Kinematic Variables for Dark Matter at the LHC and Beyond

HARVARD
UNIVERSITY
Christopher Rogan
Kinematic variables for
Dark Matter at the LHC and Beyond
University of Chicago HEP Seminar – March 9, 2014

Christopher Rogan - University of Chicago HEP - March 9, 2015
▪ Weakly interacting particles at the LHC
▪ Why? How?
▪ Kinematic handles for studying them
▪ MET
▪ singularity variables
▪ Recursive Jigsaw Reconstruction
▪ ex. di-leptons (i.e. super-razor variables)
▪ ex. di-leptonic tops/stops (something sexier)
2
Talk Outline

▪ Why are they interesting?
▪ Dark Matter
▪ It exists - but what is it? Would like to know if
we’re producing these particles at the LHC
▪ Electroweak bosons
▪ Decays of W and Z often produce neutrinos
▪ New symmetries
▪ Discrete symmetries (ex. R-parity) make
lightest new ‘charged’ particles stable
3
Weakly interacting particles @ LHC

▪ How do we study them?
▪ Can infer their presence through missing transverse energy
▪ Hermetic design of LHC experiments allows us to infer
‘what’s missing’
4
Weakly interacting particles @ LHC
ATLAS Calorimeters
~Emiss
T =
cellsX
i
~ET
▪ full azimuthal coverage, up to
|Ƞ| of ~5
▪ stopping power of ~12-20
interaction lengths
▪ ECAL+HCAL components
with segmentation comparable
to lateral shower sizes

Christopher Rogan - University of Chicago HEP - March 9, 2015 5
CERN-LHCC-2006-021
Missing transverse energy [GeV]
Minimum bias data
∫ L dt = 11.7 nb-1
Missing transverse energy [GeV]
Figures from SUSY10 conference talk:
Missing transverse energy is a powerful observable for inferring the
presence of weakly interacting particles
But, it only tells us about their transverse momenta – often we can better
resolve quantities of interest by using additional information
Missing transverse energy

?
Missing transverse energy only tells us about the momentum of weakly
interacting particles in an event…

…not about the identity or mass of weakly interacting particles

We can learn more by using other information in an event to
contextualize the missing transverse energy

Resolving the invisible
electron
mT (`⌫) has kinematic edge at mW ⇠ 80 GeV
mT =
q
2pe
T p⌫
T (1 cos )
Missing transverse
momentum (MET)
Can use visible particles in events to contextualize missing transverse
energy and better resolve mass scales
W(e⌫)

We can learn more by using other information in an event to
contextualize the missing transverse energy ⇒
multiple weakly interacting particles?

Open vs. closed final states
CLOSED
OPEN
Can calculate all masses,
momenta, angles
Can use masses for discovery, can use information
to measure spin, CP, etc.
Under-constrained system with multiple weakly interacting
particles – can’t calculate all the kinematic information
What useful information can we calculate?
What can we measure?
12

Multiple weakly interacting particles?
S S
p
p
CM
visible
visible
invisible
invisible
Canonical open / topology
Can be single or
multiple decays
steps
Can be one or more
particles
Can be one or more
particles
Theory
SUSY
Little Higgs
UED
R-parity
T-parity
KK-parity
▪ Dark Matter
▪ Higgs quadratic
divergences
▪ ….
13

Example: slepton pair-production
p
p
CM
14
Experimental signature: di-leptons final states with
missing transverse momentum

p
p
CM
15
Main background:

p
p
CM
16
What quantities, if we could calculate them, could help us
distinguish between signal and background events?

p
p
CM
17
What information are we missing?
We don’t observe the weakly interacting particles in the
event. We can’t measure their momentum or masses.

p
p
CM
18
What do we know?
We can reconstruct the 4-vectors of the two leptons and the
transverse momentum in the event

p
p
CM
19
Can we calculate anything useful?
With a number of simplifying assumptions…
…we are still 4 d.o.f. short of reconstructing any masses of interest
~Emiss
T =
X
~p ˜0
T
m˜0 = 0

▪ State-of-the-art for LHC Run I was to use
singularity variables as observables in searches
▪ Derive observables that bound a mass or
mass-splitting of interest by
▪ Assuming knowledge of event decay topology
▪ Extremizing over under-constrained kinematic
degrees of freedom associated with weakly
interacting particles
20
Singularity Variables

Singularity Variable Example: MT2
with:
From:
Generalization of transverse mass to two
weakly interacting particle events
21

with:
LSP ‘test mass’
From:
22

with:
LSP ‘test mass’
From:
Extremization of unknown
degrees of freedom
Subject to constraints
23

with:
LSP ‘test mass’
Constructed to have a kinematic endpoint
(with the right test mass) at:
From:
Extremization of unknown
degrees of freedom
Subject to constraints
24
Mmax
T 2 (m ) = m˜` Mmax
T 2 (0) = M ⌘
m2
˜`
m2
˜
m˜`

MT2 in practice
ATLAS-CONF-2013-049
Backgrounds with leptonic W
decays fall steeply once MT2
exceeds the W mass
Searches based on singularity
variables have sensitivity to
new physics signatures with
mass splittings larger than the
analogous SM ones
From:
25

Recursive Jigsaw Reconstruction
▪ The strategy is to transform observable momenta iteratively
reference-frame to reference-frame, traveling through each
of the reference frames relevant to the topology
▪ At each step, extremize only the relevant d.o.f. related to
that transformation
▪ Repeat procedure recursively, using only the momenta
encountered in each reference frame
▪ Rather than obtaining one observable, get a
complete basis of useful observables for each event
New approach to reconstructing final states with weakly
interacting particles: Recursive Jigsaw Reconstruction
26

Recursive rest-frame reconstruction
M. Buckley, J. Lykken, CR, M. Spiropulu, PRD 89, 055020 (2014)
For two lepton case, these are the ‘super-razor variables’:
Begin with reconstructed lepton 4-vectors in lab frame
27

Remove dependence on unknown
longitudinal boost by moving from
‘lab’ to ‘lab z’ frames
28
Lab
frame
~lab! lab z
Lab z
frame

Determine boost from ‘lab z’ to ‘CM ( )’
frame by specifying Lorentz-invariant choice
for invisible system mass
29
Lab z
frame
di-slepton
CM frame

Determine asymmetric boost from
CM to slepton rest frames by minimizing
lepton energies in those frames
30
di-slepton
CM frame
slepton frame
slepton frame

Remove dependence on unknown
longitudinal boost by moving from
‘lab’ to ‘lab z’ frames
Determine boost from ‘lab z’ to ‘CM ( )’
frame by specifying Lorentz-invariant choice
for invisible system mass
Determine asymmetric boost from
CM to slepton rest frames by minimizing
lepton energies in those frames
31

