Jet Mass Spectrum for Groomed and Ungroomed Top Jets Iain Stewart MIT based on: Hoang, Mantry, Pathak, IS ( 1708.02586 + ongoing work ) Sante Fe Jets and Heavy Flavor W orkshop January 2018 1
model this Outline 0.012 d σ 0.010 Motivation for Studying Top Jets: dM • 0.008 Top Mass from Jet Mass measurement 0.006 Quantify Soft Effects M peak m t 0.004 � 2 � � p µ M 2 = 0.002 i i ∈ J 172 174 176 178 180 M tion corrections Factorization Theorems: Ungroomed and Groomed • Calibration of Monte Carlo and Comparisons • Conclusion •
The Top Quark is Special Largest Mass Largest Higgs Coupling m t = 173 GeV • i t H ∝ m i Dominates Higgs Production H 1 i t The only quark that decays before it binds into a hadron : • Top width Γ t = 1 . 4 GeV Λ QCD � 0 . 3 GeV > confinement scale u u t → bW d
The Top Quark is Special Largest Mass Largest Higgs Coupling m t = 173 GeV • i t H ∝ m i Dominates Higgs Production H 1 i t The only quark that decays before it binds into a hadron : • Top width Γ t = 1 . 4 GeV Λ QCD � 0 . 3 GeV > confinement scale u m t u t → bW d Breit Wigner 1 � 2 + Γ 2 � q 2 − m 2 t t m t
Why should I care about a precision ? m t Stability of the Standard Model vacuum! • m t Andreassen, Frost, Schwartz m Higgs uncertainty dominated by m t Butazzo, Degrassi, Giardino, Giudice, Sala
Precision Electro-weak Measurements • Direct Measurements Gfitter group, 2014 Indirect Global Fit t 6
Heaviest known elementary particle. t As heavy as 180 protons! MC Tevatron GeV m t = 174 . 34 ± 0 . 64 CMS MC m t = 172 . 44 ± 0 . 49 GeV ATLAS MC GeV m t = 172 . 84 ± 0 . 70 measured from jets with help of Monte Carlo simulations
Direct Reconstruction Methods (Tevatron & LHC) jet jet b -jet p Kinematic Fit: ¯ t m 2 t = p 2 t = ( p Jb + p J 1 + p J 2 ) 2 p t jet b -jet jet 8
L : t hadrons m pole , m t , m MSR , . . . t t ¯ t Theory (QFT) Simulation Λ shower = 1 GeV (Monte Carlo) m MC t Experiment Definition ? m t = m MC + ? t an additional uncertainty ∼ 1 GeV 9
Mass Definitions: 1 • Pole Mass ∝ / − m pole p t Mass that naturally appears in Breit Wigner. ∆ m pole Has a (renormalon) ambiguity ∼ Λ QCD t Mass MS m t • Not compatible with Breit Wigner. No Ambiguity. � X m pole = m t + 0 . 4 α s m t + . . . t � 7 GeV � Γ t = 1 . 4 GeV • MSR Mass m MSR ( R ) (Hoang, Jain, Scimemi, IS, 2008) a mass which nicely interpolates take R = 1 GeV No Ambiguity � R > Λ QCD � Breit Wigner R ∼ Γ t 10
Soft Effects in pp → t ¯ tX jet MPI / Underlying Event jet b -jet p ¯ t Perturbative soft radiation p t t Hadronization hadrons ¯ t 11
pp → t ¯ t Soft Effects can be significant. eg. Jet Mass in Pythia
pp → t ¯ Theory Issues for tX jet observable • suitable top mass scheme for jets • initial state radiation • Production Energy final state radiation • Q = 2 p T ∼ 1 TeV underlying event/MPI • m t = 173 GeV color reconnection • parton distributions Γ t � 1 . 4 GeV • sum large logs Q � m t � Γ t Λ QCD • hadronization •
First simplification: boosted top quarks, Q = 2 p T � m t • enables us to be inclusive over decay products t Use EFT tools: Q = 2 p T ∼ 1 TeV Soft-Collinear EFT (SCET) m t = 173 GeV Heavy Quark EFT (HQET) Γ t � 1 . 4 GeV factorization, logs, Λ QCD non-perturbative effects 14
Jets with Substructure t → Wb → ( u ¯ d )( b ) = 3 prong jet pp → t ¯ t
pp → t ¯ Theory Issues for tX � jet observable First • e + e − → t ¯ tX � suitable top mass for jets • and the issues � initial state radiation • � final state radiation • underlying event/MPI • � color reconnection • parton distributions • � sum large logs Q � m t � Γ t • hadronization � •
Fleming, Hoang, Mantry, IS (2007) Factorization for double jet - mass: Hard Functions control over mass scheme d 2 σ � � m, Q Answer � � = σ 0 H Q ( Q, µ m ) H m m, µ m , µ dM 2 t dM 2 ¯ hemi t t − Q � � s t − Q � � � � � S hemi ( � − k, � � − k � , µ ) F ( k, k � ) ˆ ˆ × J B m , Γ , � m, µ J B s ¯ m , Γ , � m, µ Hadronization QCD ( boosted HQET ) dominant Soft Jet Functions e ff ect is from Function Evolution and decay of top first moment quark close to mass shell SCET Perturbative Cross talk � s t ⇥ M 2 t � m 2 dk � dk k F ( k, k � ) Ω 1 = ⇤ Γ ⌅ m ˆ m d d HQET n-collinear n-collinear jet jet usoft particles
