On the Topic of Jets BOOST 2018 Eric M. Metodiev Center for Theoretical Physics Massachusetts Institute of Technology Joint work with Patrick T. Komiske and Jesse Thaler July 19, 2018 1
Quark and Gluon Jets Quarks are color triplets and Gluons are color octets. We observe color-singlet hadrons. No unambiguous hadron-level definition of jet flavor. We often rely on unphysical notions such as parton shower event records to define jet flavor in practice. Can quark and gluon be made well-defined nonetheless? Similar to defining jets themselves. Ubiquitous concepts. From BOOST 2018 so far: Eric M. Metodiev, MIT 2 On the Topic of Jets
What are “Quark” and “Gluon” Jets? Word Count 3 4 9 12 16 22 30 [Les Houches 2015 Report] [P . Gras, et al. , 1704.03878] Eric M. Metodiev, MIT 3 On the Topic of Jets
[P . Gras, et al. , 1704.03878] Eric M. Metodiev, MIT 4 On the Topic of Jets
[P . Gras, et al. , 1704.03878] Eric M. Metodiev, MIT 5 On the Topic of Jets
Our Plan: An operational definition of quark and gluon jets That definition : [A quark jet is defined by:] This talk : Translating those 30 words to these 2 equations: 𝑞 quark 𝒚 ≡ 𝑞 𝐵 𝒚 −𝜆 AB 𝑞 𝐶 𝒚 𝑞 gluon 𝒚 ≡ 𝑞 𝐶 𝒚 −𝜆 BA 𝑞 𝐵 𝒚 1−𝜆 AB 1−𝜆 BA Eric M. Metodiev, MIT 6 On the Topic of Jets
A picture of quark and gluon jets Anti-kT R=0.4 jets 1. Take your favorite jet algorithm Z+jet and Dijets Consistuent Multiplicity 2. Consider two jet samples A and B of QCD jets 3. Choose a jet substructure observable 𝒚 4. “Assume” that “ quark ” and “ gluon ” jets exist 5. “Assume” “ quark/gluon ” jet mutual irreducibility The samples A and B are statistical mixtures of quark and gluon: 𝑟 𝑞 quark 𝒚 + 𝑔 𝑞 gluon 𝒚 , = 1 − 𝑔 𝑟 𝑞 sample 𝐵 𝒚 = 𝑔 𝑔 𝐵 𝐵 𝐵 𝐵 𝑟 𝑞 quark 𝒚 + 𝑔 𝑞 gluon (𝒚), = 1 − 𝑔 𝑟 𝑞 sample 𝐶 𝒚 = 𝑔 𝑔 𝐶 𝐶 𝐶 𝐵 Similar picture to template- and fraction-based methods. Eric M. Metodiev, MIT 7 On the Topic of Jets
A/B Likelihood Ratio 𝑟 𝑞 quark 𝒚 + 1 − 𝑔 𝑟 𝑞 gluon (𝒚) 𝑞 sample 𝐵 𝒚 = 𝑔 𝐵 𝐵 𝑟 𝑞 quark 𝒚 + 1 − 𝑔 𝑟 𝑞 gluon (𝒚) 𝑞 sample 𝐶 𝒚 = 𝑔 𝐶 𝐶 𝑟 𝑀 quark 𝑟 𝑔 𝒚 + 1 − 𝑔 𝐵 𝐵 𝒚 ≡ 𝑞 𝐵 𝒚 gluon 𝑀 A 𝑞 𝐶 𝒚 = 𝑟 𝑀 quark 𝑟 𝑔 𝒚 + 1 − 𝑔 B 𝐶 𝐶 gluon The A/B and quark/gluon likelihood ratios are monotonic! Classification without labels (CWoLa) • Optimal A/B classifier is the optimal quark/gluon classifier. • Use machine learning to approximate A/B likelihood ratio. See Ben’s talk! [EMM, B. Nachman, J. Thaler, 1708.02949] 𝑟 𝑟 𝑔 1−𝑔 The A/B likelihood ratio is bounded between 𝑟 and 𝑟 ! 𝐵 𝐵 𝑔 1−𝑔 𝐶 𝐶 Jet T opics • “Mutually irreducibility” means the bounds saturate • Obtain the maxima and minima of the A/B likelihood ratio. Solve for the quark/gluon fractions and distributions. • [EMM, J. Thaler, 1802.00008] Eric M. Metodiev, MIT 8 On the Topic of Jets
