Transcript Slide 1
RAzr Update
All Hadronic/GMSB SUSY Meeting 16-12-10
Christopher Rogan
California Institute of Technology
With Joseph Lykken, Maurizio Pierini and Maria Spiropulu
Razor Variables
Two variables designed to be used together for discovery
and characterization of SUSY
arXiv:1006.2727v1 [hep-ph]
Doesn’t involve MET
Uses both transverse and
longitudinal information
Invariant under long. boosts
Peaks for signal:
Dimension-less variable used for S/B discrimination
Not only suppresses backgrounds, but also shapes their
distributions in the variable
in a predictable and wellunderstood way - the Razor
Recent previous CMS Talks:
http://indico.cern.ch/contributionDisplay.py?contribId=1&confId=99188
http://indico.cern.ch/contributionDisplay.py?contribId=3&confId=105112
http://indico.cern.ch/contributionDisplay.py?contribId=3&confId=95896
Christopher Rogan - All Hadronic/GMSB SUSY Meeting 16-12-10
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Selection/Sample Details
For everything shown in this talk:
7 TeV MC (see back-up slide for list of samples)
7 TeV Data (11.1 (PromptReco+June/July ReReco) or 35 (Nov4 ReReco) pb1 shown here)
PF MET used
Require di-jets satisfying (parallel analyses):
Corrected Calo jets
Loose jet ID
Corrected PF jets
Loose jet ID
Uncorrected Track jets
Only high quality tracks
w/ vertex consistent
with reco PV considered
for clustering
NO explicit lepton/photon reco or ID in constructing these variables
If > 2 reco jets, form two hemispheres by minimizing invariant masses
added in quadrature (see back-up slides) - dphi cut between hemispheres
Christopher Rogan - All Hadronic/GMSB SUSY Meeting 16-12-10
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PF jets
The Razor in practice
LM1 MC
QCD MC
(ALPGEN)
Cut on R gives many orders of magnitude
suppression of QCD background
More importantly, cut on R dictates the
shape of the surviving background events
(QCD and others) in the variable MR (see
next slide)
Christopher Rogan - All Hadronic/GMSB SUSY Meeting 16-12-10
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The Razor and MR
DATA behaves as
expected
Backgrounds fall exponentially after exceeding relevant scale (set by process
scale+trigger/reco
requirements) - slope set by R cut
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Physics Object “Boxes”
o VBTF W muon
selection + triggers
o Muon isolation
o VBTF W electron
MU Box
inversion for QCD
muon control sample
selection + triggers
ELE Box o Electron isolation
inversion for QCD
electron control
sample
Orthogonal boxes based
on physics object ID
allows us to isolate
different physics
processes
o Veto on lepton boxes
QCD Control Box
o HLT_DiJetAve15U
Lepton boxes, along with
a QCD control sample, are
used for the background
prediction in the hadronic
signal box
HAD Box
(pre-scaled) gives QCD
control sample
HAD Signal Box
o HLT_HT{100,140,150}U
defines “signal” box
Christopher Rogan - All Hadronic/GMSB SUSY Meeting 16-12-10
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QCD Control BOX and QCD scaling
Calo Jets
Using the HLT_DiJetAve15U (pre-scaled) allows us to
measure the un-biased MR distribution for QCD events
Exponential slopes of MR scale with R2
Christopher Rogan - All Hadronic/GMSB SUSY Meeting 16-12-10
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HAD Box QCD Control Measurements
Track Jets
PF Jets
Slope Param = a + b (R cut)2
Scaling behavior
same for all jets types
“a” values related by
ratios of JES’s
Slope Parameters Measured in Data
Similar “b” values
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MU Box MC Slopes
For each box (MU, ELE, HAD)
and for each different process
(W(), W(e), ttbar(+X), etc.)
We measure the exponential
slopes as a function of R cut for
MC and DATA (when possible)
HAD Box
MU Box
HAD Box
Christopher Rogan - All Hadronic/GMSB SUSY Meeting 16-12-10
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MU Box MC Slopes
For each box (MU, ELE, HAD)
HAD Box
MU Box
and for each different process
(W(), W(e), ttbar(+X), etc.)
