[PPT] - Scaling properties in multijet events towards high multiplicities PowerPoint Presentation

SLIDE 1

Scaling properties in multijet events

–– towards high multiplicities ––

Peter Schichtel

Durham University

@ Higgs plus Jets 2014

SLIDE 2

Content

Introduction

➝ a simple QED example ➝ generating functionals ➝ scaling limits & beyond

Jet radiation in QCD (FSR)

➝ data driven background stud ➝ theoretical uncertainties in multi-jet observables ➝ jet scaling patterns ➝ pdf effects ➝ learning from data ➝ understanding Higgs (vetoes, using BDTs)

Hadron colliders

SLIDE 3

Theoretical uncertainties

2 3 4 5 6

jets

dn dN

2

10

3

10

4

10

5

10

6

10

2 ≥

j

n > 50 GeV

T, j

p

1

L = 1 fb W+jets µ W+jets, 1/4 µ W+jets, 4 2 ≥

j

n > 50 GeV

T, j

p

1

L = 1 fb W+jets µ W+jets, 1/4 µ W+jets, 4 2 ≥

j

n > 50 GeV

T, j

p

1

L = 1 fb W+jets µ W+jets, 1/4 µ W+jets, 4 2 ≥

j

n > 50 GeV

T, j

p

1

L = 1 fb W+jets µ W+jets, 1/4 µ W+jets, 4

2 3 4 5 6

jets

dn dN

2

10

3

10

4

10

5

10

6

10

2 3 4 5 6 variation

s

α 0.5 1 1.5

theoretical uncertainty statistical uncertainty

2 3 4 5 6 variation

s

α 0.5 1 1.5

jets

n 2 3 4 5 6 variation µ 1 10

jets

n 2 3 4 5 6 variation µ 1 10

pdf uncertainties & scale choice

(smaller at NLO)

understand jets ➝ controll jet dependent observables jet sprectrum effective mass

200 400 600 800

[1/100 GeV]

eff

dm dN

3

10

4

10

5

10

2 ≥

j

n > 50 GeV

T, j

p

1

L = 1 fb W+jets µ W+jets, 1/4 µ W+jets, 4 2 ≥

j

n > 50 GeV

T, j

p

1

L = 1 fb W+jets µ W+jets, 1/4 µ W+jets, 4 2 ≥

j

n > 50 GeV

T, j

p

1

L = 1 fb W+jets µ W+jets, 1/4 µ W+jets, 4 2 ≥

j

n > 50 GeV

T, j

p

1

L = 1 fb W+jets µ W+jets, 1/4 µ W+jets, 4

200 400 600 800

[1/100 GeV]

eff

dm dN

3

10

4

10

5

10

200 400 600 800 variation

s

α 0.9 1 1.1

theoretical uncertainty statistical uncertainty

200 400 600 800 variation

s

α 0.9 1 1.1 [GeV]

eff

m 200 400 600 800 variation µ 1 10 [GeV]

eff

m 200 400 600 800 variation µ 1 10

meff = / pT + X

all jets

pT,jet

uncertainties highly correlated

[Englert, Plehn, P .S., Schumann: Phys.Rev. D83 (2011) 095009]

SLIDE 4

W/Z plus jets in the past

discoverd at SPS

UA1

[Ellis,Kleis,Stirling(1985)]

CDF

bserved at Tevatron and LHC

[Alioli et al, JHEP (2011) 095]

staircase like jet spectrum

[Aad et al. Phys. Rev. D 85 092002 (2012)]

ATLAS

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exclusive: challenge for uncertainty estimation ratios: cancel systematics visualization

Aside: exclusive cross section ratios

exclusive: statistically independent

SLIDE 6

staircase scaling Poisson scaling

R n+1

n

= σn+1 σn = R0 R n+1

n

= σn+1 σn = ¯ n n + 1

constant ratios falling ratios

σexcl.

n

= σ0e−bn σexcl.

n

= σ0 ¯ nne−¯

n

n!

[Steve Ellis,Kleis,Stirling(1985); Berends(1989)] [Peskin & Schroeder; Rainwater, Zeppenfeld(1997)]

Scaling patterns

Can we understand these from basic principles?

same for exclusive and inclusive

[Phys. Rev. D 83 095009 (2011)]

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LHC: 7 TeV data

confirmed at LHC staircase small tilt Poisson flattens out

needs high jet

Can we understand these from basic principles?

[1304.7098]

pT

SLIDE 8

Bremsstrahlung in QED

schematic Peskin & Schröder

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Bremsstrahlung in QED

P(n) = ¯ nne−¯

n

n!

factorization theorem

n independet emissions normalization bosonic phase space

∆i(t) = exp 2 4−

t

Z

t0

dt0 X

jl

Γi!jl 3 5

Sudakov form factor: non splitting prob.

dσn+1 = dσn × dt t dz αs 2π Pi→jl(z)

soft collinear limit: resolvable unresolvable Peskin & Schröder

resummed

phase space boundary

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QCD:

Φ(u) := X

n

unP(n) P(n) = 1 n! dn dun Φ(u)

u=0

generating functional formalism

jet rate

Bremsstrahlung in QCD

more complicated: gluon self interaction formal way to deal with

[Konishi te al. (1979); Ellis, Stirling, Webber (1996); Gerwick, Gripaios, Schumann, Webber (2012) ]

