the razor variables: a primerhep.caltech.edu/~crogan/files/rogan_15_11_10.pdf · christopher rogan...

The Razor Variables: a primer

CMG Meeting 15-11-10

Christopher RoganCalifornia Institute of Technology

With Joseph Lykken, Maurizio Pierini and Maria Spiropulu

Christopher Rogan - CMG Meeting 15-11-10 2

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


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


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


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


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


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


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


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)


QCD Control Box

Track Jets PF Jets

Scaling behavior same for alljets types

p0 values related by ratios ofJES’s

Similar p1 values


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


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


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


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)


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


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


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


BACK-UP SLIDES


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)


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]


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


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.


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


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)


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


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

the razor variables: a primerhep.caltech.edu/~crogan/files/rogan_15_11_10.pdf · christopher rogan...

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