Post on 02-Aug-2020
The Razor Variables: a primer
CMG Meeting 15-11-10
Christopher RoganCalifornia Institute of Technology
With Joseph Lykken, Maurizio Pierini and Maria Spiropulu
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Razor Variables: A Primer
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Two variables designed to be used together for discovery and characterization of SUSY
Doesn’t involve MET Uses both transverse and
longitudinal information Invariant under long. boosts
Peaks for signal:
arXiv:1006.2727v1 [hep-ph]
Dimension-less variable used for S/B discrimination Not only suppresses backgrounds, but also shapes their
distributions in the variable in a predictable and well-understood way - the Razor
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Inclusive SUSY becomes SUSY quasi-dijets
The most generic signal process is pair production of two heavyparticles each decaying to an unseen LSP + jets (+ leptons).
Using hemispheres, can treat all jet final states on an equalfooting, as “quasi-dijets” (similar trick used to apply tomultijets).
The signal kinematics is then equivalent to pair production oftwo heavy squarks with whereare the two LSPs.
In the approximation that the heavy squarks are produced atthreshold, the CM frame kinematics are very simple:
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R frame
Event by event, we do an APPROXIMATE partial reconstructionassuming the quasi-dijet signal topology.
The rough approximation “R frame” WOULD be the CM frame forsignal events, IF the squarks were produced at threshold and IF theCM system had no overall transverse momentum (from ISR).
The R frame is just the longitudinally boosted frame that equalizesthe 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 theunphysical region even for genuine signal events. We will(for now) discard such events in our analysis (only small loss insignal) but there are ways to recover these events which we willrevisit
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details of R frame and R variables are in arXiv:1006.2727
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R variables
To the extent that the R frame matches the true CM frame, the simplekinematics tells us that, for signal events, the maximum value of both. and is .
We define another transverse variable whose maximum value forsignal 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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details of R frame and Rvariables are inarXiv:1006.2727
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Properties of
For signal events, in the limit where the R frame and the true CMframe coincide:
More generally, we expect the distribution for signalevents to peak around the high scale .
For, e.g., QCD dijets, the only relevant scalefor 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 backgroundto a manageable level.
To do this our main cut is the “Razor”, a selection based on the ratio ofour two R frame variables:
Recall that for signal events the transverse variable has amaximum value of .
Thus for signal events the maximum value of R is 1, and thedistribution peaks around R .
For QCD dijets R, being proportional to , has a very steeply fallingdistribution (with additional suppression due to angular terms).
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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 pb-1 shown here) PF MET used (tcMET or corrected caloMET fine too) Require di-jets satisfying (parallel analyses):
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)
Corrected Calo jets Corrected PF jets Uncorrected Track jets
Loose jet ID Loose jet ID Only high quality tracksw/ vertex consistent
with reco PV consideredfor clustering
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The Razor in practice
QCD MC
(ALPGEN)
LM1 MC
Cut on R gives many orders of magnitudesuppression of QCD background
More importantly, cut on R dictates theshape of the surviving background events(QCD and others) in the variable MR (seenext slide)
PF jets
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The Razor and MR
Backgrounds fall ~exponentially after exceeding relevant scale (set by processscale+trigger/reco requirements) - slope set by R cut
DATA behaves asexpected
PF jets
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Boxes
MU Boxo VBTF W muonselection + triggerso Muon isolationinversion for QCDmuon control sample
HAD Box
ELE Boxo VBTF W electronselection + triggerso Electron isolationinversion for QCDelectron controlsample
o Veto on lepton boxeso HLT_DiJetAve15U (pre-scaled) gives QCD controlsampleo HLT_HT{100,140,150}Udefines “signal” box
Orthogonal boxes based onphysics object ID allows us toisolate different physicsprocesses
Lepton boxes, along with a QCDcontrol sample, are used for thebackground prediction in thehadronic signal box
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QCD Control BOX and QCD scaling
Using the HLT_DiJetAve15U (pre-scaled) allows us to measure the un-biasedMR distribution for QCD events
Exponential slopes of MR scale with (R cut)2 (can be explained analytically)
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QCD Control Box
Track Jets PF Jets
Scaling behavior same for alljets types
p0 values related by ratios ofJES’s
Similar p1 values
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Lepton Box QCD Control
