The Lund jet plane: organising QCD radiation at colliders Gavin P . - PowerPoint PPT Presentation

g JEWEL v. data JEWEL+PYTHIA Pb+Pb (0 − 10 %) √ s NN = 5.02 TeV 2 PbPb/pp CMS Data with medium response ➤ arXiv:1707.01539, by Milhano, without medium response 1 . 5 anti- k ⊥ R= 0 . 4 jets Wiedemann and Zapp with 140 GeV < p jet ⊥ < 160 GeV SoftDrop z cut = 0.1; β = 0; ∆ R 12 > 0.1 medium response 1 0 . 5 JEWEL+PYTHIA Pb+Pb ( 0 − 10% ) ( 2 . 76 TeV) ( 1/ N jets ) d N /d M ch-jet 0 ALICE data 1 . 4 w/ Recoils, 4 MomSub 0 . 1 MC/Data 1 . 2 SD z g w/o Recoils 1 Δ R anti- k ⊥ R = 0 . 4 jets 0 . 08 0 . 8 1 2 | η jet | < 0.5 0 . 6 100 < p ch-jet < 120 GeV ⊥ 0 . 06 0 . 1 0 . 15 0 . 2 0 . 25 0 . 3 0 . 35 0 . 4 0 . 45 0 . 5 z g 0 . 04 mass 0 . 02 0 0 5 10 15 20 25 charged jet mass M ch-jet [GeV] � 29

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sha1_base64="HaKr5rIstygUSorlRGTefHh1EzQ=">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</latexit> recurrent theme in heavy-ion calculations: 2d phasespace plots ln 1 /z ω E ω QW paradig c θ qq VETOED ~50% of t ω ωθ 2 L=2 ω θ θ 3 4 =2q ln p T R 2 L = Casalderrey, Milhano, Λ t f > L 2 At high-pT, ma 1 ln p T R 4 / 3 can be resolved inside q 1 / 3 θ ˆ ( ω , θ ) medium “new” source of ln p T R/Qs ω 1 Casald θ c θ 1 outside θ 2 M ω 2 k ⊥ = ω tan θ t f < L 2 x (1 − x ) medium ω θ Blue region corr k ⊥ ln p T / ω c θ x, k ⊥ unresolved spl FIG. 1. Schematic representation of the phase-space available for VLEs, including an example of a cascade with “1” the last emission inside the medium and “2” the first emission outside. ω P . Caucal, E. Iancu, 
 θ = R ln 1 /R ln 1 / θ c ln 1 / θ L ln 1 / θ A.H. Mueller, G. Soyez 1 − x x x = z cut x = 1 − z cut Mehtar-Tani & Tywoniuk@QM18 θ = ∆ x 1 / 2 0 1 Yang-Ting Chien a,b and Ivan Vitev a � 30

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sha1_base64="HaKr5rIstygUSorlRGTefHh1EzQ=">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</latexit> <latexit sha1_base64="HaKr5rIstygUSorlRGTefHh1EzQ=">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</latexit> <latexit sha1_base64="HaKr5rIstygUSorlRGTefHh1EzQ=">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</latexit> <latexit sha1_base64="HaKr5rIstygUSorlRGTefHh1EzQ=">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</latexit> <latexit sha1_base64="HaKr5rIstygUSorlRGTefHh1EzQ=">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</latexit> recurrent theme in heavy-ion calculations: 2d phasespace plots ln 1 /z ω E ω QW paradig c θ qq VETOED ~50% of t ω ωθ 2 L=2 ω θ θ 3 4 =2q ln p T R 2 L = Casalderrey, Milhano, Λ t f > L 2 At high-pT, ma 1 ln p T R 4 / 3 can be resolved inside q 1 / 3 θ ˆ ( ω , θ ) medium “new” source of ln p T R/Qs ω 1 Casald Can we design observables to θ c θ 1 outside θ 2 M ω 2 k ⊥ = ω tan θ t f < L 2 x (1 − x ) medium ω θ Blue region corr directly probe the 2d phasespace? k ⊥ ln p T / ω c θ x, k ⊥ unresolved spl FIG. 1. Schematic representation of the phase-space available for VLEs, including an example of a cascade with “1” the last emission inside the medium and “2” the first emission outside. ω P . Caucal, E. Iancu, 
 θ = R ln 1 /R ln 1 / θ c ln 1 / θ L ln 1 / θ A.H. Mueller, G. Soyez 1 − x x x = z cut x = 1 − z cut Mehtar-Tani & Tywoniuk@QM18 θ = ∆ x 1 / 2 0 1 Yang-Ting Chien a,b and Ivan Vitev a � 30

