VtbDileptonicEventSelection < Main

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<table>
<tr>
<th width=200 bgcolor=#FFFFCC valign=center align=center><big>Event selection</big></th>
<td width=400 valign=center align=left>  %TOC%  </td>
<td>&nbsp;</td>
</tr>
</table>

---++ Object selection

---+++10 TeV
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---+++14 TeV
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---++++ Leptons
Leptons are reconstructed in the following way:

   * electrons - ==pixelMatchGsfElectrons==
   * muons - ==globalMuons==

---+++++ Observables for leptons

The main characteristic for leptons coming from the W decay is the fact that they should be prompt and isolated. Other variables can be used to clean the leptons of interest: electromagnetic fraction, E/p, lepton identification, etc.

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|*Reconstructed lepton observables*||||||
|  | *%$p_{T}$% spectrum* | *%$\eta$% distribution* | *Track impact parameter* | *%$\frac{E}{p_{track}}$%* |
| *e* | <img src="%ATTACHURLPATH%/e_pT.png" width='200'/> | <img src="%ATTACHURLPATH%/e_eta.png" width='200'/> | <img src="%ATTACHURLPATH%/e_d0sig.png" width='200' /> | <img src="%ATTACHURLPATH%/e_EoverP.png" width='200' /> |
| *%$\mu$%* | <img src="%ATTACHURLPATH%/mu_pT.png" width='200'/> | <img src="%ATTACHURLPATH%/mu_eta.png" width='200'/> | <img src="%ATTACHURLPATH%/mu_d0sig.png" width='200'/> | <img src="%ATTACHURLPATH%/mu_EoverP.png" width='200' /> |
| | *electromagnetic fraction* | *Isolation in tracker and calorimeter* || |
| *e* | <img src="%ATTACHURLPATH%/e_emf.png" width='200' /> | <img src="%ATTACHURLPATH%/e_trackerIso.png" width='200' /> | <img src="%ATTACHURLPATH%/e_caloIso.png" width='200' /> | |
| *%$\mu$%* | <img src="%ATTACHURLPATH%/mu_emf.png" width='200' />  | <img src="%ATTACHURLPATH%/mu_trackerIso.png" width='200'/> | <img src="%ATTACHURLPATH%/mu_caloIso.png" width='200'/> | |

---+++++ Single lepton selection efficiency and purity

Our lepton selection is defined below. 

%TABLE{ sort="off" tableborder="0" cellpadding="4" cellspacing="3" cellborder="0" headerbg="#D5CCB1" headercolor="#666666" databg="#FAF0D4, #FFFFFF" headerrows="2" footerrows="0" columnwidths="100,250, 200,200" }%
| *Lepton selection* ||||
| *Selection steps* || *Electrons selected* | *Muons selected* |
| *kinematics* | %$p_{T} \geq 20 GeV/c$% ; %$\vert \eta \vert = 2.4$%  | <img src="%ATTACHURLPATH%/e_sel.png" width='200' /> | <img src="%ATTACHURLPATH%/mu_sel.png" width='200'  /> | 
| *calorimetric cuts* | %$\begin{cases}{ e & calo iso 6 GeV & \\ \mu & calo iso  5 GeV }\end{cases}$%| ^ | ^ |
| *isolation* | %$\sum_{tracks} p_{T_{i}} (\Delta R \leq 0.3) \leq 3 GeV/c$% | ^ | ^ |
| *id* | %$\begin{cases}{ e & tight & \\ \mu & none } \end{cases} $% | ^ | ^ |

After selection the lepton purity is the following:

%TABLE{ sort="off" tableborder="0" cellpadding="4" cellspacing="3" cellborder="0" headerbg="#D5CCB1" headercolor="#666666" databg="#FAF0D4, #FFFFFF" headerrows="2" footerrows="0"}%
| *Sample* | *Leptonic purity* ||
| ^ | *e* | *%$\mu$%* |
| ==Madgraph== | 1.00 %$\pm$% 0.02 | 0.98 %$\pm$% 0.02 |
| ==Alpgen== | 0.96 %$\pm$% 0.01 | 0.952 %$\pm$% 0.005 |
| <b>Purity</b> | <b>0.96 %$\pm$% 0.01 (stat) %$\pm$% 0.03 (syst)</b> | <b>0.952 %$\pm$% 0.005 (stat) %$\pm$% 0.03 (syst)</b> |

