Scaling properties in multijet events–– towards high multiplicities ––

Peter SchichtelDurham University

@ Higgs plus Jets 2014

Content

Introduction

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

Jet radiation in QCD (FSR)

➝ data driven background studies➝ BSM physics

➝ theoretical uncertainties in multi-jet observables➝ jet scaling patterns

➝ pdf effects➝ learning from data➝ understanding Higgs (vetoes, using BDTs)

Hadron colliders

Theoretical uncertainties

jetsn2 3 4 5 6

jets

dndN

210

310

410

510

610

2≥ jn

> 50 GeVT, j

p-1L = 1 fb

W+jets

µW+jets, 1/4

µW+jets, 4

2≥ jn

> 50 GeVT, j

p-1L = 1 fb

W+jets

µW+jets, 1/4

µW+jets, 4

2≥ jn

> 50 GeVT, j

p-1L = 1 fb

W+jets

µW+jets, 1/4

µW+jets, 4

2≥ jn

> 50 GeVT, j

p-1L = 1 fb

W+jets

µW+jets, 1/4

µW+jets, 4

jetsn2 3 4 5 6

jets

dndN

210

310

410

510

610

jetsn2 3 4 5 6

var

iatio

ns

α

0.5

1

1.5 theoretical uncertainty

statistical uncertainty

jetsn2 3 4 5 6

var

iatio

ns

α

0.5

1

1.5

jetsn2 3 4 5 6

var

iatio

nµ

1

10

jetsn2 3 4 5 6

var

iatio

nµ

1

10

pdf uncertainties & scale choice(smaller at NLO)

understand jets ➝ controll jet dependent observables

jet sprectrum effective mass

[GeV]effm200 400 600 800

[1/1

00 G

eV]

eff

dmdN 310

410

510

2≥ jn

> 50 GeVT, j

p-1L = 1 fb

W+jets

µW+jets, 1/4

µW+jets, 4

2≥ jn

> 50 GeVT, j

p-1L = 1 fb

W+jets

µW+jets, 1/4

µW+jets, 4

2≥ jn

> 50 GeVT, j

p-1L = 1 fb

W+jets

µW+jets, 1/4

µW+jets, 4

2≥ jn

> 50 GeVT, j

p-1L = 1 fb

W+jets

µW+jets, 1/4

µW+jets, 4

[GeV]effm200 400 600 800

[1/1

00 G

eV]

eff

dmdN 310

410

510

[GeV]effm200 400 600 800

var

iatio

ns

α 0.9

1

1.1 theoretical uncertainty

statistical uncertainty

[GeV]effm200 400 600 800

var

iatio

ns

α 0.9

1

1.1

[GeV]effm200 400 600 800

var

iatio

nµ

1

10

[GeV]effm200 400 600 800

var

iatio

nµ

1

10

me↵ = /pT +X

all jets

pT,jet

uncertainties highly correlated

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

W/Z plus jets in the past

discoverd at SPS

UA1[Ellis,Kleis,Stirling(1985)]

CDFobserved at Tevatron and LHC

[Alioli et al, JHEP (2011) 095]

staircase like jet spectrum

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

ATLAS

exclusive: challenge for uncertainty estimation

ratios: cancel systematics

visualization

Aside: exclusive cross section ratios

exclusive: statistically independent

staircase scaling Poisson scaling

Rn+1n

=�n+1

�n= R0 Rn+1

n=

�n+1

�n=

n̄

n+ 1

constant ratios falling ratios

�excl.

n = �0

e�bn �excl.

n = �0

n̄ne�n̄

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)]

LHC: 7 TeV data

confirmed at LHC

staircase small tilt

Poisson flattens outneeds high jet

Can we understand these from basic principles?

[1304.7098]

pT

Bremsstrahlung in QED

schematic

Peskin & Schröder

Bremsstrahlung in QED

P (n) =n̄ne�n̄

n!

factorization theorem

n independet emissions

normalization

bosonic phase space

�i(t) = exp

2

4�tZ

t0

dt0X

jl

�i!jl

3

5

Sudakov form factor: non splitting prob.

d�n+1 = d�n ⇥ dt

tdz

↵s

2⇡Pi!jl(z)

soft collinear limit:

resolvable unresolvable

Peskin & Schröder

resummed

phase space boundary

QCD:

�(u) :=X

n

unP (n) P (n) =1

n!