Lab
frame
di-slepton
CM frame
1st transformation: extract variable
sensitive to invariant mass of total
event:
Resulting variable is ~invariant
under pT of di-slepton system
32
∆Mdecay
γ/ 2Rs
0 0.5 1 1.5 2 2.5
a.u.
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
= 0 GeV0
1
χ∼m
= 70 GeV0
1
χ∼m
= 100 GeV0
1
χ∼m
= 120 GeV0
1
χ∼m
)νl)W(νlW(
=8 TeVs
MadGraph+PGS = 150 GeV
l
~; m
0
1
χ∼l→l
~
;l
~
l
~
→pp
s/Rs
0 0.5 1 1.5 2 2.5
[GeV]CM
T
p
0
100
200
300
400
500
600
a.u.
-5
10
-4
10
-3
10
-2
10
=8 TeVs
MadGraph+PGS 0
1
χ∼l→l
~
;l
~
l
~
→pp
= 0 GeV
1
0
χ∼m
= 150 GeVl
~m

Resonant Higgs production
CMS Collaboration, Measurement of Higgs boson production and properties in
the WW decay channel with leptonic final states, arXiv:1312.1129v1 [hep-ex]
From:
Using information from the two leptons,
and the missing transverse momentum, the
observable is directly sensitive to the
Higgs mass

di-slepton
CM frame
slepton frame
slepton frame
2nd transformation(s): extract
variable sensitive to invariant mass
of squark:
Resulting variable has kinematic
endpoint at:
34
[GeV]R
∆M
0 50 100 150 200 250
[GeV]CM
T
p
0
50
100
150
200
250
300
350
400
450
a.u.
-5
10
-4
10
-3
10
=8 TeVs
MadGraph+PGS
ν±
l→±
; W-
W+
W→pp

Variable comparison
35
More details about variable
comparisons in PRD 89, 055020
(arXiv:1310.4827) and backup slides
∆/ MT2M
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
a.u.
-5
10
-4
10
-3
10
-2
10
-1
10 = 0 GeV0
1
χ∼m
= 70 GeV0
1
χ∼m
= 100 GeV0
1
χ∼m
= 120 GeV0
1
χ∼m
=8 TeVs
l
~; m
0
1
χ∼l→l
~
;l
~
l
~
→pp
∆/ MCTM
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
a.u.
-5
10
-4
10
-3
10
-2
10
-1
10
1
= 0 GeV0
1
χ∼m
= 70 GeV0
1
χ∼m
= 100 GeV0
1
χ∼m
= 120 GeV0
1
χ∼m
=8 TeVs
l
~; m
0
1
χ∼l→l
~
;l
~
l
~
→pp
∆/ MR
∆M
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
a.u.
0
0.01
0.02
0.03
0.04
0.05
0.06
= 0 GeV0
1
χ∼m
= 70 GeV0
1
χ∼m
= 100 GeV0
1
χ∼m
= 120 GeV0
1
χ∼m
)νl)W(νlW(
=8 TeVs
l
~; m
0
1
χ∼l→l
~
;l
~
l
~
→pp
Three different singularity variables, all
attempting to measure the same thing

But what else can we calculate?
With recursive scheme can
extract the two mass scales
and almost
completely independently
36
∆Mtrue
γ/ 2Rs
0 0.5 1 1.5 2 2.5
∆/MR
∆M
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
a.u.
-5
10
-4
10
-3
10
=8 TeVs
MadGraph+PGS 0
1
χ∼l→l
~
;l
~
l
~
→pp
= 50 GeV
1
0
χ∼m
= 150 GeVl
~m
MR

Angles, angles, angles…
Recursive scheme fully specifies approximate event
decay chain, also yielding angular observables
Two transformations mean at least two independent
angles of interest (essentially the decay angle of the
state whose rest-frame you are in)
Lab
frame
di-slepton
CM frame
di-slepton
CM frame
slepton frame
slepton frame
37

Towards a kinematic basis
but
while
Underestimating the real mass means
over-estimating the boost magnitude:
From PRD 89, 055020 (2014)
38
s/Rs
0 0.5 1 1.5 2 2.5
∆/MR
∆M
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
a.u.
-5
10
-4
10
-3
10
=8 TeVs
MadGraph+PGS 0
1
χ∼l→l
~
;l
~
l
~
→pp
= 0 GeV
1
0
χ∼m
= 150 GeVl
~m
s/Rs
0 0.5 1 1.5 2 2.5∆/MR
∆M 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
a.u.
-5
10
-4
10
-3
10
=8 TeVs
MadGraph+PGS 0
1
χ∼l→l
~
;l
~
l
~
→pp
= 50 GeV
1
0
χ∼m
= 150 GeVl
~m
s/Rs
0 0.5 1 1.5 2 2.5
∆/MR
∆M
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
-4
10
-3
10
-2
10
=8 TeVs
MadGraph+PGS 0
1
χ∼l→l
~
;l
~
l
~
→pp
= 100 GeV
1
0
χ∼m
= 150 GeVl
~m

Towards a kinematic basis
but
while
Underestimating the real mass means
over-estimating the boost magnitude:
39
T
CM
β/R
β
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
a.u.
0
0.02
0.04
0.06
0.08
0.1
= 0 GeV0
1
χ∼m
= 70 GeV0
1
χ∼m
= 100 GeV0
1
χ∼m
= 120 GeV0
1
χ∼m
)νl)W(νlW(
=8 TeVs
l
~; m
0
1
χ∼l→l
~
;l
~
l
~
→pp
From PRD 89, 055020 (2014)
s/Rs
0 0.5 1 1.5 2 2.5
∆/MR
∆M
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
a.u.
-5
10
-4
10
-3
10
=8 TeVs
MadGraph+PGS 0
1
χ∼l→l
~
;l
~
l
~
→pp
= 0 GeV
1
0
χ∼m
= 150 GeVl
~m
s/Rs
0 0.5 1 1.5 2 2.5∆/MR
∆M 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
a.u.
-5
10
-4
10
-3
10
=8 TeVs
MadGraph+PGS 0
1
χ∼l→l
~
;l
~
l
~
→pp
= 50 GeV
1
0
χ∼m
= 150 GeVl
~m
s/Rs
0 0.5 1 1.5 2 2.5
∆/MR
∆M
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
-4
10
-3
10
-2
10
=8 TeVs
MadGraph+PGS 0
1
χ∼l→l
~
;l
~
l
~
→pp
= 100 GeV
1
0
χ∼m
= 150 GeVl
~m