The probability of reconstructing and selecting both hard leptons is the following:

%TABLE{ sort="off" tableborder="0" cellpadding="4" cellspacing="3" cellborder="0" headerbg="#D5CCB1" headercolor="#666666" databg="#FAF0D4, #FFFFFF" headerrows="2" footerrows="0"}%
| *Sample* | *P(select n hard leptons)* |||
| ^ | *0* | *1* | *2* |
| ==Madgraph== | 0.240 %$\pm$% 0.004 | 0.487 %$\pm$% 0.006 | 0.273 %$\pm$% 0.004 |
| ==Alpgen== | 0.227 %$\pm$% 0.001 | 0.483 %$\pm$% 0.002 | 0.290 %$\pm$% 0.002 |
| *%${\bf P_{sel} }$%* | <b>0.227 %$\pm$% 0.001 (stat) %$\pm$% 0.013 (syst)</b> | <b>0.483 %$\pm$% 0.002 (stat) %$\pm$% 0.004 (syst)</b> | <b>0.290 %$\pm$% 0.002 (stat) %$\pm$% 0.018 (syst)</b> |


---++++ Jets

Jets are reconstructed using the iterative cone algorithm with %$\Delta R=0.5$% from the calorimetric towers with %$E_{T}(min)=0.5 GeV$%. A minimum %$E_{T}$% of 2 GeV and 2 towers is required as pre-selection.  The tracks with at least 8 hits, a %$\chi^{2}\leq5.0$% and %$p_{T}\geq 1GeV/c$% are associated to the calorimetric cluster if they are matched to it within a cone of %$\Delta R=0.5$%. No jet cleaning (matching with reconstructed electrons or muons is done). 

---+++++ Observables for jets

%TABLE{ sort="off" tableborder="0" cellpadding="4" cellspacing="3" cellborder="0" headerbg="#D5CCB1" headercolor="#666666" databg="#FAF0D4, #FFFFFF" headerrows="2" footerrows="0" columnwidths="200, 200,200" }%
|*Reconstructed jet observables*||||
| *%$p_{T}$% spectrum* | *%$\eta$% distribution* | *emf* | *b-tag discriminator* |
| <img src="%ATTACHURLPATH%/jet_pT.png" width='200'/> | <img src="%ATTACHURLPATH%/jet_eta.png" width='200'/> | <img src="%ATTACHURLPATH%/jet_emf.png" width='200'/> | <img src="%ATTACHURLPATH%/jet_btag.png" width='200'/> | 
| * Calorimetric constituents * || * Associated tracks * ||
| <img src="%ATTACHURLPATH%/jet_towerET.png" width='200'/> | <img src="%ATTACHURLPATH%/jet_zMaxTowers.png" width='200'/> | <img src="%ATTACHURLPATH%/jet_trackpT.png" width='200'/> | <img src="%ATTACHURLPATH%/jet_zMaxTracks.png" width='200'/> |
| * nearest jet * | | | | |
| <img src="%ATTACHURLPATH%/jet_minDRjj.png" width='200'/> | | | |


---+++++ Likelihood ratio method
In order to increase the purity of the jets selected in an event we try to characterize better some experimentally measurable distributions of the jets (e.g. jet width, number of tracks,  charge, etc.). For each jet we compute a list of observables and we check if it can be matched to the quark generated by the top decay (b,s or d ). This allows us to define two distributions:
   * %$S(x) = %$\frac{dN_{jets}^{matched}}{dx}$%  - the "signal" distribution for the jets whose purity we want to increase.
   * %$B(x) = %$\frac{dN_{jets}^{not matched}}{dx}$% - the "background" distribution for the jets remaining, after the selection, which you want to remove.
The distributions _S(x)_ and _B(x)_ are defined with inclusive first and last bins. As so, the first(last) bin should be interpreted as the number of jets with an observable _x_ , %$x\leqx_{min}$%(%$x\geqx_{max}$%). The probability distribution function - %$f(x)=\frac{S(x)}{S(x)+B(x)}$% gives the probability that a signal jet has an observable _x_ between x and x+dx. 
Having defined the p.d.f.'s for signal jets one can define the combined likelihood as:
   * %$L=\prod_{i} \frac{f(x_{i})}{\bar{f}(x_{i})} = \prod_{i} \frac{f(x_{i})}{1-f(x_{i})}$% 
In order to reduce possible bias sources the different  p.d.f.'s must:
   * have low correlations (%$\rho = \frac{cov(x,y)}{\sigma_{x}\sigma_{y}} \leq 30\% $%)
   * not bias towards the selection of a specific jet flavor (b,s,d)
The table below summarizes the distributions for the observables chosen and the correspondent likelihood obtained when using Madgraph (==All b== and ==All q== samples). 

