Search for supersymmetry with razor variables in pp
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EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)
CERN-PH-EP/2014-057
2014/05/15
CMS-SUS-12-005
Search for supersymmetry √ with razor variables in pp
collisions at s = 7 TeV
—Supplemental Material—
A guide to emulating the razor analysis technique for
phenomenology
The CMS Collaboration
Submitted to Physical Review D
c 2014 CERN for the benefit of the CMS Collaboration. CC-BY-3.0 license1 1 Introduction This document provides a guide to implementing√ in phenomenology studies the CMS search techniques for supersymmetry (SUSY) on s = 7 TeV pp collisions, based on the razor vari- ables MR and R2 . Starting from a sample of simulated SUSY events produced in pp collisions, this document describes how to account for detector effects in the reconstruction of the physics objects used in the analysis, such as jets, missing transverse energy ETmiss , electrons, muons, and b-tagged jets, how to compute the razor variables, how to associate each event with a search box, and how to derive a limit on a given model. This document is organized as follows: Section 2 describes the detector efficiency and resolu- tion related to the reconstruction of leptons, jets, and the missing transverse energy ETmiss . Sec- tions 3 and 4 describe how to compute the razor variables and how to associate each event with its corresponding box, respectively. The comparison of the analysis emulation to the nominal CMS result is discussed in section 5. The derivation of the exclusion-limit setting is described in section 6. 2 Reconstruction of physics objects The reconstruction of the physics objects goes through three steps: (i) definition of the input at generator level, (ii) detector response due to resolution, and (iii) detector efficiency (for leptons, muons, and b-tagged jets). We neglect the effect of jets misidentified as electrons, since the reconstruction efficiency is much higher than the mistag rate and the effect is negligible for a sample of events with real electrons. It should be understood that this approximation would underestimate the background. For more demanding studies a detailed simulation of the CMS detector should be used, which is beyond the scope of this document. 2.1 Generator level All the detectable stable particles in the event should be taken as input to the analysis emula- tion: electrons, muons, photons, charged hadrons, and neutral hadrons. The ETmiss in the event should be computed as the absolute value of ~ETmiss = −Σi~pTi . The four momenta of all the stable visible particles (except identified muons, described below) should be clustered using the anti-kT jet algorithm with jet size R = 0.5. All the muons in the event with pT < 5 GeV or |η | > 2.1 should be discarded. All the electrons in the event with pT < 5, |η | > 2.5, or 1.4442 < |η | < 1.566 should be discarded. For both electrons and muons, the generator- level isolation should be calculated as the scalar sum of the pT of all the particles around the considered lepton (i.e. with ∆R(lepton,particle) < 0.3), normalized to the lepton momen- tum. One should consider a jet as a b-jet at generator level if a q-quark is found inside the jet (∆R(jet,b quark) < 0.5) with transverse momentum above 10 GeV. 2.2 Detector Resolution For each object, the detector response can be modeled as a Gaussian function to a reasonable level of accuracy. The σ parameter of the Gaussian is different for muons, electrons, jets, or ETmiss , and it is a function of the object pT and (when applicable) η, as illustrated in Fig. 1. In order to take into account the momentum resolution, a ”reconstructed” momentum should be extracted on an lepton-by-lepton basis, according to a Gaussian function centered at the generator-level pT and with a σ parameter given by the corresponding root mean square (RMS). To a good level of accuracy, one can neglect the detector effects on η and φ such that the recon- structed values can be taken equal to the corresponding generator-level values.
2 3 Computing the Razor Variables
50
CMS simulation 0 < |η| < 1.4442 CMS simulation 0 < |η| < 1.4
Electron resolution [GeV]
40 t t s = 7 TeV 1.566 < |η| < 2.5 t t s = 7 TeV 1.4 < |η| < 2.4
Muon resolution [GeV]
30 10
20
10
0 1
50 100 150 200 250 300 0 50 100 150 200 250
GenElectron p [GeV] GenMuon p [GeV]
T T
Figure 1: Momentum resolution for (left) electrons and (right) muons within the barrel region
of the CMS detector (squares) and in the endcaps (triangles).