the “Lund plane” can we construct observables that are (a) more transparent in terms of the physical info they extract? (b) close to optimal for multivariate techniques & machine-learning? � 31

the Cambridge / Aachen (C/A) jet algorithm Cambridge/Aachen 1. Identify pair of particles, i & j, with smallest Δ R ij p t /GeV 2. If Δ R ij < R (jet radius parameter) 50 A. recombine i & j into a single particle 40 B. loop back to step 1 3. Otherwise, stop the clustering 30 20 10 Dokshitzer, Leder, Moretti & Webber ’97 
 Wobisch & Wengler ‘98 0 0 1 2 3 4 y � 32

Cambridge/Aachen A sequence of jet substructure tools taggers p t /GeV ➤ 1993: k t declustering for boosted W’s: [Seymour] 50 ➤ 2002: Y-Splitter (k t declustering with a cut) [Butterworth. 40 Cox, Forshaw] 30 ➤ 2008: Mass-Drop Tagger (C/A declustering with a k t /m cut) 20 [Butterworth, Davison, Rubin, GPS] 10 ➤ 2013: Soft Drop, β =0 [Dasgupta, Fregoso, Marzani, GPS] 0 0 1 2 3 4 y ➤ 2014: Soft Drop, β≠ 0 [Larkoski, Marzani, Soyez, Thaler] 
 1. Undo last clustering of C/A jet into subjets 1, 2 ◆ β ✓ ∆ R 12 z = min( p t 1 , p t 2 ) 2. Stop if > z cut p t 1 + p t 2 R 3. Else discard softer branch, repeat step 1 with harder branch � 33

Cambridge/Aachen A sequence of jet substructure tools taggers p t /GeV ➤ 1993: k t declustering for boosted W’s: [Seymour] 50 ➤ 2002: Y-Splitter (k t declustering with a cut) [Butterworth. 40 Cox, Forshaw] 30 ➤ 2008: Mass-Drop Tagger (C/A declustering with a k t /m cut) 20 [Butterworth, Davison, Rubin, GPS] 10 ➤ 2013: Soft Drop, β =0 [Dasgupta, Fregoso, Marzani, GPS] 0 0 1 2 3 4 y ➤ 2014: Soft Drop, β≠ 0 [Larkoski, Marzani, Soyez, Thaler] ➤ 2017: Iterated Soft Drop [Frye, Larkoski, Thaler, Zhou] 
 count number of iterations until you reach 1 particle ➤ 2018/19: ? � 34

Phase space: two key variables (+ azimuth) Δ R ( or just Δ ) opening angle of a splitting Δ p t p t (or p ⊥ ) is transverse k t = p t Δ momentum wrt beam k t is ~ transverse Δ momentum wrt jet axis � 35 Δ

jet with R= 0.4, p t = 200 GeV 40 logarithmic kinematic plane whose two variables are 
 20 ∆ R ij k t = min( p ti , p tj ) ∆ R ij k t = p t Δ R [GeV] 10 5 Introduced for understanding Parton Shower Monte Carlos by 
 B. Andersson,G. Gustafson L. Lonnblad and Pettersson 1989 2 1 The Lund Plane 0.4 0.2 0.1 0.05 0.02 0.01 Δ R � 36

jet with R= 0.4, p t = 200 GeV 40 logarithmic kinematic plane whose two variables are 
 20 ∆ R ij k t = min( p ti , p tj ) ∆ R ij k t = p t Δ R [GeV] 10 5 2 Introduced for understanding Parton Shower Monte Carlos by 
 B. Andersson,G. Gustafson L. Lonnblad and Pettersson 1989 1 The Lund Plane 0.4 0.2 0.1 0.05 0.02 0.01 Δ R � 37

jet with R= 0.4, p t = 200 GeV 40 logarithmic kinematic plane whose two variables are 
 20 ∆ R ij k t = min( p ti , p tj ) ∆ R ij k t = p t Δ R [GeV] 10 5 2 Introduced for understanding Parton Shower Monte Carlos by 
 B. Andersson,G. Gustafson L. Lonnblad and Pettersson 1989 1 The Lund Plane 0.4 0.2 0.1 0.05 0.02 0.01 Δ R � 38

jet with R= 0.4, p t = 200 GeV 40 logarithmic kinematic plane whose two variables are 
 20 ∆ R ij k t = min( p ti , p tj ) ∆ R ij k t = p t Δ R [GeV] 10 5 2 Introduced for understanding Parton Shower Monte Carlos by 
 B. Andersson,G. Gustafson L. Lonnblad and Pettersson 1989 1 The Lund Plane 0.4 0.2 0.1 0.05 0.02 0.01 Δ R � 39