%TABLE{ sort="off" tableborder="0" cellpadding="4" cellspacing="3" cellborder="0" headerbg="#D5CCB1" headercolor="#666666" databg="#FAF0D4, #FFFFFF" headerrows="2" footerrows="0" columnwidths="100,200,200,200" }%
|*Jet properties*||||||
| *x* | *S(x) and B(x) * |  *%$f(x)=\frac{S}{S+B}$%* | *Cross correlations* |
| %$\eta_{jet}$% | <img src="%ATTACHURLPATH%/jet_eta_SandB.png" width='200'/> |<img src="%ATTACHURLPATH%/jet_eta_f.png" width='200'/> |<img src="%ATTACHURLPATH%/jet_eta_corr.png" width='200'/> |
| %$\frac{E_{T}}{jet\; area}}$% | <img src="%ATTACHURLPATH%/jet_etdens_SandB.png" width='200'/> |<img src="%ATTACHURLPATH%/jet_etdens_f.png" width='200'/> |<img src="%ATTACHURLPATH%/jet_etdens_corr.png" width='200'/> |
| %$n_{90}$%<small>, number of towers with %$90\%$% of the jet energy</small> | <img src="%ATTACHURLPATH%/jet_n90_SandB.png" width='200'/> |<img src="%ATTACHURLPATH%/jet_n90_f.png" width='200'/> |<img src="%ATTACHURLPATH%/jet_n90_corr.png" width='200'/> |
| %$i_{jet}$%<small>, jet index in a %$p_{T}$% ordered jet collection</small> | <img src="%ATTACHURLPATH%/jet_ijet_SandB.png" width='200'/> |<img src="%ATTACHURLPATH%/jet_ijet_f.png" width='200'/> |<img src="%ATTACHURLPATH%/jet_ijet_corr.png" width='200'/> |
| %$\min \Delta \eta(jet,lepton)$% | <img src="%ATTACHURLPATH%/jet_mindetajl_SandB.png" width='200'/> |<img src="%ATTACHURLPATH%/jet_mindetajl_f.png" width='200'/> |<img src="%ATTACHURLPATH%/jet_mindetajl_corr.png" width='200'/> |
|*Combined Likelihood*||||
| *likelihood* || *signal efficiency vs. background efficiency* ||
| <img src="%ATTACHURLPATH%/jetCombLR.png" width='300' /> || <img src="%ATTACHURLPATH%/jetCombLR_eff.png" width='300' /> ||

---+++++ Single jet selection efficiency and purity

Our jet selection is defined below

%TABLE{ sort="off" tableborder="0" cellpadding="4" cellspacing="3" cellborder="0" headerbg="#D5CCB1" headercolor="#666666" databg="#FAF0D4, #FFFFFF" headerrows="2" footerrows="0" columnwidths="100,250,200,200" }%
| *Jet selection* |||||
| *Selection steps*|| *Jets surviving selection* | *Multiplicity* | *Likelihood (after pre-selection)* |
| *kinematics* | %$p_{T} \geq 20 GeV/c$% ; %$\vert \eta \vert \leq 2.4$% | <img src="%ATTACHURLPATH%/jet_sel.png" width='200' /> | <img src="%ATTACHURLPATH%/jet_multiplicity.png" width='200' /> | <img src="%ATTACHURLPATH%/jet_combLR.png" width='200' /> |
| *calorimetric cuts* | %$ emf \leq 0.95 $%  | ^ | ^ | ^ |
| *topology* | %$\Delta R(jet,leptons/jets) \geq 0.5 $% | ^ | ^ | ^ |
| *likelihood* | %$comb L \geq 0$% | ^ | ^ | ^ |

After selection the jet purity is lower than lepton purity (as expected due to the high jet multiplicity):

%TABLE{ sort="off" tableborder="0" cellpadding="4" cellspacing="3" cellborder="0" headerbg="#D5CCB1" headercolor="#666666" databg="#FAF0D4, #FFFFFF" headerrows="2" footerrows="0"}%
| *Sample* | *Jet purity* ||
| ==Madgraph== | 0.726 %$\pm$% 0.007 |
| ==Alpgen== | 0.725 %$\pm$% 0.003 | 
| <b>Purity</b> | <b>0.725 %$\pm$% 0.003 (stat) %$\pm$% 0.01 (syst)</b> |

