[PPT] - Mapping the QCD radiation spectrum Keith Pedersen PowerPoint Presentation

SLIDE 1

Mapping the QCD radiation spectrum

Keith Pedersen (kpeders1@hawk.iit.edu) In collaboration with Zack Sullivan DPF 2017

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Outline

1

The shape of QCD Can we probe QCD like the CMB power spectrum? Can we suppress/identify pileup?

2

A multipole expansion The power spectrum of the Fox-Wolfram moments (FWM) Interpreting the power spectrum

3

Jet shapes from the QCD power spectrum Three jet kinematics in high pileup Reconstructing a parton shower

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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? ρm

l =

dΩ Y m

l ∗(θ, φ) ρ(θ, φ)

Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 1 / 17

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Can we probe QCD like the CMB?

Hard scatter Fragmentation Initial state radiation Pileup

Can we identify broad, universal shapes with known physics?

Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 2 / 17

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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

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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

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Outline

1

The shape of QCD Can we probe QCD like the CMB power spectrum? Can we suppress/identify pileup?

2

A multipole expansion The power spectrum of the Fox-Wolfram moments (FWM) Interpreting the power spectrum

3

Jet shapes from the QCD power spectrum Three jet kinematics in high pileup Reconstructing a parton shower

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The Fox-Wolfram moments (FWM)

FWM expand a single event’s energy distribution ρ(θ, φ) into Y m

l (θ, φ)

Hl =

i, j

fi fj Pl(cos θij)

energy fraction fi ≡ |

pi| Evis and interior angle θij

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

2017

≫ 19 GeV

1978

. . . it’s time to revisit the FWM.

Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 5 / 17

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Hl of simple matrix elements (in the CM frame)

0.2 0.4 0.6 0.8 1 200 400 600 800 1000 Hl l Every two-jet matrix element even

dd

Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 6 / 17

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Hl of simple matrix elements (in the CM frame)

0.2 0.4 0.6 0.8 1 200 400 600 800 1000 Hl l Event A - matrix element Event B - matrix element Event B - showered even

dd

A B Hl ≈

l→∞

f 2

i ∼ 1/N

Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 6 / 17

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The Nyquist frequency of angular sampling

∞

−∞

δ(x)e−i k xdx = 1 ρ(θ, φ) =

i

fi δ3(ˆ pi − ˆ r) δ(x) has unlimited angular power Hl are the multipole expansion

f a discrete sample!

0.2 0.4 0.6 0.8 1 200 400 600 800 1000 Hl l Every two-jet matrix element even

dd

Convert pi into extensive objects smeared by a “Nyquist” angle σ.

Suppresses high-frequencies.

Nyquist angle σ is determined by event multiplicity and structure, not detector resolution.

Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 7 / 17

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The smearing function

Ansatz for smearing function h(θ): Smear in polar angle θ to observed ˆ pi. Gaussian at small angles. No cusp as θ → π.

10−3 10−2 10−1 100 100 200 300 400 500 Hl suppression (smeared/raw) l clones = 2 clones = 32 Hl of h(θ)

h(θ) = exp(−2 sin2( θ

2)/σ2)

σ2(1 − e−2/σ2) Convolution theorem Scale the power spectrum Hl of

bserved ˆ

pi by the power spectrum of the smearing function.

Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 8 / 17

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Showered, smeared power spectra

Hl =

i, j

fifjPl(cos θij) f (z) =

l

(2l + 1)Hl Pl(z)

f (z) z = cos(θij) σ = .04 (5◦ obj.) 2 4 6 8 10

1
0.5

0.5 1

Apeak ∼ fifj

Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 9 / 17

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Showered, smeared power spectra

Hl =

i, j

fifjPl(cos θij) f (z) =

l

(2l + 1)Hl Pl(z)

f (z) z = cos(θij) σ = .01 (1◦ obj.) σ = .04 (5◦ obj.) 2 4 6 8 10

1
0.5

0.5 1

Apeak ∼ fifj

Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 9 / 17

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Showered, smeared power spectra

Hl =

i, j

fifjPl(cos θij) f (z) =

l

(2l + 1)Hl Pl(z)

f (z) z = cos(θij) σ = 10−3 (0.1◦ obj.) σ = .01 (1◦ obj.) σ = .04 (5◦ obj.) 2 4 6 8 10

1
0.5

0.5 1

Apeak ∼ fifj Hl at small l (the coarse event shape) is IR and collinear safety.

Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 9 / 17

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Outline

1

The shape of QCD Can we probe QCD like the CMB power spectrum? Can we suppress/identify pileup?

2

A multipole expansion The power spectrum of the Fox-Wolfram moments (FWM) Interpreting the power spectrum

3

Jet shapes from the QCD power spectrum Three jet kinematics in high pileup Reconstructing a parton shower

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3-jet kinematics at e + e − (√s = 1 TeV)

Calculate Hl for 3-parton toy system; fit to observed Hl by minimizing χ2. Hl =

i, j

fifjPl(cos θij), fi ≡ Ei √s

p1 p2 p3 pPU

p2

j =0

p2

PU =f 2 PU

p = 0

= ⇒ 3 d.o.f. 3 angles θij from f1, f2, fPU. But Hl ≈ f 2

i ∼ 1/N as

l → ∞ . . . 3 partons won’t match Hl for real jets (N ≫ 3).

0.1 0.2 0.3 0.4 0.5 0.6 20 40 60 80 100 120 Hl l N = 3 N = 75 N = 232

Take a cue from smearing . . . for n-parton system, only fit the first n

2

modes (one per θij).

Jet kinematics without R parameter! (p1 + p2)2 = s

(f1 + f2)2 − f 2

3

Keith Pedersen (IIT)

Mapping the QCD radiation spectrum DPF 2017 10 / 17

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Fitting the 3-jet matrix element

Mapping 3 → 3 partons gives a perfect fit.

0.2 0.4 0.6 0.8 1 2 4 6 8 10 12 14 Hl l Fit ME fit

ME Fit ME ˜ f1 0.433 0.434 (+0.2%) ˜ f2 0.426 0.425 (−0.2%) ˜ f3 0.141 0.141 (±0.0%) fPU — — normalized ˜ f = f /(1 − fPU)

Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 11 / 17

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Fitting the showered 3-jet matrix element

Fitting 3 partons to jets overestimates l > 4.

0.2 0.4 0.6 0.8 1 2 4 6 8 10 12 14 Hl l Fit Showered fit

ME Fit showered ˜ f1 0.434 0.445 (+2.5%) ˜ f2 0.425 0.410 (−3.5%) ˜ f3 0.141 0.145 (+2.8%) fPU — 0.012 normalized ˜ f = f /(1 − fPU)

Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 12 / 17

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Pseudo-detector with mild pileup (S/N = 6)

Isotropic pileup suppresses Hl versus H0.

0.2 0.4 0.6 0.8 1 2 4 6 8 10 12 14 Hl l Fit Showered + Pileup Fit

no PU Fit w/ PU ˜ f1 0.445 0.446 (+0.2%) ˜ f2 0.410 0.401 (−2.2%) ˜ f3 0.145 0.153 (+5.5%) fPU 0.012 0.136 normalized ˜ f = f /(1 − fPU)

Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 13 / 17

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Pseudo-detector with extreme pileup (S/N = 1/3)

Partons still visible through extreme pileup.

1 10−2 10−1 2 4 6 8 10 12 14 Hl l Fit Showered + Pileup Fit

no PU Fit w/ PU ˜ f1 0.445 0.455 (+2.5%) ˜ f2 0.410 0.387 (−5.6%) ˜ f3 0.145 0.158 (+8.2%) fPU 0.012 0.625 normalized ˜ f = f /(1 − fPU)

Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 14 / 17

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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.

m z a c b φ

fb = z fa fc = (1 − z) fa

collision

Keith Pedersen (IIT) Mapping the QCD radiation spectrum DPF 2017 15 / 17

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