[P . Gras, et al. , 1704.03878] “quarks” “gluons” 𝑀 quark 𝒚 → ∞ 𝑀 quark 𝒚 → 0 gluon gluon Mutual irreducibility! These concepts are not new in physics, and have been around for a while. Quark/gluon mutual irreducibility : There are some substructure phase space regions where quark and gluon jets are pure. 𝑟 𝑟 𝑞 𝐵 𝒚 𝑞 𝐶 𝒚 = 1 − 𝑔 𝑞 𝐶 𝒚 𝑞 𝐵 𝒚 = 𝑔 𝐶 𝐵 min min 𝑟 𝑟 1 − 𝑔 𝑔 𝒚 𝒚 𝐶 𝐵 Eric M. Metodiev, MIT 9 On the Topic of Jets
Demixing the mixtures 𝑟 𝑞 quark 𝒚 + 1 − 𝑔 𝑟 𝑞 gluon (𝒚) 𝑞 𝐵 𝒚 = 𝑔 𝐵 𝐵 𝑟 𝑞 quark 𝒚 + 1 − 𝑔 𝑟 𝑞 gluon (𝒚) 𝑞 𝐶 𝒚 = 𝑔 𝐶 𝐶 𝑞 𝐵 𝒚 𝑞 𝐶 𝒚 𝜆 AB ≡ min 𝜆 BA ≡ min 𝑞 𝐶 𝒚 𝒚 𝑞 𝐵 𝒚 𝒚 𝑟 𝑟 1−𝑔 𝑔 𝐵 = 𝐶 = 𝑟 𝑟 1−𝑔 𝑔 𝐶 𝐵 Solve for the quark and gluon distributions and fractions: 𝑟 = 𝜆 BA (1 − 𝜆 AB ) 1 − 𝜆 AB 𝑟 = 𝑔 𝑔 B 𝐵 1 − 𝜆 AB 𝜆 BA 1 − 𝜆 AB 𝜆 BA 𝑞 quark 𝒚 = 𝑞 𝐵 𝒚 −𝜆 AB 𝑞 𝐶 𝒚 𝑞 gluon 𝒚 = 𝑞 𝐶 𝒚 −𝜆 BA 𝑞 𝐵 𝒚 1−𝜆 AB 1−𝜆 BA Eric M. Metodiev, MIT 10 On the Topic of Jets
Demixing the mixtures 𝑟 𝑞 quark 𝒚 + 1 − 𝑔 𝑟 𝑞 gluon (𝒚) 𝑞 𝐵 𝒚 = 𝑔 𝐵 𝐵 Defined from data Ambiguous? 𝑟 𝑞 quark 𝒚 + 1 − 𝑔 𝑟 𝑞 gluon (𝒚) 𝑞 𝐶 𝒚 = 𝑔 𝐶 𝐶 𝑞 𝐵 𝒚 𝑞 𝐶 𝒚 𝜆 AB ≡ min 𝜆 BA ≡ min 𝑞 𝐶 𝒚 𝒚 𝑞 𝐵 𝒚 𝒚 𝑟 𝑟 1−𝑔 𝑔 𝐵 = 𝐶 = 𝑟 𝑟 1−𝑔 𝑔 𝐶 𝐵 Solve for the quark and gluon distributions and fractions: 𝑟 = 𝜆 BA (1 − 𝜆 AB ) 1 − 𝜆 AB 𝑟 = 𝑔 𝑔 B 𝐵 1 − 𝜆 AB 𝜆 BA 1 − 𝜆 AB 𝜆 BA 𝑞 quark 𝒚 = 𝑞 𝐵 𝒚 −𝜆 AB 𝑞 𝐶 𝒚 𝑞 gluon 𝒚 = 𝑞 𝐶 𝒚 −𝜆 BA 𝑞 𝐵 𝒚 1−𝜆 AB 1−𝜆 BA Eric M. Metodiev, MIT 11 On the Topic of Jets
An operational definition of quark and gluon jets Quark and Gluon Jet Definition (Operational) : Given two samples A and B of QCD jets at a fixed 𝑞 𝑈 obtained by a suitable jet-finding procedure, taking A to be “quark - enriched” compared to B, and a jet substructure feature space 𝒚 , quark and gluon jet distributions are defined to be: 𝑞 quark 𝒚 ≡ 𝑞 𝐵 𝒚 −𝜆 AB 𝑞 𝐶 𝒚 𝑞 gluon 𝒚 ≡ 𝑞 𝐶 𝒚 −𝜆 BA 𝑞 𝐵 𝒚 1−𝜆 AB 1−𝜆 BA Well-defined and operational statement in terms of hadronic cross sections. Not a per-jet flavor label, but rather an aggregate distribution label. Defined in the context of a specific pair of samples A and B, regardless of whether the observable in question has a rigorous factorization theorem. Additional jet processing (e.g. grooming) can be folded into definition of A and B. Extracting topics well is fundamentally easier than tagging well. Eric M. Metodiev, MIT 12 On the Topic of Jets
