Jet counting & QCD scaling patterns

Peter Schichtel@ IMPRS-PTFS seminar 2013

based on:Englert, P.S., Schumann, Plehn: Phys.Rev. D83 (2011) 095009Gerwick, Schumann, Plehn: Phys.Rev.Lett. 108 (2012) 032003Englert, P.S., Schumann, Plehn: JHEP 1202 (2012) 030Gerwick, P.S., Schumann, Plehn: JHEP 1210 (2012) 162Gerwick, Gripaios, Schumann, Webber: JHEP 1304 (2013) 089and still some stuff to come ...

jets?

[CMS multi-jet event ➝]

jet algorithm

distance measure [e.g. algorithm]

jets are a collimated spray of hadrons

clustering scheme:1.) smallest ➝ cluster i and j2.) smallest ➝ call it a jet

1.)

2.)

many algorithms, different parameters yield different jets

kT

i and j can be anything: particles, detector cells, partons,...

yij =�Rij

Rmin

�p2T,i, p

2T,j

�

yiB = p2T,i

why jets?LHC is a discovery machine: Higgs(✔), BSM(?)

LHC is a SM machine: precision test

backgrounds:➝ W/Z plus jets [Higgs, missing energy]

➝ top plus jets [decay chains, missing energy]

➝ pure QCD jets [fake missing energy]

physics processes:➝ Drell-Yan [Z plus jets, mirror process to e+e-]

➝ WBF Higgs [tagging jets]

➝ strong coupling [2 vs. 3 jets]

➝ di-jet resonances [new physics]

understanding jets is essential for LHC physics

proton collider: QCD machinethis talk is all about LHC physics

[CMS multi-jet event ➝]

LHC physics

tracksparticle flowcalorimeter cells

what kind of information?

jet algorithm

jets

Experiments:a theorists point of view

sources of uncertainty:➝ systematics ➝ statistcs

➝ cross sections

LHC physics

total cross section

Theory:

PDFs

partonic cross section (LO, NLO, ...)

hadronization, event cuts, ...

�

pp!P+XLHC (

ps, µF , µR) =

X

a,b

Zdxadxb fp(xa, µF )fp(xb, µF ) �̂

ab!P (xa, xb,ps, µF , µR)⇥ F

cuts

soft

[from: fnal.gov/Run2Physics]

master equation is inclusive: n + X jets

sources of uncertainty:➝ PDFs➝ factorization scale

jet countingexclusive: exactly n jets

→ excl. jet rates are ambiguous (ISR?)→ closer to real event structure→ statistical independent→ correlation to other multi-jet observables

inclusive: at least n jets

→ easily calculable→ n jets in matrix element→ PDF‘s sum collinear radiation X→ higher order leads to smaller uncertainty

analysis # excl. jets

Higgs WBF 0,1,2

Higgs WW* 2

di-boson 0,1

top mass 4

new physics 4,8,n(?)

count exclusive jets

jets are counted in addition to the hard event

use exclusive jet cross-section ratios

observe two different patterns: staircase and Poisson scaling

scaling patternsstaircase 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)]

evidenve: UA1, LEP,Tevatron, LHC

rates depend on jet algorithm and hard processfeatures NOT!

nn+11/0 2/1 3/2 4/3 5/4

nn+1

R

0.1

0.2

0.3

0.4

0.5

0.6

0.7 staircase scaling

nn+11/0 2/1 3/2 4/3 5/4

nn+1

R

0.1

0.2

0.3

0.4

0.5

0.6

0.7 Poisson scaling

[idealized example] [idealized example]

the same for inclusive! [NLO]

theory behind QCD scaling

�µ /q + /k

(q + k)2! qµ

qk

M

P (n) =n̄ne�n̄

n!