jet with R= 0.4, p t = 200 GeV 40 logarithmic kinematic plane whose two variables are 
 20 ∆ R ij k t = min( p ti , p tj ) ∆ R ij k t = p t Δ R [GeV] 10 5 2 Introduced for understanding Parton Shower Monte Carlos by 
 B. Andersson,G. Gustafson L. Lonnblad and Pettersson 1989 1 The Lund Plane 0.4 0.2 0.1 0.05 0.02 0.01 Δ R � 40

jet with R= 0.4, p t = 200 GeV 40 logarithmic kinematic plane whose two variables are 
 20 ∆ R ij k t = min( p ti , p tj ) ∆ R ij k t = p t Δ R [GeV] 10 5 2 Introduced for understanding Parton Shower Monte Carlos by 
 B. Andersson,G. Gustafson L. Lonnblad and Pettersson 1989 1 The Lund Plane 0.4 0.2 0.1 0.05 0.02 0.01 Δ R � 41

jet with R= 0.4, p t = 200 GeV 40 logarithmic kinematic plane whose two variables are 
 20 ∆ R ij k t = min( p ti , p tj ) ∆ R ij k t = p t Δ R [GeV] 10 5 2 Introduced for understanding Parton Shower Monte Carlos by 
 B. Andersson,G. Gustafson L. Lonnblad and Pettersson 1989 1 The Lund Plane 0.4 0.2 0.1 0.05 0.02 0.01 Δ R � 42

jet with R= 0.4, p t = 200 GeV 40 logarithmic kinematic plane whose two variables are 
 20 ∆ R ij k t = min( p ti , p tj ) ∆ R ij k t = p t Δ R [GeV] 10 5 2 Introduced for understanding Parton Shower Monte Carlos by 
 B. Andersson,G. Gustafson L. Lonnblad and Pettersson 1989 1 The Lund Plane 0.4 0.2 0.1 0.05 0.02 0.01 Δ R � 43

jet with R= 0.4, p t = 200 GeV 40 logarithmic kinematic plane whose two variables are 
 20 ∆ R ij k t = min( p ti , p tj ) ∆ R ij k t = p t Δ R [GeV] 10 5 2 Introduced for understanding Parton Shower Monte Carlos by 
 B. Andersson,G. Gustafson L. Lonnblad and Pettersson 1989 1 The Lund Plane 0.4 0.2 0.1 0.05 0.02 0.01 Δ R � 44

jet with R= 0.4, p t = 200 GeV 40 20 k t = p t Δ R [GeV] decluster a C/A jet: 
 10 at each step record Δ R,kt 
 5 as a point in the Lund plane repeatedly follow harder branch 2 5th heavy-ion workshop @ CERN, 1808.03689 
 Dreyer, Soyez & GPS, 1807.04758 (for pp applications) 1 0.4 0.2 0.1 0.05 0.02 0.01 constructing the Lund plane Δ R � 45

40 20 k t = p t Δ R [GeV] decluster a C/A jet: 
 10 at each step record Δ R,kt 
 5 as a point in the Lund plane repeatedly follow harder branch 2 5th heavy-ion workshop @ CERN, 1808.03689 
 Dreyer, Soyez & GPS, 1807.04758 (for pp applications) 1 0.4 0.2 0.1 0.05 0.02 0.01 constructing the Lund plane Δ R � 46

40 20 k t = p t Δ R [GeV] decluster a C/A jet: 
 10 at each step record Δ R,kt 
 5 as a point in the Lund plane repeatedly follow harder branch 2 5th heavy-ion workshop @ CERN, 1808.03689 
 Dreyer, Soyez & GPS, 1807.04758 (for pp applications) 1 0.4 0.2 0.1 0.05 0.02 0.01 constructing the Lund plane Δ R � 47

40 20 k t = p t Δ R [GeV] decluster a C/A jet: 
 10 at each step record Δ R,kt 
 5 as a point in the Lund plane repeatedly follow harder branch 2 5th heavy-ion workshop @ CERN, 1808.03689 
 Dreyer, Soyez & GPS, 1807.04758 (for pp applications) 1 0.4 0.2 0.1 0.05 0.02 0.01 constructing the Lund plane Δ R � 48