We measure the exponential
slopes as a function of R cut for
MC and DATA (when possible)
Slope Param = a + b (R cut)2
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Background Predictions in the Lepton
Boxes
R > 0.45
R > 0.5
MR shapes take from direct measurement or MC with MC/DATA correction
Normalize W(l) using 200 GeV < MR < 390 GeV region
Use this to normalize other non-QCD processes, using ttbar / Z / W x-sections
measured by CMS (with corresponding errors) [TOP-10-005, EWK-10-005]
With fixed non-QCD predictions fixed, we float the QCD normalization (shape fixed taken from LEP Box QCD control samples)
Christopher Rogan - All Hadronic/GMSB SUSY Meeting 16-12-10
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Background Predictions in the Lepton
Boxes
R > 0.45
LEP Box MR > 400 GeV Yields
R cut
R > 0.5
MU Box Predicted MU Box Observed ELE Box Predicted ELE Box Observed
R > 0.40
10.6 +/- 4.0
14
1.0 +/- 0.4
2
R > 0.45
5.5 +/- 2.4
5
0.31 +/- 0.16
1
R > 0.50
2.7 +/- 1.4
1
0.09 +/- 0.05
0
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Background Prediction in the Hadronic
Box
R > 0.5
R > 0.45
non-QCD processes normalized using measurements from MU and ELE Boxes
LMU BOX (R > 0.4) = 11.4 +/- 1.6 pb-1
LELE BOX(R > 0.4) = 11.1 +/- 1.4 pb-1
QCD normalization + HT turn-on parameters are floated simultaneously in a
binned likelihood fit in the range 75 GeV < MR < 350 GeV
Errors from fit propagated to bkgr. prediction (toys to check coverage and
systematic bias and background
prediction in high MR region - see back-up)
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Background Prediction in the Hadronic
Box
R > 0.45
R > 0.5
HAD Box Predicted Yield (Observed Yield)
R cut \ MR Cut
MR > 400 GeV
R > 0.45
11.2 +/- 2.4 (16)
R > 0.50
5.34 +/- 1.3 (2)
MR > 500 GeV
MR > 600 GeV
2.70 +/- 0.69 (5)
0.65 +/- 0.19 (2)
1.1 +/- 0.3 (0)
0.24 +/- 0.08 (0)
Christopher Rogan - All Hadronic/GMSB SUSY Meeting 16-12-10
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Blind R and MR Cut Optimization
Expected background
R cut \ MR Cut
MR > 400 GeV
MR > 500 GeV
MR > 600 GeV
R > 0.40
24.2 +/- 4.8
6.2 +/- 1.5
1.65 +/- 0.44
R > 0.45
11.2 +/- 2.4
2.70 +/- 0.69
0.65 +/- 0.19
R > 0.50
5.34 +/- 1.3
1.1 +/- 0.3
0.24 +/- 0.08
Expected signal (SUSY LM1 - LO x-section)
R cut \ MR Cut
MR > 400 GeV
MR > 500 GeV
MR > 600 GeV
R > 0.40
11.0
9.6
7.4
R > 0.45
8.1
7.0
5.2
R > 0.50
5.8
4.8
3.4
Expected 95%-prob limit for no signal (no sys)
R cut \ MR Cut
MR > 400 GeV
MR > 500 GeV
MR > 600 GeV
R > 0.40
13.7 +/- 5.6
6.8 +/- 2.8
3.5 +/- 1.6
R > 0.45
9.3 +/- 3.8
4.6 +/- 2.0
2.4 +/- 0.9
R > 0.50
6.3 +/- 2.7
2.8 +/- 1.3
1.9 +/- 0.6
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mSUGRA Limit
Expected Limit
Expected Limit
R > 0.45
MR > 600 GeV
R > 0.50
MR > 500 GeV
LO signal x-sections
used
Expected Limit
R > 0.50
MR > 600 GeV
Preliminary
Expected limits are comparable, we use the point
with largest signal efficiency (R > 0.45, MR > 600 GeV)
Observed Limit
R cut \ MR Cut
Expected Limit
Observed Limit
R > 0.45
MR > 600 GeV
2.4+/- 0.9
4
R > 0.50
MR > 500 GeV
2.8+/- 1.3
1.7
R > 0.50
MR > 600 GeV
1.9+/- 0.6
1.7
R > 0.45
MR > 600 GeV
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QCD background
Question: Does the QCD background have a second component at large MR?
In the 11 pb-1 data there was no evidence of a second component in the QCD control box
Update: with the latest runs added (higher jet thresholds, pre-scaled QCD triggers) there
Calo Jets
is still no evidence of a second QCD component - please also keep in mind that there are
EWK processes contributing to the MR tail in this control sample, as expected.