Create “QCD leptoncontrol” samples byinverting lepton isolation inMU/ELE boxes
For electrons, remove H/Eand sigmaiEtaiEta cuts
MC tells us that shape ofcontrol is very similar toshape in “signal” leptonbox - measure controlshape, as a function of Rcut
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Lepton Box QCD Control (DATA)
MU Box
ELE Box
Lepton QCD control sampleshapes exhibit same (R cut)2
scaling
Will use these shapes todescribe QCD bkg to VBTFselection, eventually floatingthe normalization
Calo Jets
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MU Box
For each box (MU, ELE, HAD)and for each different process(W(µν), W(eν), ttbar(µ+X), etc.)We measure the exponentialslopes as a function of R cut forMC and DATA (when possible)
Calo Jets
HAD Box
HAD Box
MU Box
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Lepton Boxes (DATA/MC comparison)Calo Jets
Measure exponential slope inDATA in lepton boxes in W(lν)dominated region
Good DATA/MC agreementfor slopes W(lν) slopes
DATA/MC ratios for theseslopes give us correctionfactor (and error) which isapplied to _all_ slopes whichare not measured directly inDATA (correction factorscurrently consistent with 1)
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Background Predictions in the LeptonBoxes
MR shapes take from direct measurement or MC with MC/DATA correction Normalize W(lν) 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) With fixed non-QCD predictions fixed, we float the QCD normalization (shape
fixed)
R > 0.4 R > 0.5
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Background Prediction in the HadronicBox
R > 0.5
non-QCD processesnormalized usingmeasurements from MU andELE Boxes
QCD normalization, along withparameters describing the HTtrigger turn-on curve for QCDand non-QCD processes arefloated simultaneously in abinned likelihood fit in therange 75 < MR < 350
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Outlook
SUSY search using variables MR and R appears to have good potential forSUSY discovery - DATA behaves as expected in MR and R variables
Analysis is easily evolved as a function of integrated luminosity: With more data, we can make more precise measurements of slopes, reducing
bkg prediction uncertainties - can also measure Z/ttbar contributions directly inee, µµ, and eµ boxes
Can optimize “signal region” cuts using background predictions from data -eventually, we will move to a full ML Fit rather than a cut-and-count approach(are already predicting the full background shape)
Include more final state boxes (photons, taus, b-tags, etc.)
For example: Di-tau final stateSUSY search with R/MR by
Virginia Azzolini andEmmanuele Salvati
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BACK-UP SLIDES
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SUSY dijets
Let’s consider a SUSY di-jet final state topology where two squarks areproduced and each decay to a quark and an LSP
x
z
For the moment we neglect any potential transverse boostto 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 fromprevious 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 squarksare produced exactly at threshold) then
We find that, even if deviates from 1 (which it will inpractice) 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 highsuch that we will not be able to observe this signal without someadditional discriminating variable(s)
Such a variable is the Razor, denoted and defined as:( )
behaves similarly to the stransverse mass or , such that if. Then has a kinematic endpoint at
Hence, similarly to or , we take the ratio of two variables withdimension mass (or energy if you prefer) and cut on a scale-lessvariable.
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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 twojet’s momentum
The large transverse momentum imbalance that can result from jetmis-measurements or jets falling outside of phase-spaceacceptance, or unclustered energy - which can result in potentiallylarge missing ET - is largely protected against by the use of theRazor. MT
R and MR measure the same scale, but are also largelyuncorrelated
Rather than demonstrating this analytically, we will see some ofthese 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. Fora number of reasons we would like to generalize to a multi-jet (oreven 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 invariantmasses of the two hemispheres
We have studied several other “hemisphere” algorithms, and findthat these results are not sensitive to this choice (since all thealgorithms get the assignments often wrong anyway)
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Toy examples
What were our two jets are now two hemispheres, and MR is definedas before with this substitution (hemisphere masses set to zero, likejets)
To understand what should happen to MR in a more general class ofscenarios, 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 C
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MC samples
NLO x-sections fromhttps://twiki.cern.ch/twiki/bin/viewauth/CMS/StandardModelCrossSections used when available for backgrounds, otherwise LO x-sectionsreturned 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/muonenriched QCD
MADGRAPH: Single top (s-chan,t-chan, tW), ttbar, W(lν)+jets,Z(ll)+jets, Z(νν)+jets, γ+jets
ALPGEN: QCD