M

eikonal approximation

factorization

n independet emissions

probabilitynormalization

bosonic phase space

three gluon vertex → secondary emissions

factorization still holds➝ resummation➝ parton shower➝ iterated Poisson

splitting kernel → integrate

QED:

QCD:

�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)

theory behind QCD scaling

evolution equation

�(u) :=X

n

unP (n) P (n) =1

n!

dn

dun�(u)

����u=0

�i(t) = u exp

2

4tZ

t0

dt0X

jl

�i!jl

✓�j(t0)�l(t0)

�i(t0)� 1

◆3

5

generating functional formalism

jet resolution

jet rate

scale of hard process

smallest resolvable splitting

electron collider: Durham algorithm

yij = 2 min

�E2

i , E2j

�1� cos ✓ij

t

simultaneous evolution in energy and distance

t = 2EiEj(1� cos ✓ij)

ycut =t0t

[time like evolution]

theory behind QCD scaling

Rn+1n

= (1��g(t))

1 +

1

B + (n+ 1)

�

nn+11/0 11/10 21/20 31/30

nn+1

R

1

2

3

4

5=1PeVs

= 10GeVR: R = 0.3, ETanti-k

= 3.00nPoisson: = 0.6730staircase: R

staircase: B = -3.57

← simulation of e+e� ! qq̄ + n⇥ g

kT

new

t � t0

t ! t0 �g(t) =1

1 + 1�uu�g(t)

large log limit: primary emissions dominate → Poisson scaling

democratic limit exact solutionfirst time! [JHEP 1210 (2012) 162]

→ staircase scaling Rn+1n

:=P (n+ 1)

P (n)= 1��g(t)

[JHEP 1304 (2013) 089]

compute staircase scaling breaking terms

excpected to be negative

generalized algorithm:➝ independent evolution in energy and distance

hadron collider effects

n1 2 3 4 5 6 7

nB

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1Higgs kinematics

all jets recoil←

T balanced in p←

gluon initial state 100 GeV≥ lead

Tp

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

pdf effects on jet ratios

Bn

=

������

f(x(n+1),Q)

f(x(n),Q)

f(x(n+2),Q)

f(x(n+1),Q)

������

2

at leading log pdfs and jet evolution factorize

assume threshold kinematics

x

(0) ⇡ mZ

2Ebeamx

(1) ⇡

rm

2Z + 2

⇣pT

pp

2T +m

2Z + p

2T

⌘

2Ebeam

suppression of low n

[JHEP 1210 (2012) 162]

sweet spot

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

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

=-0.0004dndR=0.1490R

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

1R

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

photon plus jets

high cross-section: signal free

tune between patterns

→ understand experimentally

translate to Z plus jets

same hard process (QCD p.o.v.)

but: important background

great laboratory!

learn, test, ...

[JHEP 1202 (2012) 030]

learn, test, ...

[arXiv:1304.7098][arXiv:1304.7098]

actual LHC study

Note:➝ staircase has tilt➝ Poisson flattens out➝ exactly as predicted➝ NLO stops at 4 jets

Z plus jets

Higgs vetos

WBF cutsask for two hard tagging jets

signal stays staircase like

... and use! .

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

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

before cuts

both staircase

background becomes Poisson

[Phys.Rev.Lett. 108 (2012) 032003]

LHC gap studies(extending an existing study)

nn+1

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

nn+1

R

0

0.1

0.2

0.3

0.4

0.5

y < 2Δ1 < = 20 GeV

Vp

< 150 GeVT

p 120 GeV < ←

< 120 GeVT

p 90 GeV < ←

< 90 GeVT

p 70 GeV < ←

nn+1

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

nn+1

R

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

y < 3Δ2 < = 20 GeV

Vp

< 150 GeVT

p 120 GeV < ←

< 120 GeVT

p 90 GeV < ←

< 90 GeVT

p 70 GeV < ←

define two hard tagging jets

measure gap fraction P (0) =�0

�tot

jet veto pV

in addition: measure jet sprectrum➝ expect Poisson

... and use! .