Angular Variables
Angle between
lab ➔ CM frame boost and
di-leptons in CM frame is
sensitive to
rather than
Incorrect boost magnitude
induces correlation
40
β
R
φ∆
0 0.5 1 1.5 2 2.5 3
a.u.
0.02
0.04
0.06
0.08
0.1 = 0 GeV0
1
χ∼m
= 70 GeV0
1
χ∼m
= 100 GeV0
1
χ∼m
= 120 GeV0
1
χ∼m
)νl)W(νlW(
)+jetsllZ(
=8 TeVs
l
~; m
0
1
χ∼l→l
~
;l
~
l
~
→pp
~Uncorrelated with other super-
razor variables

Angular Variables
In the approximate di-slepton rest frame,
reconstructed decay angle sensitive to particle
spin and production
41
|
R
θ| cos
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
a.u.
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
= 0 GeV0
1
χ
∼m
= 70 GeV0
1
χ
∼m
= 100 GeV0
1
χ
∼m
= 120 GeV0
1
χ
∼m
)νl)W(νlW(
=8 TeVs
MadGraph+PGS
= 150 GeV
l
~; m
0
1
χ
∼
l→l
~
;l
~
l
~
→pp

Angular Variables
In the approximate slepton rest frames,
reconstructed slepton decay angle sensitive to
particle spin correlations
42
|R+1θ| cos
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
[GeV]R
∆M
0
20
40
60
80
100
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
=8 TeVs
MadGraph+PGS ν±
l→±
; W
-
W+
W→pp
|R+1θ| cos
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
[GeV]R
∆M
0
20
40
60
80
100
120
140
160
180
0.0005
0.001
0.0015
0.002
0.0025
=8 TeVs
MadGraph+PGS 0
1
χ∼l→l
~
;l
~
l
~
→pp
= 50 GeV
1
0
χ∼m
= 150 GeVl
~m

Angular Variables
Also allows us to better resolve the kinematic
endpoint of interest
43
|R+1θ| cos
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
[GeV]R
∆M
0
20
40
60
80
100
120
140
160
180
0.0005
0.001
0.0015
0.002
0.0025
=8 TeVs
MadGraph+PGS 0
1
χ∼l→l
~
;l
~
l
~
→pp
= 50 GeV
1
0
χ∼m
= 150 GeVl
~m

Super-razor variable basis
Sensitive to mass of CM
Good for resonant production
of heavy parents
Mass-squared difference
resonant/non-resonant prod.
Sensitive to ratio of invisible
and visible masses
Spin correlations, better
resolution of mass edge
44
| cos ✓R| Spin and production
[GeV]0
χ∼m
0 50 100 150 200 250 300
σN
0
1
2
3
4
5
+ CMS selectionCTM
+ CMS selection∆
R
M
Rθcos×
β
R
φ∆×∆
R
M
0
χ∼l
0
χ∼l→Ll
~
Ll
~
= 350 GeV
L
l
~m
-1
= 20 fbL dt∫= 8 TeVs MadGraph+PGS
95% C.L. Can improve sensitivity while
removing MET cuts!
Can re-imagine a di-lepton analysis
in new basis of variables

Generalizing further
Recursive Jigsaw approach can be generalized to arbitrarily
complex final states with weakly interacting particles

Example: the di-leptonic top basis
46
In more complicated decay topologies there can be
many masses/mass-splittings, spin-sensitive angles and
other observables of interest that can be used to
distinguish between the SM and SUSY signals

Singularity Variables for Tops

If there are multiple masses or mass splittings of interest in the
event, appearing at different points in the decay chains, then
singularity variables correspond to different extremizations of
missing d.o.f.
What are the correlations between the
different singularity variables estimating
different mass splittings? Can be large/
complicated when using MCT or MT2 in
this case
What if the two tops/stops are decaying differently
through different particles?
48
Singularity Variables for Tops
Polesello and Tovey,
JHEP, 1003:030, 2010

Recursive Jigsaw reconstruction
Move through each reference frame of interest in the event,
specifying only d.o.f. relevant to each transformation:
lab frame di-top frame di-top frame
top frame
top frame
top frame W frame
b`b` b`b`
b`b`
b`
b`
` `
2b2l system treated as one visible object
Each bl system treated
as visible object
individual leptons resolved independently
2 X

The scales can be extracted independently
Mtop [GeV]
MW /Mtop

In fact the scales can be extracted independently for each top –
the reconstruction chains are decoupled
Mtop [GeV]
Mtop [GeV]

b-tagged jet
The di-leptonic top basis
b-tagged jet
lepton lepton
MET
2 X
a b
T 1,T 2
T,W
Mt¯t, ~pt¯t, cos ✓T T
Etop frame
b , cos ✓T
EW frame
` , cos ✓W

largely independent
information about
five different masses
true
b
/ E
top-frame
b1
E
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
true
b
/E
top-frame
b2
E
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
a.u.
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
=8 TeVs
MadGraph GEN
νlb→; ttt→pp
true
b
/ E
top-frame
b
E
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
true
l
/E
W-frame
l
E
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
a.u.
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
=8 TeVs
MadGraph GEN
νlb→; ttt→pp
true
l
/ E
W-frame
1l
E
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
true
l
/E
W-frame
2l
E
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
a.u.
0
0.0005
0.001
0.0015
0.002
0.0025
=8 TeVs
MadGraph GEN
νlb→; ttt→pp
true
tt
/ M
tt
M
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
true
b
/E
top-frame
b
E
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
a.u.
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
=8 TeVs
MadGraph GEN
νlb→; ttt→pp
true
tt
/ M
tt
M
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
true
l
/E
W-frame
l
E
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
=8 TeVs
MadGraph GEN
νlb→; ttt→pp

Previous state-of-the-art
Mass-sensitive
singularity variables
are not necessarily
independent
) [GeV]
2
,b
1
(b
T2
M
0 20 40 60 80 100 120 140 160
)[GeV]
2
l,
1
l(
T2
M
0
20
40
60
80
100
a.u.
-4
10
-3
10
-2
10
=8 TeVs
MadGraph GEN
νlb→; ttt→pp
) [GeV]
2
l
2
,b
1
l
1
(b
T2
M
0 20 40 60 80 100 120 140 160 180
)[GeV]
2
,b
1
(b
T2
M
0
20
40
60
80
100
120
140
160
a.u.
-4
10
-3
10
-2
10
=8 TeVs
MadGraph GEN
νlb→; ttt→pp
) [GeV]
2
l
2
,b
1
l
1
(b
T2
M
0 20 40 60 80 100 120 140 160
)[GeV]
2
l,
1
l(
T2
M
0
10
20
30
40
50
60
70
80
90 a.u.
-4
10
-3
10
-2
10
=8 TeVs
MadGraph GEN
νlb→; ttt→pp

largely independent information about decay angles
true
TT
θ-
TT
θ
-1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1
TT
θcos
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
a.u.0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
=8 TeVs
MadGraph GEN
νlb→; ttt→pp
true
tt
/ M
tt
M
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
TT
θcos
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
a.u.
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0.0018
0.002
0.0022
=8 TeVs
MadGraph GEN
νlb→; ttt→pp
Here, the decay angle of the top/anti-top system