The probability of reconstructing and selecting both hard jets from the top decay is, however higher than the one obtainde for leptons:

%TABLE{ sort="off" tableborder="0" cellpadding="4" cellspacing="3" cellborder="0" headerbg="#D5CCB1" headercolor="#666666" databg="#FAF0D4, #FFFFFF" headerrows="2" footerrows="0"}%
| *Sample* | *P(select n hard jets)* |||
| ^ | *0* | *1* | *2* |
| ==Madgraph== | 0.137 %$\pm$% 0.003 | 0.427 %$\pm$% 0.005 | 0.435 %$\pm$% 0.005 |
| ==Alpgen== | 0.124 %$\pm$% 0.001 | 0.425 %$\pm$% 0.002 | 0.451 %$\pm$% 0.002 |
| *%${\bf P_{sel} }$%* | <b>0.124 %$\pm$% 0.001 (stat) %$\pm$% 0.013 (syst)</b> | <b>0.425 %$\pm$% 0.002 (stat) %$\pm$% 0.003 (syst)</b> | <b>0.451 %$\pm$% 0.002 (stat) %$\pm$% 0.016 (syst)</b> |


---++++ MET

In the di-leptonic channel the missing transverse energy has two main sources:
   * neutrinos emitted by the decay of the W's generated by the top decay
   * neutrinos emitted in the leptonic decay of %$\tau$%'s
The spectrum of the MET reconstructed by the ==corMetType1Icone5== algorithm, after selecting at least 2 leptons and 2 jets, is shown below:

<center>
<img src="%ATTACHURLPATH%/MET.png" width='300' />
</center>

Our MET pre-selection is defined as: <b>MET > 50 GeV </b>.


---+++ Event selection

---++++ Trigger

We require a =or= of HLT trigger bits dedicated to single leptons:
   1 ==HLT1ElectronRelaxed== 
   1 ==HLT1Electron== 
   1 ==HLT1MuonIso== 
   1 ==HLT1MuonNonIso==

---++++ Selection

The table below summarizes the event selection used for the di-leptonic channel:

%TABLE{ sort="off" tableborder="0" cellpadding="4" cellspacing="3" cellborder="0" headerbg="#D5CCB1" headercolor="#666666" databg="#FAF0D4, #FFFFFF" headerrows="2" footerrows="0" }%
| *Selection step * | *Constraints* | *Event selection* |
| %$trigger $% | ==or== of HLT trigger bits for single leptons | |
| %$\geq$% 2 leptons | %$p_{T} \geq 20 GeV/c$% ; %$\vert \eta \vert =  2.4$%  | <img src="%ATTACHURLPATH%/evsel.png" width='300' /> |
| ^ | %$\begin{cases}{ e & calo iso 6 GeV & \\ \mu & calo iso  5 GeV }\end{cases}$% | ^ |
| ^ | %$\sum_{tracks} p_{T_{i}} (\Delta R \leq 0.3) \leq 3 GeV/c$%  | ^ |
| ^ | _id_ : %$\begin{cases}{ e & tight & \\ \mu & none } \end{cases} $% | ^ |
| %$\geq$% 2 jets | %$p_{T} \geq 20 GeV/c$% ; %$\vert \eta \vert \leq 2.4$% | ^ |
| ^ | %$ emf \leq 0.95 $%  | ^ |
| ^ | %$\Delta R(jet,leptons/jets) \geq 0.5 $% | ^ |
| ^ | %$comb L \geq 0$% | ^ |
| %$\displaystyle{\not} E_{T}$% | %$\geq 50 GeV/c $% | ^ |
| op. sign leptons | %$\geq 2$% | ^ |

The table below summarizes the events surviving each selection step (computed from the ==CSA07== samples).