Fleming, Hoang, Mantry, IS (2007) Factorization for double jet - mass: d 2 σ � � m, Q Answer � � = σ 0 H Q ( Q, µ m ) H m m, µ m , µ dM 2 t dM 2 ¯ hemi t t − Q � � s t − Q � � � � � S hemi ( � − k, � � − k � , µ ) F ( k, k � ) ˆ ˆ × J B m , Γ , � m, µ J B s ¯ m , Γ , � m, µ s + . . . ) + Q Ω 1 M peak � m t + Γ t ( α s + α 2 m t 0.012 d σ measure extract 0.010 this this dM 0.008 0.006 M peak m t 0.004 0.002 172 174 176 178 180 M
One application: Top Mass Calibration Butenschoen, Dehnadi, Hoang, Mateu, Preisser, IS m t = m MC PRL 2016 + . . . t � determined by fit to common observable τ 2 ∼ M 2 t + M 2 2 ¯ t m pole , m t , m MSR boosted , . . . t t e + e − → t ¯ t Theory (QFT) calibration Simulation e + e − = ⇒ pp (Monte Carlo) Experiment m MC t 19
Example from Fit to Pythia8 Simulation: Results: • Depend on which QFT based theory mass is used for fit. • Provides uncertainties: input: m MC = 173 GeV t m pole = 172 . 43 ± 0 . 28 GeV t m MSR = 172 . 82 ± 0 . 22 GeV t
Calculate pp → t ¯ t boosted top: jet jet b -jet p T � m t p ¯ t p t jet mass jet M J b -jet jet 21
pp → t ¯ Theory Issues for tX Jet Mass in Jet of radius R � jet observable • � suitable top mass for jets • can handle with � Jet veto � initial state radiation SCET/HQET • � final state radiation • underlying event/MPI • “contamination” � color reconnection • multiple channels � parton distributions • sum large logs � Q � m t � Γ t • hadronization � •
N-jettiness event shapes for hadron colliders IS, Tackmann, Waalewijn (2010) X T 2 = min min { ρ jet ( p i , n t ) , ρ jet ( p i , n ¯ t ) , ρ beam ( p i ) } jet t n t ,n ¯ t i ¯ = T t 2 + T beam t beam 2 + T , 2 XCone is a particularly nice choice for jet and 2 = M 2 gives jet-mass T t J 1 Q t gives jet-veto T beam ¯ t 2 jet Ungroomed Factorization Formula: Hoang, Mantry, Pathak, IS (to appear soon) � ˆ d 2 σ H Qm ˆ S ( T beam � = tr , R, . . . ) ⊗ F ⊗ J B ⊗ J B ⊗ II ⊗ ff 2 dM 2 J 1 dM 2 J 2 d T beam PDFs 2 hadronization pert. soft hard initial state radiation generalizes ee result to LHC same Jet functions! 23
Hadronization effects x 2 = Ω 2 − Ω 2 higher moments first moment dominates 1 Ω 1 , … Ω 2 Ω 2 1 give smaller effects MPI / UE effects: Ω MPI 1 jet mass from massless quarks & gluons, known that using a larger Ω MPI > Ω 1 1 accurately captures MPI effects (IS, Tackmann, Waalewijn 2015) 24
pp → t ¯ t Issue is that MPI contamination is significant (Pythia), so uncertainty from this modeling may be too large for a precision measurement.
Larkoski, Marzani, Soyez, Thaler 2014 Soft Drop Grooms soft radiation from the jet z > z cut θ β min( p T i , p T j ) � ∆ R ij � β ie. > z cut p T i + p T j R 0 two grooming parameters Can still carry out calculations: Larkoski, Marzani, Soyez, Thaler 2014 Fri, Larkoski, Schwartz, Yan 2016 26
Hoang, Mantry, Pathak, IS (2017) Light Soft Drop for tops z cut ∼ 0 . 01 Q = 2 p T cosh( η J ) ⇣ Q To derive ⌘ β > Γ t ⇠ z cut fact. theorem: 4 m t 4 m t ✓ Γ t Remove soft 1 4 m 2 cut � 1 ◆ 2+ β 1 t 2+ β , z contamination. Q 2 2 m t Decouples top-jet from rest of the event! soft radiation groomed top decay products & radiation leftover “collinear-soft” radiation R
Light Soft Drop for tops z cut ∼ 0 . 01 Modes: Q = 2 p T cosh( η J ) ⇣ Q ⌘ β > To derive Γ t ⇠ z cut fact. theorem: 4 m t 4 m t ✓ Γ t Remove soft 1 4 m 2 cut � 1 ◆ 1 2+ β t 2+ β , z contamination. Q 2 2 m t Decouples top-jet from rest of the event! soft radiation groomed top decay products & radiation leftover “collinear-soft” radiation R
MPI contamination reduced by factor of 5 with Light Soft Drop (eg. 4.5 GeV to 0.9 GeV): 29
Hoang, Mantry, Pathak, IS (2017) Factorization with Soft Drop on one jet: ⇣ ⇣ M 2 J − m 2 d � ( Φ J ) t − Q ` Z Z s 0 d Φ d D t (ˆ ⌘ s 0 , Φ d , m/Q ) s 0 , � m, µ = N ( Φ J , z cut , � , µ ) d ˆ d ` J B − ˆ dM J m t ` − mk Φ d , m Z h⇣ �⌘ 1 i 1+ β , � , µ (2 β Qz cut ) � dk S C Q h F C ( k, 1) × Q 30
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