Here, the decay angle of one of the top quarks
true
b
/ E
top-frame
b
E
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6T
θcos -1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
a.u.
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0.0018
0.002
=8 TeVs
MadGraph GEN
νlb→; ttt→pp
true
T
θ-
T
θ
-1 -0.5 0 0.5 1
T
θcos
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
a.u.
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0.0018
=8 TeVs
MadGraph GEN
νlb→; ttt→pp
largely independent information about decay angles

The di-leptonic top basis vs. signals
Different variables in the basis are useful for different signals
First, we consider resonant ttbar production through a graviton
v.s.
t¯t G
t(b`⌫) t(b`⌫) t(b`⌫) t(b`⌫)

The di-leptonic top basis vs. gravitons
Distributions of top/W/neutrino mass-splitting-sensitive
observables are nearly identical since graviton signal and
non-resonant background both contain on-shell tops
[GeV]
top-frame
b
E
0 20 40 60 80 100
a.u.
0
0.2
0.4
0.6
0.8
1 )νl)(bνl(b→tt
= 1 TeV
G
m
= 2 TeV
G
m
= 3 TeV
G
m
=8 TeVs
MadGraph GEN
νlb→; ttt→G→pp
[GeV]
W-frame
l
E
0 20 40 60 80 100
a.u.
0
0.2
0.4
0.6
0.8
1
)νl)(bνl(b→tt
= 1 TeV
G
m
= 2 TeV
G
m
= 3 TeV
G
m
=8 TeVs
MadGraph GEN

The di-leptonic top basis vs. gravitons
Instead, observables related to the production of the
two tops are sensitive to the intermediate resonance
[GeV]
tt
M
0 1000 2000 3000 4000 5000
a.u.
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
)νl)(bνl(b→tt
= 1 TeV
G
m
= 2 TeV
G
m
= 3 TeV
G
m
=8 TeVs
MadGraph GEN
TT
θcos
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
a.u.
0.2
0.4
0.6
0.8
1
)νl)(bνl(b→tt
= 1 TeV
G
m
= 2 TeV
G
m
= 3 TeV
G
m
=8 TeVs
MadGraph GEN

The di-leptonic top basis vs. stops
SUSY stops decaying
through charginos
v.s.
t¯t ˜t˜t
t t ˜t ˜t
b b b b
W W ˜±
˜±
⌫ ⌫
˜0
˜0` ` W(`⌫) W(`⌫)

Mass-splitting-sensitive observables can be used
to distinguish presence of signals
[GeV]
top-frame
b
E
0 50 100 150 200 250 300
a.u.
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
)νl)(bνl(b→tt
= 340 GeV
1
±
χ
∼m
= 500 GeV
1
±
χ
∼m
= 650 GeV
1
±
χ
∼m
=8 TeVs
MadGraph GEN
1
0
χ
∼
)νlW(→
1
±
χ
∼
;
1
±
χ
∼
b→t
~
;t
~
t
~
→pp
= 300 GeV
1
0
χ
∼m
= 700 GeV
t
~m
[GeV]
W-frame
l
E
0 20 40 60 80 100 120 140 160 180 200 220
a.u.
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
)νl)(bνl(b→tt
= 340 GeV
1
±
χ
∼m
= 500 GeV
1
±
χ
∼m
= 650 GeV
1
±
χ
∼m
=8 TeVs
MadGraph GEN
1
0
χ
∼
)νlW(→
1
±
χ
∼
;
1
±
χ
∼
b→t
~
;t
~
t
~
→pp
= 300 GeV
1
0
χ
∼m
= 700 GeV
t
~m

m˜t = 700 GeV
m˜0 = 300 GeV
650
500
340
Here, the azimuthal
angle between the
the top and W decay
planes
and the angle
between the two top
decay planes
T 1,W 1
T 1,T 2T1,T2
φ∆
0 1 2 3 4 5 6
T1,W1
φ∆
0
1
2
3
4
5
6
a.u.
0.005
0.01
0.015
0.02
0.025
=8 TeVs
MadGraph GEN
(300)
1
0
χ
∼
)νlW(→
1
±
χ
∼
(340);
1
±
χ
∼
b→t
~
(700);t
~
t
~
→pp
T1,T2
φ∆
0 1 2 3 4 5 6
T1,W1
φ∆
0
1
2
3
4
5
6
a.u.
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
=8 TeVs
MadGraph GEN
(300)
1
0
χ
∼
)νlW(→
1
±
χ
∼
(500);
1
±
χ
∼
b→t
~
(700);t
~
t
~
→pp
T1,T2
φ∆
0 1 2 3 4 5 6
T1,W1
φ∆
0
1
2
3
4
5
6
a.u.
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0.0018
=8 TeVs
MadGraph GEN
(300)
1
0
χ
∼
)νlW(→
1
±
χ
∼
(650);
1
±
χ
∼
b→t
~
(700);t
~
t
~
→pp
T1,T2
φ∆
0 1 2 3 4 5 6
T1,W1
φ∆
0
1
2
3
4
5
6
a.u.
0.0005
0.001
0.0015
0.002
0.0025
=8 TeVs
MadGraph GEN
νlb→; ttt→pp
m˜± = GeV

Summary
▪ The strategy of Recursive Jigsaw Reconstruction is to not only
develop ‘good’ mass estimator variables, but to decompose each
event into a basis of kinematic variables
▪ Through the recursive procedure, each variable is (as much as
possible) independent of the others
▪ The interpretation of variables is straightforward; they each
correspond to an actual, well-defined, quantity in the event
▪ Can be generalized to arbitrarily complex final states with many
weakly interacting particles
▪ Code package to be released imminently (RestFrames - see back-up)
▪ First papers nearing completion
(Recursive Jigsaw Reconstruction,
The Di-leptonic ttbar basis - with Paul Jackson)
63

▪ Recursive Jigsaw Reconstruction is a systematic recipe for deriving a
kinematic basis for any open final state
▪ Mixed decay cases can now be treated in a sensible way
▪ Lots of potential applications – some I’m currently thinking about:
• Di-lepton searches and differential measurements
• stop / top-quark partner and resonant ttbar searches
• other signatures (SUSY, exotica)
• spin measurements
• …
64
vs.
vs.
vs.
Outlook

