Mapping the QCD radiation spectrum Keith Pedersen - PowerPoint PPT Presentation

Mapping the QCD radiation spectrum Keith Pedersen (kpeders1@hawk.iit.edu) In collaboration with Zack Sullivan DPF 2017

Outline The shape of QCD 1 Can we probe QCD like the CMB power spectrum? Can we suppress/identify pileup? A multipole expansion 2 The power spectrum of the Fox-Wolfram moments (FWM) Interpreting the power spectrum Jet shapes from the QCD power spectrum 3 Three jet kinematics in high pileup Reconstructing a parton shower

The ideal event shape variable Jet clustering discards lots of information — at each step, the evolution is guided by only one 2-particle correlation. Event shape variables (sphericity) are more holistic, but tend to be 1-dim. Ideally, a shape curve could describe a single event , and we could: Extract jet kinematics. Tag interesting signatures. Probe QCD at new scales. A multipole expansion of E density? � ρ m d Ω Y m l = ∗ ( θ, φ ) ρ ( θ, φ ) l Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 1 / 17

Can we probe QCD like the CMB? Hard scatter Pileup Initial state radiation Fragmentation Can we identify broad, universal shapes with known physics? Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 2 / 17

The Pb-Pb ridge versus the p-p ridge Can the ridge be quark-gluon plasma if we see it in pp collisions? Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 3 / 17

Pileup at the HL-LHC Pileup at the HL-LHC will be intense . We will need to: Remove pileup from jets and identify pileup-only jets. Distinguish boosted top from QCD jets + pileup . Find W → q ¯ q for precision electroweak measurements. Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 4 / 17

Outline The shape of QCD 1 Can we probe QCD like the CMB power spectrum? Can we suppress/identify pileup? A multipole expansion 2 The power spectrum of the Fox-Wolfram moments (FWM) Interpreting the power spectrum Jet shapes from the QCD power spectrum 3 Three jet kinematics in high pileup Reconstructing a parton shower

The Fox-Wolfram moments (FWM) FWM expand a single event’s energy distribution ρ ( θ, φ ) into Y m l ( θ, φ ) � � energy fraction f i ≡ | � p i | � H l = f i f j P l ( cos θ ij ) and interior angle θ ij E vis i , j Limitations : Rotational invariance loses the event’s absolute orientation Conflates correlations from across the collider. Not Lorentz invariant . . . works best at lepton colliders. Must have high particle multiplicity (hobbled by shot noise). Particle multiplicity at 13 TeV ≫ 19 GeV . . . it’s time to revisit the FWM. � �� � � �� � 2017 1978 Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 5 / 17

H l of simple matrix elements (in the CM frame) 1 0.8 even odd 0.6 H l 0.4 0.2 Every two-jet matrix element 0 0 200 400 600 800 1000 l Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 6 / 17

H l of simple matrix elements (in the CM frame) 1 0.8 even odd A B 0.6 Event A - matrix element H l 0.4 Event B - matrix element 0.2 � f 2 H l ≈ i ∼ 1 / N l →∞ Event B - showered 0 0 200 400 600 800 1000 l Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 6 / 17

The Nyquist frequency of angular sampling � ∞ δ ( x ) e − i k x d x = 1 δ ( x ) has unlimited angular power −∞ H l are the multipole expansion � f i δ 3 (ˆ ρ ( θ, φ ) = p i − ˆ r ) of a discrete sample! i 1 Convert � p i into extensive objects 0.8 even odd smeared by a “Nyquist” angle σ . 0.6 H l Suppresses high-frequencies . 0.4 0.2 Every two-jet matrix element Nyquist angle σ is determined by 0 event multiplicity and structure, 0 200 400 600 800 1000 not detector resolution. l Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 7 / 17

The smearing function Ansatz for smearing function h ( θ ) : h ( θ ) = exp ( − 2 sin 2 ( θ 2 ) /σ 2 ) Smear in polar angle θ to observed ˆ p i . σ 2 ( 1 − e − 2 /σ 2 ) Gaussian at small angles. No cusp as θ → π . 10 0 clones = 2 clones = 32 H l suppression (smeared/raw) H l of h ( θ ) 10 − 1 Convolution theorem Scale the power 10 − 2 spectrum H l of observed ˆ p i by the power 10 − 3 spectrum of the smearing 0 100 200 300 400 500 function. l Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 8 / 17

Showered, smeared power spectra � � H l = f i f j P l ( cos θ ij ) f ( z ) = ( 2 l + 1 ) H l P l ( z ) i , j l A peak ∼ f i f j 10 (5 ◦ obj. ) σ = .04 8 6 f ( z ) 4 2 0 -1 -0.5 0 0.5 1 z = cos( θ ij ) Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 9 / 17

Showered, smeared power spectra � � H l = f i f j P l ( cos θ ij ) f ( z ) = ( 2 l + 1 ) H l P l ( z ) i , j l A peak ∼ f i f j 10 (5 ◦ obj. ) σ = .04 8 (1 ◦ obj. ) σ = .01 6 f ( z ) 4 2 0 -1 -0.5 0 0.5 1 z = cos( θ ij ) Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 9 / 17