2.3 Detector Efficiency
The reconstruction efficiencies for electrons and muons, parameterized as a function of the
lepton flavor, the selection considered (tight or loose), and the values of (pT ,η), are shown
in Fig. 2. The corresponding information for the b-tagging performances can be found the
references provided with the razor analysis paper. The inefficiency for loose muons can be
considered negligible in the pT range considered in this analysis.
For each lepton at generator level, the plots in Fig. 2 can be used to derive the corresponding
efficiency e. The reconstruction efficiency can then be taken into account by weighting the
event by a factor ei for the i-th lepton, the total weight being the product of the weights in one
event, or by using a hit-or-miss procedure. For the electrons and muons, different values for
different ranges of the generator-level isolation are quoted, to take into account the efficiency
degradation for events with large jet multiplicity, as for instance in the case of leptons generated
in SUSY cascades.
3 Computing the Razor Variables
The razor variables can be computed from the list of jets in the event, clustered from generator-
level particles by using the anti-kT jets algorithm with cone size R=0.5. Otherwise, one can
simulate the CMS detector using DELPHES default tuning. We consider all the jets with pT >
40 GeV and |η | < 3.0. We further require that the two highest-pT jets have pT > 60 GeV. The
list of the jets four-momenta is passed to a hemisphere algorithm, which returns the two four-
momenta of the mega-jets. The code we used is given here. It uses the Lorentz vector class
available in ROOT.
vector Razor::CombineJets(vector myjets){
vector mynewjets;
TLorentzVector j1, j2;
bool foundGood = false;
int N_comb = 1;
for(int i = 0; i < myjets.size(); i++){
N_comb *= 2;
}3
0.8
Efficiency
Efficiency
0.8
0.7 CMS simulation GenIso < 0.10
0.7 t t s = 7 TeV 0.10 < GenIso < 0.20
0.6 Endcap tight
0.6 GenIso > 0.20
0.5
0.5
0.4 CMS simulation GenIso < 0.10
0.4
0.3 t t s = 7 TeV 0.10 < GenIso < 0.20
Barrel tight 0.3
GenIso > 0.20
0.2 0.2
0.1 0.1
50 100 150 200 250 50 100 150 200 250
Gen Electron p [GeV] Gen Electron p [GeV]
T T
Efficiency
Efficiency
1
1
0.8 0.8
0.6 0.6
CMS simulation GenIso < 0.10 CMS simulation GenIso < 0.10
0.4 0.4
t t s = 7 TeV 0.10 < GenIso < 0.20 t t s = 7 TeV 0.10 < GenIso < 0.20
Barrel loose Endcap loose GenIso > 0.20
GenIso > 0.20
0.2 0.2
0 0
50 100 150 200 250 0 50 100 150 200 250
Gen Electron p [GeV] Gen Electron p [GeV]
T T
Efficiency
Efficiency
1 1
0.9
0.8
0.8
0.6 0.7
0.6
GenIso < 0.10
0.4 CMS simulation
0.10 < GenIso < 0.20 0.5 CMS simulation GenIso < 0.10
t t s = 7 TeV
GenIso > 0.20 t t s = 7 TeV 0.10 < GenIso < 0.20
0.2 Barrel 0.4 Endcaps GenIso > 0.20
0.3
0
50 100 150 200 250 50 100 150 200 250
Gen Muon p [GeV] Gen Muon p [GeV]
T T
Figure 2: Reconstruction efficiency for (upper left) barrel tight electrons, (upper right) endcap
tight electrons, (center left) barrel loose electrons, (center right) endcap loose electrons, (lower
left) tight barrel muons, and (lower right) endcaps, estimated from the CMS MC simulation of
tt events.4 4 Box definition
double M_min = 9999999999.0;
int j_count;
for(int i = 1; i < N_comb-1; i++){
TLorentzVector j_temp1, j_temp2;
int itemp = i;
j_count = N_comb/2;
int count = 0;