SLIDE 11

t t0 t → t0 Φg(t) = 1 1 +

1−u u∆g(t)

large log limit:

primary emissions dominate → Poisson scaling

democratic limit

exact solution [JHEP 1210 (2012) 162] → staircase scaling

Bremsstrahlung in QCD

evolution equation

Φi(t) = u exp 2 4

t

Z

t0

dt0 X

jl

Γi!jl ✓Φj(t0)Φl(t0) Φi(t0) − 1 ◆3 5 Φi(t) = u∆i(t) ∆i(t)u

➝ breaking terms ✔ ➝ phase space ✔ ➝ finite jet radius ✘

additional effects:

[Gerwick, PS: 1412.1806]

Φg ∼ 1 1 + 1−u

u∆g − R(u)

φ(n)

SLIDE 12

Bremsstrahlung in QCD

n n+1 1/0 6/5 11/10 16/15 21/20

n n+1

R 1 2 3 4 5 6

6

R = 0.5, e = 10 naive phase space Poisson = 5.2 n phase-space × staircase = 0.747, B = 4.8 R = -0.0177 dn dR

n 10 20 30 40 50 60 70 (n) φ 2 4 6 8 10 R = 0.5 φ naive R = 0.3 φ naive phase space

R n+1

n

= ✓ R0  1 + 1 B + (n + 1)

+ dR0

dn (n + 1) ◆ × φ(n + 1) φ(n)

← simulation of e+e− → q¯ q + n × g

small & vanishing as R → 0

[Gerwick, PS: 1412.1806]

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PDF effects

n

1 2 3 4 5 6 7

n

B 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 Drell-Yan kinematics all jets recoil ←

T

balanced in p ← d quark initial state 100 GeV ≥

lead T

p

effects factorize at LL threshold approximation pdf suppresion of additional jets

characterised by Bn =

f(x(n+1),Q)

f(x(n),Q) f(x(n+2),Q) f(x(n+1),Q)

2

x(0) ≈ mZ 2Ebeam x(1) ≈ r m2

Z + 2

⇣ pT p p2

T + m2 Z + p2 T

⌘ 2Ebeam

[Gerwick, Plehn, P .S., Schumann: JHEP 1210 (2012) 162]

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Callibrate your jets from data

2/1 3/2 4/3 5/4 6/5 7/6

n n+1

R 0.1 0.2 0.3 0.4 0.5

=-0.0004 dn dR =0.149 R

2/1 3/2 4/3 5/4 6/5 7/6 8/7

n n+1

R 0.5 1 1.5

=1.7197 n =-0.0092 R >100 GeV, T,j1 p =2.2197 n =-0.0461 R >150 GeV, T,j1 p =2.1449 n =0.0387 R >200 GeV, T,j1 p

2/1 3/2 4/3 5/4 6/5 7/6 8/7

n n+1

R 0.5 1 1.5

=1.7138 n =0.0131 R >100 GeV, T,j1 p =2.361 n =-0.0509 R >150 GeV, T,j1 p =2.6287 n =-0.0536 R >200 GeV, T,j1 p

2/1 3/2 4/3 5/4 6/5 7/6

n n+1

R 0.1 0.2 0.3 0.4 0.5

=-0.005 dn dR =0.1437 R >1.0,

,j γ min

R =0.0001 dn dR =0.1266 R >1.3,

,j γ min

R =0.0053 dn dR =0.1087 R >1.6,

,j γ min

R

photons plus jets Z plus jets exact same jet spectrum!

[Englert, Plehn, P .S., Schumann: JHEP 1202 (2012) 030]

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Understanding Higgs veto efficiencies

1

1 2 3 4 5 6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Higgs WBF Z EW

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 R(n+1)/n 1/0 2/1 3/2 4/3 5/4 6/5

1

1 2 3 4 5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Higgs WBF Z EW

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 R(n+1)/n 1/0 2/1 3/2 4/3 5/4

1

1 2 3 4 5 0.5 1 1.5 2 2.5

Higgs gluon fusion Z QCD ¯ n(Z QCD) = 1.42 ¯ n(Higgs gg fusion) = 1.80

0.5 1.0 1.5 2.0 2.5 R(n+1)/n 1/0 2/1 3/2 4/3 5/4

1

1 2 3 4 5 6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Higgs gluon fusion Z QCD

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 R(n+1)/n 1/0 2/1 3/2 4/3 5/4 6/5

note Y-axis scale→

WBF Higgs before cut after cut

mjj mjj

[Gerwick, Schumann, Plehn: Phys.Rev.Lett. 108 (2012) 032003]

pmin

T,j = 20 GeV

|yj| < 4.5 y1y2 < 0 |y1 − y2| > 4.4

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Know you backgrounds: jets & BDT

S

∈ 0.3 0.35 0.4

B

∈ 1 - 0.94 0.95 0.96 0.97 0.98

y-selection Δ FWMs,

selection

T

FWMs, p jet veto jet veto

WBF Higgs

cuts veto more jets

0. 014
0. 047
0. 083
0. 026
0. 045
0. 071

S/B pT selection ∆y selection

[Bernaciak, Mellado, Plehn, Ruan, PS: Phys. Rev D89 2014]

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cuts BDT more jets 47 % 28 % 16 % 6.9% 3.5% 2.1%

3000 fb−1 10 fb−1 Γinv/ΓSM

[Bernaciak, Plehn, PS, Tattersall: 1411.7699]

invisible Higgs (WBF)

Know you backgrounds: jets & BDT

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Conclusions

thanks for listening

➝ multi-jet observables are plagued by huge theoretical uncertainties (LO) ➝ jet spectra follow simple scaling patterns ➝ staircase scaling is a firm QCD prediction (& observed) @ LHC: low multiplicities due to PDF effects ➝ controll uncertainties & understand backgrounds from data ➝ QCD high multiplicity predictions possible [difficult with NLO]

➝ use in subsequent applications (Higgs studies, BSM, ...)