40 20 k t = p t Δ R [GeV] decluster a C/A jet: 
 10 at each step record Δ R,kt 
 5 as a point in the Lund plane repeatedly follow harder branch 2 5th heavy-ion workshop @ CERN, 1808.03689 
 Dreyer, Soyez & GPS, 1807.04758 (for pp applications) 1 0.4 0.2 0.1 0.05 0.02 0.01 constructing the Lund plane Δ R � 49

40 20 k t = p t Δ R [GeV] decluster a C/A jet: 
 10 at each step record Δ R,kt 
 5 as a point in the Lund plane repeatedly follow harder branch 2 5th heavy-ion workshop @ CERN, 1808.03689 
 Dreyer, Soyez & GPS, 1807.04758 (for pp applications) 1 0.4 0.2 0.1 0.05 0.02 0.01 constructing the Lund plane Δ R � 50

40 20 k t = p t Δ R [GeV] decluster a C/A jet: 
 10 at each step record Δ R,kt 
 5 as a point in the Lund plane repeatedly follow harder branch 2 5th heavy-ion workshop @ CERN, 1808.03689 
 Dreyer, Soyez & GPS, 1807.04758 (for pp applications) 1 0.4 0.2 0.1 0.05 0.02 0.01 constructing the Lund plane Δ R � 51

(b) (b) (a) (a) (c) JET (c) t t ln k ln k LUND DIAGRAM (b) (b) (c) (c) ln 1/ ∆ ln 1/ ∆ ln k t ln k t PRIMARY LUND PLANE (b) (b) (c) ln 1/ ∆ ln 1/ ∆ � 52

jet with R= 0.4, p t = 200 GeV ⟨ ⟩ 40 20 k t = p t Δ R [GeV] 10 5 average over many jets: 
 Lund plane density 2 5th heavy-ion workshop @ CERN, 1808.03689 
 Dreyer, Soyez & GPS, 1807.04758 (for pp applications) 1 0.4 0.2 0.1 0.05 0.02 0.01 constructing the Lund plane Δ R � 53

jet with R= 0.4, p t = 200 GeV ⟨ ⟩ 40 20 k t = p t Δ R [GeV] 10 5 average over many jets: 
 Lund plane density 2 non-perturbative region 5th heavy-ion workshop @ CERN, 1808.03689 
 Dreyer, Soyez & GPS, 1807.04758 (for pp applications) 1 0.4 0.2 0.1 0.05 0.02 0.01 constructing the Lund plane Δ R � 54

jet with R= 0.4, p t = 200 GeV ⟨ ⟩ 40 20 t f ~ 0.1 fm/c k t = p t Δ R [GeV] 10 5 average over many jets: 
 t f ~ 1.0 fm/c Lund plane density t f ~ 5.0 fm/c 2 5th heavy-ion workshop @ CERN, 1808.03689 
 Dreyer, Soyez & GPS, 1807.04758 (for pp applications) 1 0.4 0.2 0.1 0.05 0.02 0.01 constructing the Lund plane Δ R � 55

jet with R= 0.4, p t = 200 GeV ⟨ ⟩ 40 20 k t = p t Δ R [GeV] 10 5 average over many jets: 
 Lund plane density ) m 2 f / V e G 2 = ˆ 2 q ( ˆ t q 2 = f k t 5th heavy-ion workshop @ CERN, 1808.03689 
 Dreyer, Soyez & GPS, 1807.04758 (for pp applications) 1 0.4 0.2 0.1 0.05 0.02 0.01 constructing the Lund plane Δ R � 56

application to pp QCD studies � 57

Herwig (7.1.1) Pythia (8.233, Monash13) average pp Lund density: parton level Pythia8.2330(M13), parton level Herwig7.1.1, parton level 0.9 0.9 pp 14 TeV 
 pp 14 TeV 
 C/A, R=1 
 C/A, R=1 
 0.8 0.8 6 6 p t,jet > 2 TeV p t,jet > 2 TeV 0.7 0.7 4 4 0.6 0.6 log(k t [GeV]) log(k t [GeV]) 0.5 0.5 2 2 0.4 0.4 0.3 0.3 0 0 0.2 0.2 0.1 0.1 -2 -2 0 0 0 1 2 3 4 5 0 1 2 3 4 5 log(1/ Δ R) log(1/ Δ R) � 58

Herwig (7.1.1) Pythia (8.233, Monash13) average pp Lund density: hadron level (no underlying event / MPI) Pythia8.2330(M13), hadron level Herwig7.1.1, hadron level 0.9 0.9 pp 14 TeV 
 pp 14 TeV 
 C/A, R=1 
 C/A, R=1 
 0.8 0.8 6 6 p t,jet > 2 TeV p t,jet > 2 TeV 0.7 0.7 4 4 0.6 0.6 log(k t [GeV]) log(k t [GeV]) 0.5 0.5 2 2 0.4 0.4 0.3 0.3 0 0 0.2 0.2 0.1 0.1 -2 -2 0 0 0 1 2 3 4 5 0 1 2 3 4 5 log(1/ Δ R) log(1/ Δ R) � 59