As an exercise we will make a two component fit, but with the current data this is overfitting (and thus likely to give a worse prediction of the large MR behavior)
Christopher Rogan - All Hadronic/GMSB SUSY Meeting 18-11-10
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Pile-up
Question: Do the shapes of the MR distributions have a luminosity dependence?
We do not observe any significant dependence in the MR distribution as a function
Christopher Rogan - All Hadronic/GMSB SUSY Meeting 16-12-10
PF Jets
Calo Jets
of run range or instantaneous luminosity (estimated by counting primary vertices)
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Pile-up
Calo Jets
Calo Jets
PF Jets
Christopher Rogan - All Hadronic/GMSB SUSY Meeting 16-12-10
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Delta phi
Question: Do the slopes of the MR distributions for the non-QCD backgrounds
change if you vary/remove the cut on Delta phi?
Not significantly
Question: Do the shapes of the MR distributions for signal change if you
vary/remove the cut on Delta phi?
Not significantly
R > 0.4
Christopher Rogan - All Hadronic/GMSB SUSY Meeting 18-11-10
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Jet removal
Question: The appendix shows a simulation of jet loss in the ECAL and
its effect on the MR distribution. What happens if you repeat this kind of
jet removal exercise in the data and the corresponding MC samples?
We will perform this exercise in two ways:
First, we can remove jets by increasing the threshold in the jet
definition
Second, we can randomly remove a small percentage of jets, including
high pT jets. This second case is overly pessimistic given the
hermeticity of CMS, and requires careful interpretation since one is
drastically altering the event kinematics.
Christopher Rogan - All Hadronic/GMSB SUSY Meeting 18-11-10
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Uncertainty in large MR extrapolations
Question: Do you have uncertainty estimates for the final background MR
distributions and do the uncertainties get larger for large MR?
Yes we have uncertainty bands in the PAS Figure 3 and they are larger at large MR.
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Outlook
CMS-AN2010-288 and PAS-SUS-10-009 available for review - comments/questions on
the corresponding hypernews are very welcome
Background estimations for 11 pb-1 agree in all Boxes in low and high MR regions
Updating to full 2010 7 TeV statistics AN and PAS are being updated. Can expect
(relative to 11 pb-1 analysis):
Better precision on shape measurements and LEP box normalizations
Potential for first useful measurements from the di-lepton boxes (ttbar, Z+jets shapes and
normalizations directly from data)
Combination of MU and ELE Boxes with HAD Box in limit setting
Strategy is fixed, along with procedure for optimizing cuts given background predictions
blind analysis where potential for discovery evolves rigorously
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BACK-UP SLIDES
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Lepton Box QCD Control (DATA)
Create “QCD
lepton control”
samples by
inverting lepton
isolation in
MU/ELE boxes
MC tells us that
shape of control
is very similar to
shape in “signal”
lepton box measure control
shape, as a
function of R cut
QCD MU Box
Lepton QCD control sample shapes exhibit same
cut)2
(R
scaling as QCD in HAD Box
Use these shapes to describe QCD bkg to VBTF selection,
eventually floating the normalization
Christopher Rogan - All Hadronic/GMSB SUSY Meeting 16-12-10
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Lepton Boxes (DATA/MC comparison)
Measure exponential slope in DATA in
lepton boxes in W(l) dominated region
in LEP BOXES
DATA/MC ratios for these slopes give
us correction factor () which is applied
to _all_ slopes which are not measured
directly in DATA (correction factors
inter-consistent)
MU Box
ELE Box
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MR HT Trigger Turn-on
Signal HAD Box events are
selected using HT triggers
HT MR non-trivial MR
turn-on curve
W() MU Box MC
W() HAD Box MC
DATA/MC agreement (within
large errors) for these turn-on
curves
Turn-on curves are very
similar between different
processes (see backup) and
largely independent of Box
For high R cuts (~R > 0.3) MR HT trigger turn-ons are well-described by function:
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HAD Box Background Prediction
Over the course of data taking, different HT triggers are used trigger turn-on is
an integrated luminosity fraction-weighted sum of individual HT turn-ons:
The PDF (MR shape) for an individual background process is made of several parts:
Process shape
X
=
X
parameters
(from DATA or
Un-biased (w.r.t. HT)
Total PDF for Normalization Turn-on ensemble
MC*DATA/MC)
for
process
shape
function
process
Total non-QCD contribution is given by:
Turn-on scale factors
(floated in fit)
Sum over different Process HT turn-on
non-QCD processes param from MC
Normalization
from LEP Boxes
Total QCD contribution is given by:
Floated in fit
Ratio of HT thresh.