while(j_count > 0){
if(itemp/j_count == 1){
j_temp1 += myjets[count];
} else {
j_temp2 += myjets[count];
}
itemp -= j_count*(itemp/j_count);
j_count /= 2;
count++;
}
double M_temp = j_temp1.M2()+j_temp2.M2();
// smallest mass
if(M_temp < M_min){
M_min = M_temp;
j1 = j_temp1;
j2 = j_temp2;
}
}
if(j2.Pt() > j1.Pt()){
TLorentzVector temp = j1;
j1 = j2;
j2 = temp;
}
mynewjets.push_back(j1);
mynewjets.push_back(j2);
return mynewjets;
}
4 Box definition
Events are classified according to the lepton multiplicity. The boxes are filled hierarchically:
each event fills only the first box it falls in, in this order:
MU-ELE, events with one tight electron (pT > 20 GeV, |η | < 2.5) and one tight muon (pT >
12 GeV, |η | < 2.1),
MU-MU, events with one tight muon (pT > 15 GeV, |η | < 2.1) and one loose muon (pT >
10 GeV, |η | < 2.1),
ELE-ELE, events with one tight electron (pT > 20 GeV, |η | < 2.5) and one loose electron
(pT > 10 GeV, |η | < 2.5),
MU, events with one tight muon (pT > 12 GeV, |η | < 2.1),
ELE, Events with one tight electron (pT > 20 GeV, |η | < 2.5),
HAD, All the other events.5
Keep in mind that the electrons in the transition region between the ECAL barrel and endcap
(1.4442 < |η | < 1.566) are not considered as good reconstructed electrons. Compute R and MR
given that the four momenta of the two hemispheres, MR is computed as
double CalcMR(TLorentzVector ja, TLorentzVector jb){
double A = ja.P();
double B = jb.P();
double az = ja.Pz();
double bz = jb.Pz();
TVector3 jaT, jbT;
jaT.SetXYZ(ja.Px(),ja.Py(),0.0);
jbT.SetXYZ(jb.Px(),jb.Py(),0.0);
double ATBT = (jaT+jbT).Mag2();
double temp = sqrt((A+B)*(A+B)-(az+bz)*(az+bz)-
(jbT.Dot(jbT)-jaT.Dot(jaT))*(jbT.Dot(jbT)-jaT.Dot(jaT))/(jaT+jbT).Mag2());
double mybeta = (jbT.Dot(jbT)-jaT.Dot(jaT))/
sqrt(ATBT*((A+B)*(A+B)-(az+bz)*(az+bz)));
double mygamma = 1./sqrt(1.-mybeta*mybeta);
//gamma times MRstar
temp *= mygamma;
return temp;
}
To compute MTR you also need the muon-corrected ETmiss . This can be computed with a detector
simulation (e.g. DELPHES) or by (vectorially) summing the transverse momenta of all the visible
particles (including muons). MTR is then computed as
double CalcMTR(TLorentzVector ja, TLorentzVector jb, TVector3 met){
double temp = met.Mag()*(ja.Pt()+jb.Pt()) - met.Dot(ja.Vect()+jb.Vect());
temp /= 2.;
temp = sqrt(temp);
return temp;
}
The razor variable is defined as the ratio R = MTR /MR .
5 Comparison with CMS simulation
We show here three reference plots (for MR , R2 , and the box-by-box efficiency) for a sample
of pair-produced gluinos with 800 GeV mass, each one decaying to two top quarks and a neu-
tralino with 300 GeV mass. We show the distribution obtained with this simplified detector
simulation and what is used in the official analysis.
6 Exclusion limit
Once MR and R have been computed for your SUSY events, you need to build the 2D pdf for
your signal. We use the binning described in the figure. With ROOT, you can define a TH2D
histogram with this binning:
double MRbins[17] = {300, 350, 400, 450, 500, 550, 600, 650, 700,
800, 900, 1000, 1200, 1600, 2000, 2800, 3500};
double Rsqbins[6] = {0.11, 0.18, 0.20, 0.30, 0.40, 0.50};
TH2D* signalPDF = new TH2D("signalPDF", "signalPDF",
16, MRbins, 5, Rsqbins);6 6 Exclusion limit
0.12 0.6
efficiency
0.08
CMS fast simulation CMS fast simulation
a.u.
a.u.