Herwig (7.1.1) Pythia (8.233, Monash13) average pp Lund density: hadron level (with underlying event / MPI) Pythia8.2330(M13), phadron U E level Herwig7.1.1, hadron+UE level 0.9 0.9 pp 14 TeV 
 pp 14 TeV 
 C/A, R=1 
 C/A, R=1 
 0.8 0.8 6 6 p t,jet > 2 TeV p t,jet > 2 TeV 0.7 0.7 4 4 0.6 0.6 log(k t [GeV]) log(k t [GeV]) 0.5 0.5 2 2 0.4 0.4 0.3 0.3 0 0 0.2 0.2 0.1 0.1 -2 -2 0 0 0 1 2 3 4 5 0 1 2 3 4 5 log(1/ Δ R) log(1/ Δ R) � 60

ρ Δ Pythia (8.233, Monash13) average pp Lund density: cross sections 1 0.5 0.2 0.1 0.02 0.01 0.25 Pythia8.2330(M13), phadron U E level 44.7 < k t < 54.6 GeV 0.2 0.9 pp 14 TeV 
 0.15 ρ ( Δ ,k t ) C/A, R=1 
 0.8 6 ρ Δ ρ Δ p t,jet > 2 TeV 0.1 0.7 p t > 2 TeV 0.05 hadron+MPI 4 0.6 0 log(k t [GeV]) 1 0.5 0.2 0.1 0.02 0.01 0.5 0.25 Δ 2 9.0 < k t < 11.0 GeV 0.4 0.2 ρ ( Δ ,k t ) 0.15 0.3 0 ρ Δ ρ Δ Pythia8.230 (Monash13) 0.1 0.2 Herwig7.1.1 (default) 0.05 Sherpa2.2.4 (default) 0.1 -2 0 1 0.5 0.2 0.1 0.02 0.01 0 0.25 0 1 2 3 4 5 Δ Δ log(1/ Δ R) � 61 ρ Δ Δ

ρ Δ Data would be valuable input for calibrating / validating generators Pythia (8.233, Monash13) Pythia/Sherpa agree best, but no two generators agree everywhere 
 15 ‒ 30% differences between generators 
 average pp Lund density: cross sections 1 0.5 0.2 0.1 0.02 0.01 0.25 Pythia8.2330(M13), phadron U E level 44.7 < k t < 54.6 GeV 0.2 0.9 pp 14 TeV 
 0.15 ρ ( Δ ,k t ) C/A, R=1 
 0.8 6 ρ Δ ρ Δ p t,jet > 2 TeV 0.1 0.7 p t > 2 TeV 0.05 hadron+MPI 4 0.6 0 log(k t [GeV]) 1 0.5 0.2 0.1 0.02 0.01 0.5 0.25 Δ 2 9.0 < k t < 11.0 GeV 0.4 0.2 ρ ( Δ ,k t ) 0.15 0.3 0 ρ Δ ρ Δ Pythia8.230 (Monash13) 0.1 0.2 Herwig7.1.1 (default) 0.05 Sherpa2.2.4 (default) 0.1 -2 0 1 0.5 0.2 0.1 0.02 0.01 0 0.25 0 1 2 3 4 5 Δ Δ log(1/ Δ R) � 61 ρ Δ Δ

analytic perturbative QCD control To leading order in perturbative QCD and for ∆ ⌧ 1 , one expects for a quark initiated jet ρ ' α s ( k t ) C F k t z � z ) � p gq ( ¯ z ) + p gq ( 1 � ¯ ¯ z ⇤ ¯ , p t , jet ∆ π LO analytic / MC 8 3 2 6 I Lund plane can be calculated 4 analytically. ln k t /GeV 1 2 I Calculation is systematically improvable. 0 0.5 -2 0.3 0 1 2 3 4 5 ln 1/ Δ 12 � 62

application to HI collisions � 63

jet with R= 0.4, p t = 200 GeV Splittings map for difference of data and embedded PYTHIA 2 40 ALICE Preliminary (Data - Embedded) 0.1 PbPb - PYTHIA Embedded s = 2.76 TeV NN 0 ch,rec 80 < p < 120 GeV/ c , anti- k R = 0.4 T T,jet 20 0.05 − 2 ) R Su Suppression ∆ − 4 0 Enhancement En soft drop β =0 region k t = p t Δ R [GeV] z ln( 10 − 6 − 0.05 SoftDrop z = 0.1, β = 0 cut − 8 Cambridge-Aachen Reclustering 5 1st SD Splitting − 0.1 − 10 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 1 La Large angle Col Collinear ln( ) ∆ R 2 This is not the average density, but the density of the 1st soft-drop splitting 1 0.4 0.2 0.1 0.05 0.02 0.01 Δ R � 64