BACKUP SLIDES
65

RestFrames software library
RestFrames: Soon-to-be-public code that can be used to
calculate kinematic variables associated with any decay
chain and can implement “Recursive Jigsaw” rules
Example: Di-leptonic ttbar decays - how to use the code to
initialize a decay tree, implement a jigsaw rule for
determining the neutrino four-momenta, and analyze events
www.RestFrames.com

initialize all your reference
frames of interest
connect them according to
the decay tree you want to
impose on the event

…and you’ll see this
draw your decay tree…
lab
tt
a
t
a
b
a
W
a
l
a
ν
b
t
b
b
b
W
b
l
b
ν
Lab State
Decay States
Visible States
Invisible States

Christopher Rogan - RestFrames - Jan 29, 2015 69
RestFrames example: di-leptonic top
Set the 4-vector input and
MET for an event
Get observables directly from decay tree

tt
a
t
a
b
a
W
a
l
a
ν
b
t
b
b
b
W
b
l
b
ν
Decay States
Visible States
Invisible States
a
t
a
b
a
W
a
l
a
ν
Decay States
Visible States
Invisible States

number of elements
that _have_ to go to
this frame from the
group each event exclusive (true) or
inclusive (false) counting

tt
a
t
a
b
a
W
a
l
a
ν
b
t
b
b
b
W
b
l
b
ν
tt
a
t
a
b
a
W
a
l
a
ν
b
t
b
b
b
W
b
l
b
ν
Decay States
Visible States
Invisible States
Invisible Jigsaw

event-by-event will choose
b-tag jet combinatoric
assignment that minimizes
the masses of these two
collections

tt
a
t
a
b
a
W
a
l
a
ν
b
t
b
b
b
W
b
l
b
ν
tt
a
t
a
b
a
W
a
l
a
ν
b
t
b
b
b
W
b
l
b
ν
Decay States
Visible States
Invisible States
Invisible Jigsaw
Combinatoric Jigsaw

Invisible system mass Jigsaw
Invisible system rapidity Jigsaw
Contraboost invariant JigsawContraboost invariant Jigsaw
b
ν+
a
ν
b
ν+
a
ν
b
ν+
a
ν
a
ν
b
ν
Invisible Frame Jigsaws

's Jigsaw
lb
Minimize m 's Jigsaw
lb
Minimize m
b
+ b
a
b
a
b
b
b
B-tagged jet Jigsaws

some toy input
analyze the event

tracking of combinatoric elements

Christopher Rogan - RestFrames - Jan 29, 2015
▪ To make shared library ‘lib/libRestFrames.so’
▪ To set environmental variables
(ex. for running ROOT macros):
82
RestFrames setup
<$ make
<$ source setup.sh

Christopher Rogan - RestFrames - Jan 29, 2015
▪ To run ‘macros/TestDiLeptonicTop.C’ macro:
83
<$ root
root [0] .x macros/TestDiLeptonicTop.C

Singularity variables
From:
84

Singularity variables
From:
85

Example: MCT
Constructed to have a
kinematic endpoint at:
From:
assuming ~mass-less leptons
86

MCT in practice
Singularity variables (like MCT) can be sensitive to quantities that
can vary dramatically event-by-event
Kinematic endpoint
‘moves’ with nonzero
CM system pT
87

The mass challenge
The invariant mass is invariant under coherent Lorentz
transformations of two particles
The Euclidean mass (or contra-variant mass) is invariant under anti-
symmetric Lorentz transformations of two particles
Even the simplest case requires variables with both properties!
Lab
frame
di-slepton
CM frame
di-slepton
CM frame
slepton frame
slepton frame
88

Correcting for CM pT
▪ Want to boost from lab-frame to CM-frame
▪ We know the transverse momentum of the CM-
frame:
▪ But we don’t know the energy, or mass, of the CM-
frame:
89

pT corrections for MCT
with:
Attempts have been made to mitigate this problem:
(i) ‘Guess’ the lab ➔ CM frame boost:
(ii) Only look at event along axis perpendicular to boost:
x – parallel to boost
y – perp. to boost
90

MCTperp in practice
CMS-SUS-PAS-13-006
‘peak position’ of signal and
backgrounds due to other cuts (pT,
MET) and only weakly sensitive
to sparticle masses
From:
91
50 100 150 200 250 300
10 2
10 1
100
101
102
103
entries/10GeV
Data
Top
WW
WZ
ZZ
Rare SM
Z/g⇤
Non-prompt
m ˜c± = 500 GeV
m ˜c± = 300 GeV
50 100 150 200 250 300
MCT? (GeV)
0.6
0.8
1.0
1.2
1.4
ratio
CMS Preliminary
p
s = 8 TeV, Lint = 19.5 fb 1

is a singularity variable – in fact it is essentially identical to MCT but
evaluated in a different reference frame. Boost procedure ensures that
new variable is invariant under the previous transformations
92
[GeV]R
∆M
0 50 100 150 200 250
[GeV]CM
T
p
0
50
100
150
200
250
300
350
400
450
a.u.
-5
10
-4
10
-3
10
=8 TeVs
MadGraph+PGS
ν±
l→±
; W-
W+
W→pp
[GeV]CTM
0 50 100 150 200 250
[GeV]CM
T
p
0
50
100
150
200
250
300
350
400
450
a.u.
-5
10
-4
10
-3
10
=8 TeVs
MadGraph+PGS
ν±
l→±
; W-
W+
W→pp

From:
The between the leptons is evaluated in the R-frame, removing dependence
on the pT of the Higgs and correlation with
CMS uses 2D fit of variables to measure Higgs mass in this channel

From:
The shape of the distribution, for the Higgs signal and backgrounds, is used
to extract both the Higgs mass and signal strength – even while information is lost
with the two escaping neutrinos

What other info can we extract?
Mass and Spin Measurement with M(T2) and MAOS Momentum - Cho, Won Sang et al.
Nucl.Phys.Proc.Suppl. 200-202 (2010) 103-112 arXiv:0909.4853 [hep-ph]
From:
Ex. MT2 extremization assigns values to
missing degrees of freedom – if one takes
these assignments literally, can we
calculate other useful variables?
When we assign unconstrained d.o.f. by extremizing one
quantity, what are the general properties of other variables we
calculate? What are the correlations among them?
95