dn

dun�(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) ]

t � t0

t ! t0 �g(t) =1

1 + 1�uu�g(t)

large log limit:primary emissions dominate → Poisson scaling

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

Bremsstrahlung in QCD

evolution equation �i(t) = u exp

2

4tZ

t0

dt0X

jl

�i!jl

✓�j(t0)�l(t0)

�i(t0)� 1

◆3

5

�i(t) =u�i(t)

�i(t)u

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

additional effects:

[Gerwick, PS: 1412.1806]

�g ⇠ 1

1 + 1�uu�g

�R(u)�(n)

Bremsstrahlung in QCD

nn+11/0 6/5 11/10 16/15 21/20

nn+1

R

1

2

3

4

5

6 6R = 0.5, e = 10naive phase spacePoisson = 5.2n

phase-space×staircase = 0.747, B = 4.80R

= -0.0177dn0dR

n10 20 30 40 50 60 70

(n)

φ

2

4

6

8

10 R = 0.5φnaive

R = 0.3φnaive

phase space

Rn+1n

=

✓R0

1 +

1

B + (n+ 1)

�+

dR0

dn(n+ 1)

◆⇥ �(n+ 1)

�(n)

← simulation of e+e� ! qq̄ + n⇥ g

small & vanishing as R ! 0[Gerwick, PS: 1412.1806]

PDF effects

n1 2 3 4 5 6 7

nB

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1Drell-Yan kinematics

all jets recoil←

T balanced in p←

d quark initial state 100 GeV≥ lead

Tp

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

2Ebeamx

(1) ⇡

rm

2Z + 2

⇣pT

pp

2T +m

2Z + p

2T

⌘

2Ebeam

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

Callibrate your jets from data

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

nn+1

R

0

0.1

0.2

0.3

0.4

0.5

=-0.0004dndR=0.1490R

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

nn+1

R

0

0.5

1

1.5 =1.7197n=-0.00920R

>100 GeV, T,j1

p

=2.2197n=-0.04610R

>150 GeV, T,j1

p

=2.1449n=0.03870R

>200 GeV, T,j1

p

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

nn+1

R

0

0.5

1

1.5 =1.7138n=0.01310R

>100 GeV, T,j1

p

=2.361n=-0.05090R

>150 GeV, T,j1

p

=2.6287n=-0.05360R

>200 GeV, T,j1

p

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

nn+1

R

0

0.1

0.2

0.3

0.4

0.5

=-0.005dndR

=0.14370R>1.0, ,jγ

minR

=0.0001dndR

=0.12660R>1.3, ,jγ

minR

=0.0053dndR

=0.10870R>1.6, ,jγ

minR

photons plus jets

Z plus jets

exact same jet spectrum!

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

Understanding Higgs veto efficiencies

1

n!/n+1!-1 0 1 2 3 4 5 6

) n!/

n+1

!R(

0

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

n+ 1

n

1/0 2/1 3/2 4/3 5/4 6/5

1

n!/n+1!-1 0 1 2 3 4 5

) n!/

n+1

!R(

0

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

n+ 1

n

1/0 2/1 3/2 4/3 5/4

1

n!/n+1!-1 0 1 2 3 4 5

) n!/

n+1

!R(

0

0.5

1

1.5

2

2.5

Higgs gluon fusion

Z QCD

n̄(Z QCD) = 1.42

n̄(Higgs gg fusion) = 1.80

0.5

1.0

1.5

2.0

2.5

R(n+1)/n

n+ 1

n

1/0 2/1 3/2 4/3 5/4

1

n!/n+1!-1 0 1 2 3 4 5 6

) n!/

n+1

!R(

0

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

n+ 1

n

1/0 2/1 3/2 4/3 5/4 6/5

note Y-axis scale→

WBF Higgs

before cut

after cutmjj

mjj

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

pminT,j = 20 GeV |yj | < 4.5

y1y2 < 0 |y1 � y2| > 4.4

Know you backgrounds: jets & BDT

S∈0.3 0.35 0.4

B∈1

-

0.94

0.95

0.96

0.97

0.98y-selectionΔFWMs, -selection

TFWMs, p

jet veto

jet veto

WBF Higgs

cuts veto more jets0. 014 0. 047 0. 0830. 026 0. 045 0. 071

S/B

pT selection

�y selection

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

cuts BDT more jets

47 % 28 % 16 %

6.9% 3.5% 2.1%3000 fb�1

10 fb�1

�inv/�SM

[Bernaciak, Plehn, PS, Tattersall: 1411.7699]

invisible Higgs (WBF)

Know you backgrounds: jets & BDT

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, ...)