0.35 0.35 0.35 2 2 2 ) ) ) θ θ θ ln(z ln(z ln(z QPYTHIA JEWEL wo/recoil JEWEL w/recoil HI MC studies p > 130 GeV/ c , anti- k R = 0.4 p > 130 GeV/ c , anti- k R = 0.4 p > 130 GeV/ c , anti- k R = 0.4 0.3 0.3 0.3 T T T T,jet T,jet T,jet 0 0 0 Cambridge-Aachen Declustering Cambridge-Aachen Declustering Cambridge-Aachen Declustering 0.25 0.25 0.25 2 2 2 − − − Andrews et al, 1808.03689 0.2 0.2 0.2 4 4 4 − − − 0.15 0.15 0.15 6 6 6 − − − ➤ clear potential for 0.1 0.1 0.1 8 8 8 − − − 0.05 0.05 0.05 distinguishing 10 0 10 0 10 0 − − − 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 between models, ln(1/ ) ln(1/ ) ln(1/ ) θ θ θ with clear physical 0.3 0.3 0.3 2 2 2 ) ) ) θ θ θ ln(z ln(z ln(z QPYTHIA (med-vac) JEWEL wo/recoil (med - vac) JEWEL w/recoil (med - vac) 0.25 0.25 0.25 p > 130 GeV/ c , anti- k R = 0.4 p > 130 GeV/ c , anti- k R = 0.4 p > 130 GeV/ c , anti- k R = 0.4 picture of where the T T T 0 T,jet 0 T,jet 0 T,jet Cambridge-Aachen Declustering Cambridge-Aachen Declustering Cambridge-Aachen Declustering 0.2 0.2 0.2 di ff erences arise 2 2 2 − − − 0.15 0.15 0.15 0.1 0.1 0.1 4 4 4 − − − 0.05 0.05 0.05 6 6 6 − − − 0 0 0 8 8 8 − − − 0.05 0.05 0.05 − − − 10 0.1 10 0.1 10 0.1 − − − − − − 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 ln(1/ ) ln(1/ ) ln(1/ ) θ θ θ Figure 4: Lund diagram reconstructed from jets generated by QPYTHIA (left column), JEWEL without recoils (middle column) and JEWEL with recoils (right column). The lower panels correspond to the di ff erence of the radiation pattern with and without jet quenching e ff ects. Note that the scale of the z -axes varies between the panels. � 65

application to high-p t physics e.g. new-physics searches and Higgs studies � 66

Comparing quark/gluon v. W-induced jets � 67

40 20 k t = p t Δ R [GeV] 10 Beyond average density: 
 5 any jet is a collection of points 
 in the (primary) Lund plane 2 1 0.4 0.2 0.1 0.05 0.02 0.01 Δ R � 68

long-short-term memory networks (LSTMs) 
 gave us the best performance Lund declustering points as inputs to machine-learning I Simple recurrent networks unable to handle dependencies that are widely separated in the data. I LSTM networks designed to have memory over longer periods, by adding four layers for each module and including a no-activation function. [Hochreiter, Schmidhuber (1997)] Figures from http://colah.github.io/posts/2015-08-Understanding-LSTMs/ � 69

Lund declustering points as inputs to hand-crafted likelihood calculation ➤ Identify emission that generates the jet mass (with Soft-Drop) ➤ Assume all other emissions are independent of each other, i.e. random distribution just set by average density ➤ Get MC ratio of average densities for W (Signal ≡ S) v. QCD (background ≡ B) jets ➤ Build likelihood discriminator L n ` ( ∆ ( i ) , k ( i ) X L tot = L ` ( m ( ` ) , z ( ` ) ) + t ; ∆ ( ` ) ) + N ( ∆ ( ` ) ) i 6 = ` ⇣ ⌘ ⇢ ( n ` ) ⇢ ( n ` ) L n ` ( ∆ , k t ; ∆ ( ` ) ) = ln � S B dn ( n ` ) � dN X ⇢ ( n ` ) emission ,X X ( ∆ , k t ; ∆ ( ` ) ) = / ∆ d ln ∆ ( ` ) d ln ∆ ( ` ) d ln k t d ln 1 � 70

signal efficiency background rejection Performance: 
 background rejection v. signal efficiency Lund + machine-learning (LSTM) Lund + likelihood 
 (gets to within 70-80% of performance of best machine learning) ciencies. � 71