Measured w/ QCD control sample
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HAD Box strategy
We have the shapes (without HT cut) from MC, with slope corrections
from MU/ELE boxes
Shape in the HAD box is this shape, times the HT trigger turn-on for
that process (different for different processes, but not necessarily
dramatic differences)
Turn on function is a weighted sum of trigger turn-ons for different
HT values (weighted by luminosity for that trigger)
Normalization in HAD box (for non-QCD processes) taken from MU
and ELE box normalizations
We measure the trigger turn-on parameters for each non-QCD
process, as a function of R cut, in MC
We will float the QCD normalization and trigger parameters directly in
a fit in the low MR region in the HAD box
We will float “universal” scale factors (
), which will
_multiply_ the turn-on parameters for each non-QCD process, in the
same fit in the low MR region in the HAD BOX
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HAD Box fit Toys
In this example, we look at toys for the fit performed in the HAD
box with R > 0.4 (We have toys for different R/MR cuts)
We take the values of the parameters that maximize the
likelihood on DATA as the central values - use this to generate
toys (binned likelihood fit so we do Poisson fluctuations on
each bin in the pseudo-DATA histogram around central values)
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HAD Box Fit Toys
Fit has negligible effect on background prediction in high MR region
(fraction of a percent, even less for higher MR cuts
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ECAL Dead Cells Toy
We vary the fraction of jets (f)
for which we:
“Remove” a random fraction
(0 100%) of the ECAL energy
from the jet
Propagate this removal to the
MET (“add” the missing ECAL
energy back to MET)
Re-calculate all observables
(event-by-event)
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ECAL Dead Cells Toy
Exaggerated dead cell effect systematically shift
MR to lower values
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Lepton Box QCD Control (DATA)
Create “QCD
lepton control”
samples by
inverting lepton
isolation in
MU/ELE boxes
MC tells us that
shape of control
is very similar to
shape in “signal”
lepton box measure control
shape, as a
function of R cut
QCD ELE Box
Lepton QCD control sample shapes exhibit same
cut)2
(R
scaling as QCD in HAD Box
Will use these shapes to describe QCD bkg to VBTF
selection, eventually floating the normalization
Christopher Rogan - All Hadronic/GMSB SUSY Meeting 16-12-10
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To the HAD Box - HT Trigger Turn-ons
Z(nunu) HAD BOX MC
Ttbar(mu+X) HAD BOX MC
Turn-ons are similar for different processes
For high enough (R > ~0.3) R cuts, the trigger turn-ons are well-parameterized by:
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To the HAD Box - HT Trigger Turn-ons
Ttbar(no mu) HAD BOX MC
Ttbar(no mu) HAD BOX MC
Mu parameter scales with HT threshold as expected
For high enough (R > ~0.3) R cuts, the trigger turn-ons are well-parameterized by:
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Inclusive SUSY becomes SUSY quasi-dijets
The most generic signal process is pair production of two
heavy particles each decaying to an unseen LSP + jets (+
leptons).
Using hemispheres, can treat all
jet final states on an
equal footing, as 2 “mega-jets” (similar trick used to apply
to
multijets).
The signal kinematics is then equivalent to pair production of
two heavy squarks
with
where
are the two LSPs.
In the approximation that the heavy squarks are produced at
threshold, the CM frame kinematics are very simple:
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R frame
details of R frame and R variables are in arXiv:1006.2727
Event by event, we do an APPROXIMATE partial reconstruction
assuming the pseudo-dijet signal topology.
The rough approximation “R frame” WOULD be the CM frame for
signal events, IF the squarks were produced at threshold and IF the
CM system had no overall transverse momentum (from ISR).
The R frame is just the longitudinally boosted frame that equalizes
the magnitude of the two jet 3-momenta.
This longitudinal boost is uniquely defined by
Note because of the approximations
can turn out to be in the
unphysical region
even for genuine signal events. We will
(for now) discard such events in our analysis (only small loss in
signal) but there are ways to recover these events which we will
revisit
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details of R frame and R
variables are in
arXiv:1006.2727
R variables
To the extent that the R frame matches the true CM frame, the simple
kinematics tells us that, for signal events, the maximum value of
both
.
and
is
.
We define another transverse variable whose maximum value for
signal events in the same limit is also
:
Obviously signal events are characterized by the heavy scale
,
while background events are not.