Example: the di-leptonic top basis
96
[GeV]
top-frame
b
E
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
a.u.
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
)νl)(bνl(b→tt
= 340 GeV
1
±
χ
∼m
= 500 GeV
1
±
χ
∼m
= 650 GeV
1
±
χ
∼m
=8 TeVs
MadGraph GEN
1
0
χ
∼
)νlW(→
1
±
χ
∼
;
1
±
χ
∼
b→t
~
;t
~
t
~
→pp
= 300 GeV
1
0
χ
∼m
= 700 GeV
t
~m
[GeV]
tt
M
0 1000 2000 3000 4000 5000
a.u.
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
)νl)(bνl(b→tt
= 1 TeV
G
m
= 2 TeV
G
m
= 3 TeV
G
m
=8 TeVs
MadGraph GEN
true
tt
/ M
tt
M
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
TT
θcos
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
a.u.
0
0.0002
0.0004
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0.0018
0.002
0.0022
=8 TeVs
MadGraph GEN
νlb→; ttt→pp
A rich basis of useful Recursive Jigsaw observables can be
calculated, each with largely independent information
true
b
/ E
top-frame
b
E
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
true
l
/E
W-frame
l
E
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
a.u.
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
=8 TeVs
MadGraph GEN
νlb→; ttt→pp
true
b
/ E
top-frame
b1
E
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
true
b
/E
top-frame
b2
E
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
a.u.
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
=8 TeVs
MadGraph GEN
νlb→; ttt→pp
true
tt
/ M
tt
M
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
true
b
/E
top-frame
b
E
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
a.u.
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
=8 TeVs
MadGraph GEN
νlb→; ttt→pp
true
tt
/ M
tt
M
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
true
l
/E
W-frame
l
E
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
=8 TeVs
MadGraph GEN
νlb→; ttt→pp
true
l
/ E
W-frame
1l
E
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
true
l
/E
W-frame
2l
E
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
a.u.
0
0.0005
0.001
0.0015
0.002
0.0025
=8 TeVs
MadGraph GEN
νlb→; ttt→pp

Observables sensitive to intermediate resonances cannot
distinguish between non-resonant signals and background
T
γ
1 2 3 4 5 6 7 8
a.u.
-4
10
-3
10
-2
10
)νl)(bνl(b→tt
= 1 TeV
G
m
= 2 TeV
G
m
= 3 TeV
G
m
=8 TeVs
MadGraph GEN
T
γ
1 2 3 4 5 6
a.u.
-3
10
-2
10
-1
10
)νl)(bνl(b→tt
= 340 GeV
1
±
χ
∼m
= 500 GeV
1
±
χ
∼m
= 650 GeV
1
±
χ
∼m
=8 TeVs
MadGraph GEN
1
0
χ
∼
)νlW(→
1
±
χ
∼
;
1
±
χ
∼
b→t
~
;t
~
t
~
→pp
= 300 GeV
1
0
χ
∼m
= 700 GeV
t
~m
Mtt = 2 T Mt

vs.
Multi-dimensionalbump-hunting
98
MW/MtopMW/Mtop
Mtop [GeV]
Mtop [GeV] Mtop [GeV]
Mtop [GeV]
MW/MtopMW/Mtop

Decay angles are also sensitive to differences
between stop signals and ttbar background
[GeV]
top-frame
b
E
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
a.u.
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
)νl)(bνl(b→tt
= 340 GeV
1
±
χ
∼m
= 500 GeV
1
±
χ
∼m
= 650 GeV
1
±
χ
∼m
=8 TeVs
MadGraph GEN
1
0
χ
∼
)νlW(→
1
±
χ
∼
;
1
±
χ
∼
b→t
~
;t
~
t
~
→pp
= 300 GeV
1
0
χ
∼m
= 700 GeV
t
~m
TT
θcos
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
a.u.
0.2
0.4
0.6
0.8
1
)νl)(bνl(b→tt
= 1 TeV
G
m
= 2 TeV
G
m
= 3 TeV
G
m
=8 TeVs
MadGraph GEN

m˜t = 700 GeV
m˜0 = 300 GeV
650
500
340
Decay angles are
also sensitive to
differences
between stop
signals and ttbar
background
T1
θcos
-1 -0.5 0 0.5 1
T2
θcos
-1
-0.5
0
0.5
1
a.u.
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
=8 TeVs
MadGraph GEN
(300)
1
0
χ
∼
)νlW(→
1
±
χ
∼
(340);
1
±
χ
∼
b→t
~
(700);t
~
t
~
→pp
T1
θcos
-1 -0.5 0 0.5 1
T2
θcos
-1
-0.5
0
0.5
1
a.u.
0.0005
0.001
0.0015
0.002
0.0025
0.003
=8 TeVs
MadGraph GEN
(300)
1
0
χ
∼
)νlW(→
1
±
χ
∼
(500);
1
±
χ
∼
b→t
~
(700);t
~
t
~
→pp
T1
θcos
-1 -0.5 0 0.5 1
T2
θcos
-1
-0.5
0
0.5
1
a.u.
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0.004
=8 TeVs
MadGraph GEN
(300)
1
0
χ
∼
)νlW(→
1
±
χ
∼
(650);
1
±
χ
∼
b→t
~
(700);t
~
t
~
→pp
T1
θcos
-1 -0.5 0 0.5 1
T2
θcos
-1
-0.5
0
0.5
1
a.u.
0.0005
0.001
0.0015
0.002
0.0025
=8 TeVs
MadGraph GEN
νlb→; ttt→pp
m˜± = GeV

m˜t = 700 GeV
m˜0 = 300 GeV
650
500
340
Decay angles are
also sensitive to
differences
between stop
signals and ttbar
background
W1
θcos
-1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1
W2
θcos
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
a.u.
-4
10
-3
10
-2
10
=8 TeVs
MadGraph GEN
(300)
1
0
χ
∼
)νlW(→
1
±
χ
∼
(340);
1
±
χ
∼
b→t
~
(700);t
~
t
~
→pp
W1
θcos
-1 -0.5 0 0.5 1
W2
θcos
-1
-0.5
0
0.5
1
a.u.
-3
10
-2
10
=8 TeVs
MadGraph GEN
(300)
1
0
χ
∼
)νlW(→
1
±
χ
∼
(500);
1
±
χ
∼
b→t
~
(700);t
~
t
~
→pp
W1
θcos
-1 -0.5 0 0.5 1
W2
θcos
-1
-0.5
0
0.5
1
a.u.
-3
10
-2
10
=8 TeVs
MadGraph GEN
(300)
1
0
χ
∼
)νlW(→
1
±
χ
∼
(650);
1
±
χ
∼
b→t
~
(700);t
~
t
~
→pp
W1
θcos
-1 -0.5 0 0.5 1
W2
θcos
-1
-0.5
0
0.5
1
a.u.
-3
10
-2
10
=8 TeVs
MadGraph GEN
νlb→; ttt→pp
m˜± = GeV