[JHEP 1210 (2012) 162]

BSM searcheswith autofocus

use notorious observables:

me↵ = /pT +X

all jets

pT,jet

[GeV]effm200 400 600 800 1000 1200 1400

[1/1

00 G

eV]

eff

dmdN

-210

-1101

10

210

310

410

510 signalleptonictthadronictt

W+jetsZ+jetsQCD

[GeV]effm200 400 600 800 1000 1200 1400

[1/1

00 G

eV]

eff

dmdN

-210

-1101

10

210

310

410

510

[GeV]effm200 400 600 800 1000 1200 1400

BS+B

0.51

1.52

2.53

= 2jn-1L = 1 fb

[GeV]effm200 400 600 800 1000 1200 1400

BS+B

0.51

1.52

2.53

jetsn2 3 4 5 6 7

jets

dndN

10

210

310

410

510

610 signalleptonictthadronictt

Z+jetsW+jetsQCD

jetsn2 3 4 5 6 7

jets

dndN

10

210

310

410

510

610

jetsn2 3 4 5 6 7

BS+B

0.5

1

1.5

2

2.5-1L = 1 fb

jetsn2 3 4 5 6 7

BS+B

0.5

1

1.5

2

2.5

e.g.

... and use! .

depends on exclusive number of jets

jetsn2 3 4 5 6

jets

dndN

410

510

610

710

810

910

1010

2≥ jn

> 50 GeVT, j

p-1L = 1 fb

QCD

µQCD, 1/4

µQCD, 4

2≥ jn

> 50 GeVT, j

p-1L = 1 fb

QCD

µQCD, 1/4

µQCD, 4

2≥ jn

> 50 GeVT, j

p-1L = 1 fb

QCD

µQCD, 1/4

µQCD, 4

2≥ jn

> 50 GeVT, j

p-1L = 1 fb

QCD

µQCD, 1/4

µQCD, 4

jetsn2 3 4 5 6

jets

dndN

410

510

610

710

810

910

1010

jetsn2 3 4 5 6

var

iatio

ns

α 0.8

1

1.2 theoretical uncertainty

statistical uncertainty

jetsn2 3 4 5 6

var

iatio

ns

α 0.8

1

1.2

jetsn2 3 4 5 6

var

iatio

nµ 1

10

210

jetsn2 3 4 5 6

var

iatio

nµ 1

10

210

[GeV]effm200 400 600 800

[1/1

00 G

eV]

eff

dmdN

410

510

610

710

810

910

2≥ jn

> 50 GeVT, j

p-1L = 1 fb

QCD

µQCD, 1/4

µQCD, 4

2≥ jn

> 50 GeVT, j

p-1L = 1 fb

QCD

µQCD, 1/4

µQCD, 4

2≥ jn

> 50 GeVT, j

p-1L = 1 fb

QCD

µQCD, 1/4

µQCD, 4

2≥ jn

> 50 GeVT, j

p-1L = 1 fb

QCD

µQCD, 1/4

µQCD, 4

[GeV]effm200 400 600 800

[1/1

00 G

eV]

eff

dmdN

410

510

610

710

810

910

[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

←understand jetsdiscriminate decay chains ➝

complementary

[Phys.Rev. D83 (2011) 095009]

2 3 4 5 6nj0.2

0.4

0.6

0.8

1.

1.2

1.4

1.6meffHTeVL SPS1a, 1 inverse fb

0s

6s

2 3 4 5 6nj0.2

0.4

0.6

0.8

1.

1.2

1.4

1.6meffHTeVLSPS1a, gluino+gluino, 1 inv. fb

0s

0.6s

2 3 4 5 6nj0.2

0.4

0.6

0.8

1.

1.2

1.4

1.6meffHTeVLSPS1a, spartons+100 GeV, 5 inv fb

0s

5.8s

2 3 4 5 6nj0.2

0.4

0.6

0.8

1.

1.2

1.4

1.6meffHTeVL SPS4, 5 inv. fb

0s

4s

number of jets → color structureeffective mass → particles mass scale

... and use! .

BSM searcheswith autofocus

[Phys.Rev. D83 (2011) 095009]

log-likelihood maps → autofocus

← decay chains

SUSY benchmark points

conclusions

thanks for listening

➝ staircase scaling is a firm QCD prediction @ LHC: low multiplicities due to PDF effects

➝ compute staircase scaling breaking terms [new]

➝ staircase and Poisson scaling are an observed fact ➝ precession test of QCD at high multiplicity [not possible with NLO]

➝ tons of pheno applications: Higgs studies, photon laboratory, BSM searches, jet substructure(?)