To exploit this we also need an event-by-event estimator of
which we call
,
:
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Properties of
For signal events, in the limit where the R frame and the true CM
frame coincide:
More generally, we expect the
distribution for signal
events to peak around the high scale
.
For, e.g., QCD dijets, the only relevant scale
for
is the subprocess energy
.
Conceptually, we expect to see a peaking
signal over steeply falling backgrounds
(see slide 12).
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The Razor
To see the peaking signal, we first need to reduce the QCD background
to a manageable level.
To do this our main cut is the “Razor”, a selection based on the ratio of
our two R frame variables:
Recall that for signal events the transverse variable
maximum value of
has a
.
Thus for signal events the maximum value of R is 1, and the
distribution peaks around R
.
For QCD dijets R, being proportional to
, has a very steeply falling
distribution (with additional suppression due to angular terms).
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SUSY dijets
Let’s consider a SUSY di-jet final state topology where two squarks are
produced and each decay to a quark and an LSP
x
z
For the moment we neglect any potential transverse boost
to the entire di-squark system (from ISR for example)
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We define the variable MR as ( j1 and j2 are quark jets from
previous slide):
It is like a 1D analogue of the invariant mass, along the z-axis
It is invariant under longitudinal boosts
See paper for more details on it’s derivation:
arXiv:1006.2727v1 [hep-ph]
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Properties of
Returning to the di-squark example, if
(the squarks
are produced exactly at threshold) then
We find that, even if
deviates from 1 (which it will in
practice) that MR still peaks
For QCD di-jets (assuming no
mis-measurements, no pt to dijet
system etc.)
Conceptually, we expect to see a
peaking signal over a steeply falling
background
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The Razor
Unfortunately, the rate of QCD (even at high
) is prohibitively high
such that we will not be able to observe this signal without some
additional discriminating variable(s)
Such a variable is the Razor, denoted
.
and defined as:(
behaves similarly to the stransverse mass or
Then
has a kinematic endpoint at
)
, such that if
Hence, similarly to
or
, we take the ratio of two variables with
dimension mass (or energy if you prefer) and cut on a scale-less
variable.
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Properties of
As defined, MR is very robust against jet mis-measurements,
especially ‘catastrophic’ under-measurements of jets’ energy
This is because it is, in a sense, a geometric average of the two
jet’s momentum
The large transverse momentum imbalance that can result from
jet mis-measurements or jets falling outside of phase-space
acceptance, or unclustered energy - which can result in potentially
large missing ET - is largely protected against by the use of the
Razor. MTR and MR measure the same scale, but are also largely
uncorrelated
Rather than demonstrating this analytically, we will see some of
these properties illustrated in these slides
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Generalizing to an inclusive environment
Up until this point, we restricted ourselves to a 2 jet final state. For
a number of reasons we would like to generalize to a multi-jet (or
even fully inclusive) final state
final state radiation will occur, and is something we don’t really capture
in our current MC samples
For better or worse, if nature includes SUSY then we shouldn’t restrict
ourselves to looking for right-handed squarks decaying directly to LSP’s
To do this, we will take all the jets (or all the objects) in our final
state and group them into two mega-jets, or hemispheres
In the following examples, we do this my minimizing the invariant
masses of the two hemispheres
We have studied several other “hemisphere” algorithms, and find
that these results are not sensitive to this choice (since all the
algorithms get the assignments often wrong anyway)
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Toy examples
What were our two jets are now two hemispheres, and MR is defined
as before with this substitution (hemisphere masses set to zero, like
jets)
To understand what should happen to MR in a more general class of
scenarios, we consider 3 toy examples:
(A) production of two different heavy particles with
(B) production of two identical heavy particles, with one decaying
through the lighter massive particle and then to jet+LSP
(C) Both identical heavy particles decaying like this
A
B
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C
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MC samples
NLO x-sections from
https://twiki.cern.ch/twiki/bin/viewauth/CMS/StandardModelCrossSecti
ons used when available for backgrounds, otherwise LO x-sections
returned from generator
Samples those listed in:
https://twiki.cern.ch/twiki/bin/view/CMS/ProductionSummer2009at7TeV
PYTHIA: QCD, LM signal points, di-bosons, QCD di-photon, EM/muon
enriched QCD
MADGRAPH: Single top (s-chan,t-chan, tW), ttbar, W(l)+jets,
Z(ll)+jets, Z()+jets, +jets
ALPGEN: QCD
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