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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, ...)