%TABLE{ sort="off" tableborder="0" cellpadding="4" cellspacing="3" cellborder="0" headerbg="#D5CCB1" headercolor="#666666" databg="#FAF0D4, #FFFFFF" headerrows="2" footerrows="0"}%
| *Total events accepted (L=100/pb)* |||||||||
| *Selection step* | *Physics process* ||||||||
| ^ | %$t\bar{t}\leftrightarrow e\mu$% | other %$t\bar{t}$% | %$W+jets$% | %$Z+jets$% | %$tW$% | %$WW$% | %$WZ$% | %$ZZ$% |
| _triggered_ | 2528 %$\pm$% 11 | 22048 %$\pm$% 31 | 869 %$\pm$% 0.6 %$\cdot 10^{3}$% | 169 %$\pm$% 0.2 %$\cdot 10^{3}$% | 2684 %$\pm$% 11 | 4734 %$\pm$% 12 | 1300 %$\pm$% 6 |530 %$\pm$% 4 | 
| _%$\geq 2$% leptons_ | 773 %$\pm$% 6 | 29 %$\pm$% 1 | 134 %$\pm$% 5 | 275 %$\pm$% 6 | 111 %$\pm$% 2 | 176 %$\pm$% 2 | 25.6 %$\pm$% 0.8 | 9.4 %$\pm$% 0.6 |
| _%$\geq 2$% jets_ | 492 %$\pm$% 5 | 21 %$\pm$% 1 | 13.4 %$\pm$% 0.8 | 19.4 %$\pm$% 1.4 | 31.3 %$\pm$% 0.8 | 11.4 %$\pm$% 0.6 | 2.5 %$\pm$% 0.3 | 1.1 %$\pm$% 0.2 |
| _MET_ | 350 %$\pm$% 4 | 13.4 %$\pm$% 0.8 | 5.5 %$\pm$% 0.8 | 6.8 %$\pm$% 0.7 | 21.2 %$\pm$% 0.7 | 7.6 %$\pm$% 0.5 | 1.4 %$\pm$% 0.2 | 0.4 %$\pm$% 0.1 | 
| _opposite sign_ | 346 %$\pm$% 4 | 8.3 %$\pm$% 0.6 | 1.8 %$\pm$% 0.5 | 6.4 %$\pm$% 0.7 | 20.4 %$\pm$% 0.6 | 7.5 %$\pm$% 0.5 | 0.8 %$\pm$% 0.1 | 0.3 %$\pm$% 0.1 |

After the last selection step the acceptance for the total %$t\bar{t}$% cross section is the following:

%TABLE{ sort="off" tableborder="0" cellpadding="4" cellspacing="3" cellborder="0" headerbg="#D5CCB1" headercolor="#666666" databg="#FAF0D4, #FFFFFF" headerrows="2" footerrows="0"}%
| *Sample* | *%$A_{cc} \cdot Br$% * |
| ==Madgraph (all b)== | 0.0035 %$\pm$% 0.0004 | 
| ==Madgraph (all q)== | 0.0040 %$\pm$% 0.0005 | 
| ==Alpgen== | 0.0043 %$\pm$% 0.0005 | 
| *%${\bf A_{cc} \cdot Br } \times 10^{3} $%* | <b>4.3 %$\pm$% 0.5 (stat) %$\pm$% 0.8 (syst)</b> |


---++++ Control distributions

Below we show some control distributions for the selected events, that can be used for the dilepton channel.

%TABLE{ sort="off" tableborder="0" cellpadding="4" cellspacing="3" cellborder="0" headerbg="#D5CCB1" headercolor="#666666" databg="#FAF0D4, #FFFFFF" headerrows="2" footerrows="0" columnwidths="200,200" }%
| *Jet multiplicity* | *%$H_{T}$%* |
| <img src="%ATTACHURLPATH%/jets_mult.png" width='200' /> | <img src="%ATTACHURLPATH%/HT.png" width='200' /> |
| *%${\not}E_{T}$%* | *b-tag multiplicity (==TC2==)* |
| <img src="%ATTACHURLPATH%/met.png" width='200' /> | <img src="%ATTACHURLPATH%/btagMult_TC2_data.png" width='200' /> |

---+++ Background estimation from data 

---++++ Flipped (and swapped) %$\chi^{2}$%  method (summary)

Below we explore how to use a %$\chi^{2}$% based method to subtract background from the data.  The baseline idea is to build %$\chi^{2}$% measure that, by a change variables, leaves the background invariant but not the signal. Having a %$\chi^{2}$% with such probabilities one can do the following event selection:
   1 _normal selection_:  %$\chi^{2} \leq \chi^{2}_{cut} $% - will select signal-like events with some quality criteria and some background events
   1 _flipped selection_:  %$\chi^{2}_{flip} \leq \chi^{2}_{cut} $% - will reject signal-like events but will select combinatorial background events
The %$\chi^{2}$% is well constructed if both selections yields more or less the same background events leaving the distributions of interest (kinematics, b-tagging multiplicity, etc.) invariant. 