S/√B resilience to non-perturbatitve effects Performance: 
 performance v. resilience [full mass information] S/ √ B v. resilience to non-perturbative QCD LH 2017+BDT no ln k t cut 20 LH 2017+BDT optimal [loose] +BDT D 2 ln k t cut = -1 Lund+likelihood 15 Lund + likelihood 
 Lund-LSTM ln k t cut = 0 performance performs better than machine learning when you exclude non- 10 perturbative region (k t < 1 GeV( Lund + machine-learning (LSTM) 5 ε W =0.4 p t >2 TeV Pythia8(Monash13), C/A(R=1) 0 0 2 4 6 8 10 resilience ! � 1 ∆ ✏ 2 2 ∆ ✏ 2 QCD W ⇣ = + h ✏ i 2 h ✏ i 2 � 72 QCD W

closing � 73

Conclusions The QCD radiation in collider events (pp & HI) is a rich source of information, which we’re only just starting to tap into. The di ffi culty is that there’s a lot of it: how do we condense it down to something we can understand, measure & exploit quantitatively? The Lund plane “construction” o ff ers an approach that ➤ maps transparently onto physically meaningful kinematic regions ➤ is amenable to calculations in QCD (work in progress) ➤ provides a powerful input to machine learning, but also can be used almost as e ff ectively in simpler multivariate frameworks. � 74

backup � 75

Initial–final symmetry � 76

choice of C/A for declustering � 77

why the C/A algorithm? 1 1 k t C/A anti − k C/A t 2 1 2 1 2 2 q q q q (a) (b) � 78

If you use jet algorithms other than C/A to provide the initial (de)clustering sequence, the jet algorithm itself introduces strong “unphysical” structure why the C/A algorithm? Figure 6 : The ρ ( ∆ , k t ) results as obtained with k t (left) and anti- k t (right) declustering, normalised to the result for C/A declustering. � 79

(αL) n mathematically, 
 logarithms, at most single C/A only produces density. the Lund-plane logarithms, (αL 2 ) n in by double structure is driven the unphysical why the C/A algorithm? 2 ) - k t 2 ) - anti-k t 2 ) - C/A Lund plane at O( α s Lund plane at O( α s Lund plane at O( α s 1200 800 800 k t anti-k t C/A 700 _ 600 1000 (k t ) L 2 (anti-k t ) L 2 (C/A) h 22 h 22 ρ 2,rc 600 400 800 200 500 0 600 400 2 2 2 ρ ρ ρ _ _ _ -200 300 400 -400 200 -600 200 100 -800 -1000 1000 250 0 200 0 2<log(1/ Δ )<2.5 2<log(1/ Δ )<2.5 2<log(1/ Δ )<2.5 2<log(1/ Δ )<2.5 2<log(1/ Δ )<2.5 2<log(1/ Δ )<2.5 200 800 2 - h 22 L 2 2 - h 22 L 2 150 2,rc 150 600 2 - ρ 100 _ 100 400 50 50 ρ _ 200 ρ ρ _ _ 0 0 0 -14 -12 -10 -8 -6 -4 -2 0 -8 -7 -6 -5 -4 -3 -2 -1 0 -14 -12 -10 -8 -6 -4 -2 0 log( κ ) log( κ ) log( κ ) (a) (b) (c) Figure 5 : Evaluations with Event2 of the second-order contribution to the Lund plane, in a bin of ln 1 / ∆ , as a function of κ , for (de)clustering sequences obtained with the k t , anti- k t and C/A jet algorithms. In (a) and (b) the dashed line corresponds to the analytic expectations, Eqs. (2.9) and (2.10) for clustering-induced double-logarithms in the k t and anti- k t algorithms. In (c), for the C/A algorithm, which is seen here to be free of double logarithms, the dot-dashed line corresponds to the (single-logarithmic) running coupling correction, Eq. (2.11), illustrating that it dominates the second-order correction. � 80

choice of original jet alg. � 81

the declustering sequence from C/A v. anti-k t starting points � 82

consequence for Lund plane density � 83

detector effects � 84

detector/particle detector Detector effects: with Delphes simulation (+ particle flow) I Detector e ff ects have significant impact on the Lund plane at angular scales below the hadronic calorimeter spacing. I Two enhanced regions corresponding to resolution scale of HCal and ECal. artefacts 
 induced 
 by ECal 
 & HCal 
 granularity � 85