Showered, smeared power spectra � � H l = f i f j P l ( cos θ ij ) f ( z ) = ( 2 l + 1 ) H l P l ( z ) i , j l A peak ∼ f i f j 10 (5 ◦ obj. ) σ = .04 8 (1 ◦ obj. ) σ = .01 σ = 10 − 3 (0.1 ◦ obj. ) 6 f ( z ) 4 2 0 H l at small l -1 -0.5 0 0.5 1 (the coarse event shape) is IR and z = cos( θ ij ) collinear safety. Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 9 / 17

Outline The shape of QCD 1 Can we probe QCD like the CMB power spectrum? Can we suppress/identify pileup? A multipole expansion 2 The power spectrum of the Fox-Wolfram moments (FWM) Interpreting the power spectrum Jet shapes from the QCD power spectrum 3 Three jet kinematics in high pileup Reconstructing a parton shower

3-jet kinematics at e + e − ( √ s = 1 TeV ) Calculate H l for 3-parton toy system; 0.6 fit to observed H l by minimizing χ 2 . 0.5 N = 3 0.4 f i ≡ E i � H l = f i f j P l ( cos θ ij ) , √ s H l 0.3 i , j 0.2 N = 75 0.1 N = 232 p PU p 3 0 p 2 j = 0 0 20 40 60 80 100 120 p 1 l p 2 PU = f 2 p 2 PU Take a cue from smearing . . . � � for n -parton system, only fit the p = 0 = ⇒ 3 d.o.f. � n � first modes (one per θ ij ). 3 angles θ ij from f 1 , f 2 , f PU . 2 But H l ≈ � f 2 i ∼ 1 / N as Jet kinematics without R parameter! l → ∞ . . . 3 partons won’t ( p 1 + p 2 ) 2 = s � ( f 1 + f 2 ) 2 − f 2 � match H l for real jets ( N ≫ 3). 3 Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 10 / 17

Fitting the 3-jet matrix element Mapping 3 → 3 partons gives a perfect fit. 1 ME fit 0.8 Fit 0.6 H l ME Fit ME 0.4 ˜ f 1 0.433 0.434 (+ 0 . 2 %) ˜ 0.2 f 2 0.426 0.425 ( − 0 . 2 %) ˜ f 3 0.141 0.141 ( ± 0 . 0 %) 0 f PU — — 2 4 6 8 10 12 14 l normalized ˜ f = f / ( 1 − f PU ) Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 11 / 17

Fitting the showered 3-jet matrix element Fitting 3 partons to jets overestimates l > 4. 1 Showered fit 0.8 Fit 0.6 H l ME Fit showered 0.4 ˜ f 1 0.434 0.445 (+ 2 . 5 %) ˜ 0.2 f 2 0.425 0.410 ( − 3 . 5 %) ˜ f 3 0.141 0.145 (+ 2 . 8 %) 0 f PU — 0.012 2 4 6 8 10 12 14 l normalized ˜ f = f / ( 1 − f PU ) Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 12 / 17

Pseudo-detector with mild pileup ( S / N = 6 ) Isotropic pileup suppresses H l versus H 0 . 1 Showered + Pileup 0.8 Fit Fit 0.6 H l no PU Fit w/ PU 0.4 ˜ f 1 0.445 0.446 (+ 0 . 2 %) ˜ f 2 0.410 0.401 ( − 2 . 2 %) 0.2 ˜ f 3 0.145 0.153 (+ 5 . 5 %) 0 f PU 0.012 0.136 2 4 6 8 10 12 14 l normalized ˜ f = f / ( 1 − f PU ) Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 13 / 17

Pseudo-detector with extreme pileup ( S / N = 1 / 3 ) Partons still visible through extreme pileup. 1 Showered 10 − 1 Fit + Pileup H l Fit no PU Fit w/ PU ˜ f 1 0.445 0.455 (+ 2 . 5 %) ˜ 10 − 2 f 2 0.410 0.387 ( − 5 . 6 %) ˜ f 3 0.145 0.158 (+ 8 . 2 %) f PU 0.012 0.625 2 4 6 8 10 12 14 l normalized ˜ f = f / ( 1 − f PU ) Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 14 / 17

Reconstruct a parton shower from the top down To access information from smaller angles, the final state fit must contain many more partons. Parameterize the final state in terms of a generic branching: ( m , z , φ ) Sequentially add branches and re-fit, starting at the previous minimum. collision z φ b a m c f b = z f a f c = ( 1 − z ) f a Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 15 / 17

Sequentially fitting the same “3-jet” event 1 ME σ = 10 ◦ fit 0.8 Fit 0.6 collision H l 0.4 0.2 0 2 4 6 8 10 12 14 16 18 20 l Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 16 / 17

Sequentially fitting the same “3-jet” event 1 Showered σ = 10 ◦ fit 0.8 Fit 0.6 collision H l 0.4 0.2 0 2 4 6 8 10 12 14 16 18 20 l Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 16 / 17

Sequentially fitting the same “3-jet” event 1 Showered σ = 10 ◦ fit 0.8 Fit 0.6 collision H l 0.4 0.2 0 2 4 6 8 10 12 14 16 18 20 l Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 16 / 17