By the procedure described above one obtains two distinct distributions %$h_{normal}(x)$% and %$h_{flipped}(x)$% depending on the event selection used. By taking the difference of these distributions the background contributions will be eliminated effectively if the requirement for the %$\chi^{2}$% is met. Then %$h_{1}(x)-h_{2}(x)$% is equivalent  to %$h(x)$% obtained from a 100% pure signal sample. 
Next we discuss the construction of the %$\chi^{2}$% having in mind these requirmentes.


---+++++  Jet + lepton kinematics based %$\chi^{2}$%

As point of departure we choose 2 distributions based on the kinematics of the jet and lepton produced at a top decay vertex: the invariant mass and the transverse mass of the pair. The distributions, for these quantities, obtained at Monte-Carlo level, are shown below:

%TABLE{ sort="off" tableborder="0" cellpadding="4" cellspacing="3" cellborder="0" headerbg="#D5CCB1" headercolor="#666666" databg="#FAF0D4, #FFFFFF" headerrows="2" footerrows="0" columnwidths="200,200" }%
| *Jet+lepton pair kinematics at Monte-Carlo level* |||
| *Invariant mass*| *Transverse mass (square root)* |
| <img src="%ATTACHURLPATH%/minv_ql_compared_gen.png" width='200' /> | <img src="%ATTACHURLPATH%/sqmt_ql_compared_gen.png" width='200' /> |
| %$\chi^{2}_{inv. mass} = ( \frac{ 81.47 - P_{\mu}(jet)P^{\mu}(lepton)^{1/2} } { 36.73 } )^{2} $% | %$\chi^{2}_{m_{T}} = ( \frac{ 10.97 - P_{\mu T}(jet)P^{\mu}_{T} (lepton)^{1/4} } { 2.19  } )^{2} $% |

For each event selected we proceed as follows:
   1 select the 2 highest %$p_{T}$% leptons as the leptons from W decay generated after the top decay;
   1 if the number of selected jets is higher than 2 than we select the 3 jets with highest combined likelihood ratio value;
   1 try all jet+lepton combinations to build the %$\chi^{2}$% matrix using the formulas from the table above;
   1 find the 2 jet+lepton pairs (excluding double-counting) that minimize the %$\chi^{2}$% matrix;
   1 repeat the computation of the matrix but flipping the lepton's momentum -  %$\chi^{2}_{flip}$%;
We compute then the following quantities for the 2 pairs that minimize the %$\chi^{2}$% matrix:
   1 %$\chi^{2} = \chi^{2}( \vec{l}_{1}; \vec{j}_{1}) + \chi^{2}( \vec{l}_{2}; \vec{j}_{2})  $% - sum;
   1 %$\chi^{2}_{flip} = \chi^{2}( - \vec{l}_{1}; \vec{j}_{1}) + \chi^{2}( -\vec{l}_{2}; \vec{j}_{2}) $% - inverting the 3-momentum of the leptons;
   1 %$\chi^{2}_{swap} = \chi^{2}( \vec{l}_{2}, \vec{j}_{1}) + \chi^{2}( \vec{l}_{1}; \vec{j}_{2}) $% - swapping the leptons in each pair;
The table below shows the distributions obtained for signal and background events for these quantities:

%TABLE{ sort="off" tableborder="0" cellpadding="4" cellspacing="3" cellborder="0" headerbg="#D5CCB1" headercolor="#666666" databg="#FAF0D4, #FFFFFF" headerrows="2" footerrows="0" columnwidths="100,200,200,200,200" }%
| *%$\chi^{2}$% distributions* |||
| *Event type* | *Kinematics used in jet+lepton pairing* ||
| ^ | Invariant mass | Transverse mass (square root) |
| Signal | <img src="%ATTACHURLPATH%/chi2_minv_signal_compared.png" width='200' /> | <img src="%ATTACHURLPATH%/chi2_mt_signal_compared.png" width='200' /> |
| Background | <img src="%ATTACHURLPATH%/chi2_minv_bckg_compared.png" width='200' /> | <img src="%ATTACHURLPATH%/chi2_mt_bckg_compared.png" width='200' /> |

The coice of the cut %$x$% for %$\chi^{2}$% is made maximizing the event yield after subtraction, that is, finding %$\max \int_{0}^{x}\chi^{2}-\chi^{2}_{flip,swap}$%. The table below summarizes the cuts chosen for %$\chi^{2}$%.