A picture of quark and gluon jets Anti-kT R=0.4 jets 1. Take your favorite jet algorithm Z+jet and Dijets Consistuent Multiplicity 2. Consider two jet samples A and B of QCD jets 3. Choose a jet substructure observable 𝒚 4. “Assume” that “ quark ” and “ gluon ” jets exist 5. “Assume” “ quark/gluon ” jet mutual irreducibility The samples A and B are statistical mixtures of quark and gluon: 𝑟 𝑞 quark 𝒚 + 𝑔 𝑞 gluon 𝒚 , = 1 − 𝑔 𝑟 𝑞 sample 𝐵 𝒚 = 𝑔 𝑔 𝐵 𝐵 𝐵 𝐵 𝑟 𝑞 quark 𝒚 + 𝑔 𝑞 gluon (𝒚), = 1 − 𝑔 𝑟 𝑞 sample 𝐶 𝒚 = 𝑔 𝑔 𝐶 𝐶 𝐶 𝐵 Firm foundation for data-driven methods. Eric M. Metodiev, MIT 13 On the Topic of Jets
Exploring substructure feature spaces Why restrict ourselves to multiplicity? It works, but we can explore this choice. We can also use a trained model (with CWoLa) as an observable in its own right. Observables Models PFN-ID • Multiplicity 𝑜 const • Number of particles in the jet Full particle-level information PFN • Soft Drop Multiplicity 𝑜 SD • Probes number of perturbative emissions Full four-momentum information • Image Activity 𝑂 95 EFN • Number of pixels with 95% of jet 𝑞 𝑈 Full IRC-safe information See Patrick’s talk! (𝛾=1) • N-subjettiness 𝜐 2 EFPs • Probes how multi-pronged the jet is Full IRC-safe information, linearly • Jet Mass 𝑛 • CNN Mass of the total jet four-vector Trained on two-channel jet images Width 𝑥 • • DNN Probes the girth of the jet Trained on an N-subjettiness basis Eric M. Metodiev, MIT 14 On the Topic of Jets
Exploring substructure feature spaces PRELIMINARY Casimir scaling of mass and width is observed (gray). Count observables come closer to saturating the bounds (black) than shape observables. Lower bound easier to extract than upper. (i.e. Gluons are easy!) PRELIMINARY Models CWoLa-trained. Fully data-driven. Well-behaved likelihoods close to S/(S+B) expectation. All different models manifest the same bounds. Insensitive to the model details. [P .T. Komiske, EMM, J. Thaler, Upcoming.] Eric M. Metodiev, MIT 15 On the Topic of Jets
Extracting quark and gluon distributions PRELIMINARY PRELIMINARY PRELIMINARY PRELIMINARY PRELIMINARY PRELIMINARY Eric M. Metodiev, MIT 16 On the Topic of Jets
(Self-)calibrating quark and gluon classifiers better The extracted quark and gluon fractions can calibrate quark/gluon classifiers and evaluate tagging performance. PRELIMINARY Even the classifier that was used to extract the fractions in the first place! Note: To compare classifiers, one can just use the performance on A vs B directly. Eric M. Metodiev, MIT 17 On the Topic of Jets
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