m˜t = 700 GeV
m˜0 = 300 GeV
650
500
340
Here, the azimuthal
angle between the
the top and W decay
planes ,
for each of the two
decay chains
T 1,W 1
T1,W1
φ∆
0 1 2 3 4 5 6
T2,W2
φ∆
0
1
2
3
4
5
6
a.u.
0.001
0.002
0.003
0.004
0.005
0.006
0.007
=8 TeVs
MadGraph GEN
(300)
1
0
χ
∼
)νlW(→
1
±
χ
∼
(340);
1
±
χ
∼
b→t
~
(700);t
~
t
~
→pp
T1,W1
φ∆
0 1 2 3 4 5 6
T2,W2
φ∆
0
1
2
3
4
5
6
a.u.
0.0005
0.001
0.0015
0.002
0.0025
=8 TeVs
MadGraph GEN
(300)
1
0
χ
∼
)νlW(→
1
±
χ
∼
(500);
1
±
χ
∼
b→t
~
(700);t
~
t
~
→pp
T1,W1
φ∆
0 1 2 3 4 5 6
T2,W2
φ∆
0
1
2
3
4
5
6
a.u.
0.0005
0.001
0.0015
0.002
0.0025
0.003
=8 TeVs
MadGraph GEN
(300)
1
0
χ
∼
)νlW(→
1
±
χ
∼
(650);
1
±
χ
∼
b→t
~
(700);t
~
t
~
→pp
T1,W1
φ∆
0 1 2 3 4 5 6
T2,W2
φ∆
0
1
2
3
4
5
6
a.u.
0.0005
0.001
0.0015
0.002
0.0025
0.003
=8 TeVs
MadGraph GEN
νlb→; ttt→pp
m˜± = GeV

m˜t = 700 GeV
m˜0 = 300 GeV
650
500
340
Here, the azimuthal
angle between the
the top and W decay
planes
and the angle
between the two top
decay planes
T 1,W 1
T 1,T 2T1,T2
φ∆
0 1 2 3 4 5 6
T1,W1
φ∆
0
1
2
3
4
5
6
a.u.
0.005
0.01
0.015
0.02
0.025
=8 TeVs
MadGraph GEN
(300)
1
0
χ
∼
)νlW(→
1
±
χ
∼
(340);
1
±
χ
∼
b→t
~
(700);t
~
t
~
→pp
T1,T2
φ∆
0 1 2 3 4 5 6
T1,W1
φ∆
0
1
2
3
4
5
6
a.u.
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
=8 TeVs
MadGraph GEN
(300)
1
0
χ
∼
)νlW(→
1
±
χ
∼
(500);
1
±
χ
∼
b→t
~
(700);t
~
t
~
→pp
T1,T2
φ∆
0 1 2 3 4 5 6
T1,W1
φ∆
0
1
2
3
4
5
6
a.u.
0.0006
0.0008
0.001
0.0012
0.0014
0.0016
0.0018
=8 TeVs
MadGraph GEN
(300)
1
0
χ
∼
)νlW(→
1
±
χ
∼
(650);
1
±
χ
∼
b→t
~
(700);t
~
t
~
→pp
T1,T2
φ∆
0 1 2 3 4 5 6
T1,W1
φ∆
0
1
2
3
4
5
6
a.u.
0.0005
0.001
0.0015
0.002
0.0025
=8 TeVs
MadGraph GEN
νlb→; ttt→pp
m˜± = GeV

Razor kinematic variables
mega-jet
invisible?
▪ Assign every reconstructed object to one of two mega-jets
▪ Analyze the event as a ‘canonical’ open final state:
• two variables: MR (mass scale) , R (scale-less event imbalance)
▪ An inclusive approach to searching for a large class of new
physics possibilities with open final states
invisible?
mega-jet
PRD 85, 012004 (2012)
EPJC 73, 2362 (2013)
PRL 111, 081802 (2013)
CMS-PAS-SUS-13-004
arXiv:1006.2727v1 [hep-ph]Razor variables
CMS+ATLAS
analyses
104Christopher Rogan - University of Chicago HEP - March 9, 2015

Razor kinematic variables
mega-jet
invisible?
▪ Assign every reconstructed object to one of two mega-jets
▪ Analyze the event as a ‘canonical’ open final state:
• two variables: MR (mass scale) , R (scale-less event imbalance)
▪ An inclusive approach to searching for a large class of new
physics possibilities with open final states
invisible?
mega-jet
Two distinct mass scales in event
Two pieces of complementary information
105Christopher Rogan - University of Chicago HEP - March 9, 2015

▪ Baseline Selection
• Exactly two opposite sign leptons with
pT > 20 GeV/c and |η| < 2.5
• If same flavor, m(l l) > 15 GeV/c2
• ΔR between leptons and any jet (see below) > 0.4
• veto event if b-tagged jet with pT > 25 GeV/c and |η| < 2.5
▪ Kinematic Selection
ATLAS-CONF-2013-049CMS-PAS-SUS-12-022
‘CMS selection’ ‘ATLAS selection’
A Monte Carlo analysis to compare
From PRD 89, 055020 (arXiv:1310.4827 [hep-ph])
106

1D Shape Analysis
▪ Analysis Categories
• Consider final 9 different final states according to lepton flavor
and jet multiplicity – simultaneous binned fit includes both high
S/B and low S/B categories
Fit to kinematic distributions (in this case, MΔ
R, MT2 or MCTperp in 10 GeV
bins), over all categories for , and yields
Other jet
multiplicity and
lepton flavor
categories
+
107
[GeV]CTM
20 40 60 80 100 120 140 160 180 200 220
Events/10GeV
-1
10
1
10
2
10
3
10
4
10 TOTAL BKG
WW/WZ
+jetstt
*+jetsγZ/
= 100 GeV0
χ∼
= 350, m±
L
e~m
= 100 GeV0
χ∼
= 250, m±
L
e~m
-1
= 20 fbL dt∫= 8 TeVs Madgraph+PGS
= 0jetNee
CMS selection
[GeV]CTM
20 40 60 80 100 120 140 160 180 200
Events/10GeV
-1
10
1
10
2
10
3
10
4
10
TOTAL BKG
WW/WZ
+jetstt
*+jetsγZ/
= 100 GeV0
χ∼
= 350, m±
L
e~m
= 100 GeV0
χ∼
= 250, m±
L
e~m
-1
= 20 fbL dt∫= 8 TeVs Madgraph+PGS
= 1jet
Nee
CMS selection
+
From PRD 89, 055020

