flow Polynomials, “EFPs”: • 𝑁 𝑁 𝑇 ≃ ෍ 𝑡 𝐻 EFP 𝐻 , EFP 𝐻 ≡ ෍ … ෍ 𝑨 𝑗 1 … 𝑨 𝑗 𝑂 ෑ 𝜄 𝑗 𝑙 𝑗 ℓ 𝑕∈𝐻 𝑗 1 =1 𝑗 𝑂 =1 𝑙,ℓ ∈𝐻 Eric M. Metodiev, MIT Analyzing Jet Substructure with Energy Flow 9

Anatomy of an Energy Flow Polynomial: 𝑨 𝑗 𝜄 𝑗𝑘 𝑨 𝑘 𝑁 𝑁 𝑁 In equations: EFP G = ෍ ෍ ⋯ ෍ 𝑨 𝑗 1 𝑨 𝑗 2 ⋯ 𝑨 𝑗 𝑂 ෑ 𝜄 𝑗 𝑙 𝑗 𝑚 𝑗 1 =1 𝑗 2 =1 𝑗 𝑂 =1 𝑙,𝑚 ∈G Eric M. Metodiev, MIT 10 Eric M. Metodiev, MIT Analyzing Jet Substructure with Energy Flow 10

Anatomy of an Energy Flow Polynomial: 𝑨 𝑗 𝜄 𝑗𝑘 𝑨 𝑘 𝑁 𝑁 𝑁 In equations: EFP G = ෍ ෍ ⋯ ෍ 𝑨 𝑗 1 𝑨 𝑗 2 ⋯ 𝑨 𝑗 𝑂 ෑ 𝜄 𝑗 𝑙 𝑗 𝑚 𝑗 1 =1 𝑗 2 =1 𝑗 𝑂 =1 𝑙,𝑚 ∈G Correlator Energies Angles of and In words: Sum over all N -tuples of Product of the N One 𝜄 𝑗 𝑙 𝑗 𝑚 for each particle in the event energy fractions edge in 𝑙, 𝑚 ∈ 𝐻 Eric M. Metodiev, MIT Analyzing Jet Substructure with Energy Flow 11

Anatomy of an Energy Flow Polynomial: 𝑨 𝑗 𝜄 𝑗𝑘 𝑨 𝑘 𝑁 𝑁 𝑁 In equations: EFP G = ෍ ෍ ⋯ ෍ 𝑨 𝑗 1 𝑨 𝑗 2 ⋯ 𝑨 𝑗 𝑂 ෑ 𝜄 𝑗 𝑙 𝑗 𝑚 𝑗 1 =1 𝑗 2 =1 𝑗 𝑂 =1 𝑙,𝑚 ∈G Correlator Energies Angles of and In words: Sum over all N -tuples of Product of the N One 𝜄 𝑗 𝑙 𝑗 𝑚 for each particle in the event energy fractions edge in 𝑙, 𝑚 ∈ 𝐻 In pictures: 𝑨 𝑗 𝑘 𝜄 𝑗 𝑙 𝑗 𝑚 𝑘 𝑙 𝑚 3 𝑁 𝑁 𝑁 𝑁 1 2 (e.g.) 2 = ෍ ෍ ෍ ෍ 𝑨 𝑗 1 𝑨 𝑗 2 𝑨 𝑗 3 𝑨 𝑗 4 𝜄 𝑗 1 𝑗 2 𝜄 𝑗 2 𝑗 3 𝜄 𝑗 3 𝑗 4 𝜄 𝑗 2 𝑗 4 𝑗 1 =1 𝑗 2 =1 𝑗 3 =1 𝑗 4 =1 4 (any index labelling works) Eric M. Metodiev, MIT Analyzing Jet Substructure with Energy Flow 12

Organization of the basis EFPs are truncated by angular degree d, the order of the angular expansion. Finite number at each order in d All prime EFPs up to d=5 Exactly 1000 EFPs up to degree d=7 Image files for all of the prime EFP multigraphs up to d = 7 are available here. Eric M. Metodiev, MIT Analyzing Jet Substructure with Energy Flow 13

Familiar Jet Substructure Observables as EFPs 𝑁 𝑁 2 Scaled Jet Mass: 𝑛 𝐾 𝑨 𝑗 1 𝑨 𝑗 2 (cosh Δ𝑧 𝑗 1 𝑗 2 − cos Δ𝜚 𝑗 1 𝑗 2 ) = 1 2 = ෍ ෍ + ⋯ 𝑞 𝑈𝐾 2 𝑗 1 =1 𝑗 2 =1 𝑁 Jet Angularities: − 3 + 5 𝜇 (6) = 𝜇 (𝛽) = ෍ 𝛽 𝑨 𝑗 𝜄 𝑗 2 8 𝑗 [C. Berger, T. Kucs, and G. Sterman, hep-ph/0303051] − 3 [S. Ellis, et al ., 10010014] 𝜇 (4) = [A. Larkoski, J. Thaler, and W. Waalewijn, 1408.3122] 4 Energy Correlation Functions(ECFs): 𝑁 𝑁 𝑁 (𝛾) = ෍ 𝛾 𝑓 𝑂 ෍ ⋯ ෍ 𝑨 𝑗 1 𝑨 𝑗 2 ⋯ 𝑨 𝑗 𝑂 ෑ 𝜄 𝑗 𝑙 𝑗 𝑚 𝑗 1 =1 𝑗 2 =1 𝑗 𝑂 =1 𝑙<𝑚∈{1,⋯,𝑂} [A. Larkoski, G. Salam, and J. Thaler, 1305.0007] (𝛾) = (𝛾) = (𝛾) = 𝑓 4 𝑓 2 𝑓 3 and many more… Eric M. Metodiev, MIT Analyzing Jet Substructure with Energy Flow 14

Jet Tagging Performance – Quark vs. Gluon Jets ROC curves for quark vs. gluon jet tagging • Energy Flow Polynomials vs. q g N -subjettiness: [J. Thaler, K. Van Tilburg, 1011.2268, 1108.2701] N -subjettiness basis: [K. Datta, A. Larkoski, 1704.08249] QG CNNs: [P . Komiske, EMM, M. Schwartz, 1612.01551] ML/NN review: [A. Larkoski, I. Moult, B. Nachman, 1709.04464] Linear classification with EFPs is comparable to modern machine learning techniques Eric M. Metodiev, MIT Analyzing Jet Substructure with Energy Flow 15

Additional EFP Tagging Plots – Quark vs. Gluon Jets • Energy Flow Polynomials High 𝑒 EFPs are important High 𝑂 EFPs are important Convergence by 𝑒 ≤ 7 Eric M. Metodiev, MIT Analyzing Jet Substructure with Energy Flow 16

Top Tagging Community Comparison Community comparison of top tagging methods: 𝑞 Top jet vs. QCD jet [1902.09914] Eric M. Metodiev, MIT Analyzing Jet Substructure with Energy Flow 17

Outline Energy Flow Polynomials A basis of jet substructure observables Energy Flow Moments Tensor moments of the radiation pattern Energy Flow Networks ML architecture designed to learn from events Eric M. Metodiev, MIT Analyzing Jet Substructure with Energy Flow 18