subjet-particle rescaling algorithm (SPRA) Mitigate impact of detector granularity using a subjet particle rescaling algorithm: not a new idea! I Recluster Delphes particle-flow objects into subjets using C/A with R h ⇤ 0 . 12 . I Taking each subjet in turn, scale each PF charged-particle ( h ± ) and [82] A. Katz, M. Son, and B. Tweedie, Jet Substructure and the Search for Neutral Spin-One Resonances in Electroweak Boson Channels , JHEP 03 (2011) 011, [ arXiv:1010.5253 ]. [83] M. Son, C. Spethmann, and B. Tweedie, Diboson-Jets and the Search for Resonant Zh Production , JHEP 08 (2012) 160, [ arXiv:1204.0525 ]. photon ( γ ) candidate that it contains by a factor f 1 [84] S. Schaetzel and M. Spannowsky, Tagging highly boosted top quarks , Phys. Rev. D89 (2014), no. 1 014007, [ arXiv:1308.0540 ]. [85] A. J. Larkoski, F. Maltoni, and M. Selvaggi, Tracking down hyper-boosted top quarks , JHEP 06 (2015) 032, [ arXiv:1503.03347 ]. [86] S. Bressler, T. Flacke, Y. Kats, S. J. Lee, and G. Perez, Hadronic Calorimeter Shower Size: Õ i ∈ subjet p t , i Challenges and Opportunities for Jet Substructure in the Superboosted Regime , Phys. Lett. B756 (2016) 137–141, [ arXiv:1506.02656 ]. f 1 ⇤ [87] Z. Han, M. Son, and B. Tweedie, Top-Tagging at the Energy Frontier , Phys. Rev. D97 (2018), no. 3 036023, [ arXiv:1707.06741 ]. , Õ i ∈ subjet ( h ± , γ ) p t , i [88] CMS Collaboration, C. Collaboration, V Tagging Observables and Correlations , . [89] ATLAS Collaboration, T. A. collaboration, Jet mass reconstruction with the ATLAS Detector in early Run 2 data , . and discard the other neutral hadron candidates. I If subjet doesn’t contain photon or charged-particle candidates, retain all of the subjet’s particles with their original momenta. Recluster the full set of resulting particles (from all subjets) into a single large jet and use it to evaluate the mass and Lund plane. � 86

subjet-particle rescaling algorithm (SPRA) 0.3 9.0 < k t < 11.0 GeV 0.25 0.2 ρ ( Δ ,k t ) truth 0.15 Delphes PF 0.1 Delphes PF + SPRA1 0.05 Delphes PF + SPRA2 0 1 0.5 0.2 0.1 0.02 0.01 0.3 44.7 < k t < 54.6 GeV 0.25 0.2 ρ ( Δ ,k t ) 0.15 0.1 0.05 p t > 2 TeV 0 1 0.5 0.2 0.1 0.02 0.01 Δ � 87

Pythia v. Sherpa � 88

Sherpa 2.2.4 Pythia (8.233,M13) average pp Lund density: parton level Pythia8.2330(M13), parton level Sherpa2.2.4, parton level 0.9 0.9 pp 14 TeV 
 pp 14 TeV 
 C/A, R=1 
 C/A, R=1 
 0.8 0.8 6 6 p t,jet > 2 TeV p t,jet > 2 TeV 0.7 0.7 4 4 0.6 0.6 log(k t [GeV]) log(k t [GeV]) 0.5 0.5 2 2 0.4 0.4 0.3 0.3 0 0 0.2 0.2 0.1 0.1 -2 -2 0 0 0 1 2 3 4 5 0 1 2 3 4 5 log(1/ Δ R) log(1/ Δ R) � 89

Sherpa 2.2.4 Pythia (8.233,M13) average pp Lund density: hadron level (no underlying event / MPI) Pythia8.2330(M13), hadron level Sherpa2.2.4, hadron level 0.9 0.9 pp 14 TeV 
 pp 14 TeV 
 C/A, R=1 
 C/A, R=1 
 0.8 0.8 6 6 p t,jet > 2 TeV p t,jet > 2 TeV 0.7 0.7 4 4 0.6 0.6 log(k t [GeV]) log(k t [GeV]) 0.5 0.5 2 2 0.4 0.4 0.3 0.3 0 0 0.2 0.2 0.1 0.1 -2 -2 0 0 0 1 2 3 4 5 0 1 2 3 4 5 log(1/ Δ R) log(1/ Δ R) � 90