Systematic uncertainties
▪ 2% lepton ID (correlated btw bkgs, uncorrelated between
lepton categories)
▪ 10% jet counting (per jet) (uncorrelated between all processes)
▪ 10% x-section uncertainty for backgrounds (uncorrelated) +
theoretical x-section uncertainty for signal (small)
▪ ‘shape’ uncertainty derived by propagating effect of 10% jet
energy scale shift up/down to MET and recalculating shapes
templates of kinematic variables
▪ Uncertainties are introduced into toy pseudo-experiments
through marginalization (pdfs fixed in likelihood evaluation
but systematically varied in shape and normalization in toy
pseudo-experiment generation)
108

Compared to Reality
(GeV)
l
~m
100 150 200 250 300 350 400 450
(GeV)0
1
χ∼m
0
50
100
150
200
250
300
95%C.L.upperlimitoncrosssection(fb)
1
10
2
10
= 8 TeVs,-1
= 19.5 fb
int
CMS Preliminary L
95% C.L. CLs NLO Exclusions
theory
σ1±Observed
experiment
σ1±Expected
L
µ∼
L
µ∼,L
e~
L
e~→pp
) = 1
0
1
χ∼l→L
l
~
(Br
CMS-PAS-SUS-12-022
109

Expected Limit Comparison
110
[GeV]
Ll
~m
100 150 200 250 300 350 400 450
[GeV]0
χ∼m
0
50
100
150
200
250
300
350
400
σN
0
1
2
3
4
50
χ∼l
0
χ∼l→Ll
~
Ll
~
+ ATLAS selection∆
R
M
-1
95% C.L. excl
0
χ∼
=
m
Ll
~
m
[GeV]
Ll
~m
100 150 200 250 300 350 400 450
[GeV]0
χ∼m
0
50
100
150
200
250
300
350
400
σN0
1
2
3
4
50
χ∼l
0
χ∼l→Ll
~
Ll
~
+ ATLAS selectionT2M
-1
95% C.L. excl
0
χ∼
=
m
Ll
~
m
[GeV]
Ll
~m
100 150 200 250 300 350 400 450
[GeV]0
χ∼m
0
50
100
150
200
250
300
350
400
σN
0
1
2
3
4
50
χ∼l
0
χ∼l→Ll
~
Ll
~
+ CMS selectionCTM
-1
95% C.L. excl
0
χ∼
=
m
Ll
~
m
[GeV]
Ll
~m
100 150 200 250 300 350 400 450
[GeV]0
χ∼m
0
50
100
150
200
250
300
350
400
σN
0
1
2
3
4
50
χ∼l
0
χ∼l→Ll
~
Ll
~
+ CMS selection∆
R
M
-1
95% C.L. excl
0
χ∼
=
m
Ll
~
m
FromPRD89,055020(arXiv:1310.4827)

Charginos
111
[GeV]±
χ∼m
100 150 200 250 300 350
[GeV]0
χ∼m
0
50
100
150
200
250
300
σN
0
1
2
3
4
5
]
0
χ∼)νlW(
0
χ∼)νl[W(→
±
χ∼±
χ∼
R
M
-1
95% C.L. excl
0
χ∼
= m
±
χ∼
m
[GeV]±
χ∼m
100 150 200 250 300 350
[GeV]0
χ∼m
0
50
100
150
200
250
300
σN0
1
2
3
4
5
]
0
χ∼)νlW(
0
χ∼)νl[W(→
±
χ∼±
χ∼
+ ATLAS selectionT2M
-1
95% C.L. excl
0
χ∼
= m
±
χ∼
m
[GeV]±
χ∼m
100 150 200 250 300 350
[GeV]0
χ∼m
0
50
100
150
200
250
300
σN
0
1
2
3
4
5
]
0
χ∼)νlW(
0
χ∼)νl[W(→
±
χ∼±
χ∼
+ CMS selectionCTM
-1
95% C.L. excl
0
χ∼
= m
±
χ∼
m
[GeV]±
χ∼m
100 150 200 250 300 350
[GeV]0
χ∼m
0
50
100
150
200
250
300
σN
0
1
2
3
4
5
]
0
χ∼)νlW(
0
χ∼)νl[W(→
±
χ∼±
χ∼
+ CMS selection∆
R
M
-1
95% C.L. excl
0
χ∼
= m
±
χ∼
m
FromPRD89,055020(arXiv:1310.4827)

Super-Razor Basis Selection
112
[GeV]±
χ∼m
100 150 200 250 300 350
[GeV]0
χ∼m
0
50
100
150
200
250
300
σN
0
1
2
3
4
5
]
0
χ∼)νlW(
0
χ∼)νl[W(→
±
χ∼±
χ∼
+ Razor selection
Rθcos×
β
R
φ∆×∆
R
M
-1
95% C.L. excl
0
χ∼
= m
±
χ∼
m
[GeV]
Ll
~m
100 150 200 250 300 350 400 450
[GeV]0
χ∼m
0
50
100
150
200
250
300
350
400
σN
0
1
2
3
4
50
χ∼l
0
χ∼l→Ll
~
Ll
~
+ Razor selection
Rθcos×
β
R
φ∆×∆
R
M
-1
95% C.L. excl
0
χ∼
=
m
Ll
~
m

Comparisons
[GeV]±
χ∼m
150 200 250 300 350
σN
0
1
2
3
4
5 + ATLAS selectionT2M
R
M
Rθcos×
β
R
φ∆×∆
R
M
]
0
χ∼)νl[W(×2→
±
χ∼±
χ∼
= 100 GeV0
χ∼m
-1
95% C.L.
[GeV]±
χ∼m
150 200 250 300 350
σN
0
1
2
3
4
5 + CMS selectionCTM
+ CMS selection∆
R
M
Rθcos×
β
R
φ∆×∆
R
M
]
0
χ∼)νl[W(×2→
±
χ∼±
χ∼
= 100 GeV0
χ∼m
-1
95% C.L.
[GeV]0
χ∼m
0 50 100 150 200
σN
0
1
2
3
4
5
6
7 + CMS selectionCTM
+ CMS selection∆
R
M
Rθcos×
β
R
φ∆×∆
R
M
]
0
χ∼)νl[W(×2→
±
χ∼±
χ∼
= 250 GeV±
χ∼m
-1
95% C.L.
[GeV]0
χ∼m
0 50 100 150 200
σN
0
1
2
3
4
5
6
7 + ATLAS selectionT2M
R
M
Rθcos×
β
R
φ∆×∆
R
M
]
0
χ∼)νl[W(×2→
±
χ∼±
χ∼
= 250 GeV±
χ∼m
-1
95% C.L.
FromPRD89,055020(arXiv:1310.4827)

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