0.1 CMS fast simulation
Razor outreach Razor outreach
0.06 Razor outreach
0.08 0.4
0.04 0.06
0.04 0.2
0.02
0.02
00 0.2 0.4 0.6 0.8 1 1.2 1.4
0 1000 2000 3000 MU
-EL
MU
-MU
ELE M
-EL U
ELE HAD
E E
MR [GeV] R2
Figure 3: Comparison of the (left) MR distribution, (center) R2 distribution, and (right) the
efficiency versus box obtained from the official CMS fast simulation package and the emulation
procedure described in this appendix. The two distributions correspond to a T1tttt sample with
800 GeV gluino mass and 300 GeV LSP mass.
Notice that the baseline selection for the Had box is tighter than for the other boxes (due to the
tighter trigger), MR > 400 and R2 > 0.18, when filling the histogram. A C++ implementation
of the signal-box cut is given here, assuming the following numbering scheme: MU-ELE 0,
MU-MU 1, ELE-ELE 2, MU 3, ELE 4, HAD 5.
bool CMSRazor::SignalRegion(double mr, double rsq, double ibox){
if(ibox == 4 || ibox == 3) return SignalRegionLep(mr, rsq);
else if(ibox == 5) return SignalRegionHad(mr, rsq);
else if(ibox >=0 && ibox 650.) return true;
if(rsq>0.3 && mr>450.) return true;
return false;
}
bool CMSRazor::SignalRegionDiLep(double mr, double rsq){
if(rsq>0.5) return false;
if(rsq650.) return true;
if(rsq>0.2 && mr>450.) return true;
if(rsq>0.3 && mr>400.) return true;
return false;
}7 Computing the exclusion limit In order to compute the exclusion limit for a given model, we provide a simple python program, based on ROOT, and the expected and observed yield (for each box in each bin). The following instructions assume that you have installed ROOT and that you can run ROOT from a shell (i.e. that the environment variable ROOTSYS is configured) You need to download the tar file of the program and untar it in some directory. tar -xzf RazorStat.tar.gz cd RazorStat You then have to prepare a config file with the location of your 2D histograms, created follow- ing the instructions above. The config file should look like this BOX: HAD 0.13 razor.root HADHisto BOX: MU 0.05 razor.root MUHisto BOX: ELE 0.05 razor.root ELEHisto BOX: MUELE 0.01 razor.root MUELEHisto BOX: MUMU 0.01 razor.root MUMUHisto BOX: ELEELE 0.01 razor.root ELEELEHisto For each line, the arguments after BOX: correspond to the box name the efficiency in that box (number of events in the fit region/number of events generated) input root file path of the 2D histogram in the file You can then run the code as python razorLimit.py myconfigfile.cfg or include it in your phenomenology analysis (e.g. a CMSSM scan). For more info type python razorLimit.py The output should be something like REQUESTED Had BOX with input histogram HADHisto from razor.root REQUESTED Mu BOX with input histogram MUHisto from razor.root REQUESTED Ele BOX with input histogram ELEHisto from razor.root REQUESTED MuEle BOX with input histogram MUELEHisto from razor.root REQUESTED MuMu BOX with input histogram MUMUHisto from razor.root REQUESTED EleEle BOX with input histogram ELEELEHisto from razor.root Had LIMIT: 0.210406 pb-1 Mu LIMIT: 1.124624 pb-1 Ele LIMIT: 1.581240 pb-1 MuEle LIMIT: 0.194653 pb-1 MuMu LIMIT: 0.242139 pb-1 EleEle LIMIT: 0.337274 pb-1 TOT LIMIT: 0.104755 pb-1 where the TOT limit is obtained combining all the boxes you requested. To have a faster vs. more accurate limit you need to customize the range of cross section and the number of steps. By default the code scans the cross-section range [0–5] pb in 2000 steps: nbin = 2000 xsecMin = 0. xsecMax = 5. This procedure is validated by deriving a limit for the T1tttt and T2tt simplified models (shown in Fig. 4) and comparing the result to the nominal result. Color-scale (z-axis) indicates the ob- served cross-section upper limit for each model point, as a function of gluino and LSP mass. To within a factor of ≈2, the upper limits agree, with the emulation producing a more conservative limit. This translates into a conservative limit, close enough to the nominal result.
8 6 Exclusion limit
t t
P2 t
g̃ P2 t̃ χ̃01
χ̃01
χ̃01
P1 χ̃01
g̃ t̃
P1 t
t t
Figure 4: Bayesian upper limits, at 95% CL, on cross sections, in pb, for simplified models,
obtained by applying the razor emulation procedure described in this document: (left) T1ttt
and (right) T2tt.You can also read