%TABLE{ sort="off" tableborder="0" cellpadding="4" cellspacing="3" cellborder="0" headerbg="#D5CCB1" headercolor="#666666" databg="#FAF0D4, #FFFFFF" headerrows="2" footerrows="0" }%
| *Selection cut for %$\chi^{2}$% distributions* |||||
|*Subtraction mode* | *Kinematics used in jet+lepton pairing* ||
| ^ | *Invariant mass* | *Transverse mass (square root)* |
| Flip | 3.35 | 2.45 |
| Swap | 2.15 | 0.75 |

We select each event using the 3 %$\chi^{2}$% defined above and the cuts defined in the previous table. For each selected event we compute the b-tag multiplicity for different values of the b-tagging discriminator. The distributions obtained for each selection are shown below. We also show the results obtained after subtracting the distribution obtained with the %$\chi^{2}_{flip}$% or %$\chi^{2}_{swap}$% selections from the one obtained with the %$\chi^{2}$% selection.

%TABLE{ sort="off" tableborder="0" cellpadding="4" cellspacing="3" cellborder="0" headerbg="#D5CCB1" headercolor="#666666" databg="#FAF0D4, #FFFFFF" headerrows="2" footerrows="0" columnwidths="100,150,150,150,150,150" }%
| *b-tag multiplicity distributions* ||||||
| *b-tag working point* | *Full data* | *After background subtraction* ||||
| ^ | ^ | *Invariant mass flip* | *Invariant mass swap* | *Transverse mass (square root) flip* | *Transverse mass (square root) swap* |
| Loose point for track counting (TC2=2.3) | <img src="%ATTACHURLPATH%/btagMult_loosept_data.png" width='150' /> | <img src="%ATTACHURLPATH%/btagMult_loosept_minv_flip.png" width='150' /> | <img src="%ATTACHURLPATH%/btagMult_loosept_minv_swap.png" width='150' /> | <img src="%ATTACHURLPATH%/btagMult_loosept_mt_flip.png" width='150' /> | <img src="%ATTACHURLPATH%/btagMult_loosept_mt_swap.png" width='150' /> |
| Medium point for track counting (TC2=5.3) | <img src="%ATTACHURLPATH%/btagMult_mediumpt_data.png" width='150' /> | <img src="%ATTACHURLPATH%/btagMult_mediumpt_minv_flip.png" width='150' /> | <img src="%ATTACHURLPATH%/btagMult_mediumpt_minv_swap.png" width='150' /> | <img src="%ATTACHURLPATH%/btagMult_mediumpt_mt_flip.png" width='150' /> | <img src="%ATTACHURLPATH%/btagMult_mediumpt_mt_swap.png" width='150' /> |

%ENDTWISTY%

Attachments

Topic attachments
I	Attachment	History	Action	Size	Date	Who
png	HT.png	r2 r1	manage	54.5 K	2008-09-02 - 10:53	PedroSilva
png	HT_2leptons.png	r1	manage	16.5 K	2008-07-07 - 10:28	PedroSilva
png	HTleadingjets.png	r1	manage	16.4 K	2008-07-07 - 10:29	PedroSilva
png	MET.png	r1	manage	19.5 K	2008-07-07 - 10:29	PedroSilva
png	btagMult_TC2_data.png	r1	manage	80.5 K	2008-09-02 - 10:56	PedroSilva
png	btagMult_loosept_data.png	r1	manage	27.7 K	2008-09-02 - 13:45	PedroSilva
png	btagMult_loosept_minv_flip.png	r2 r1	manage	26.5 K	2008-09-02 - 13:46	PedroSilva
png	btagMult_loosept_minv_swap.png	r2 r1	manage	28.7 K	2008-09-02 - 13:47	PedroSilva
png	btagMult_loosept_mt_flip.png	r2 r1	manage	28.3 K	2008-09-02 - 13:47	PedroSilva
png	btagMult_loosept_mt_swap.png	r2 r1	manage	28.1 K	2008-09-02 - 13:48	PedroSilva
png	btagMult_mediumpt_data.png	r1	manage	29.2 K	2008-09-02 - 13:48	PedroSilva
png	btagMult_mediumpt_minv_flip.png	r2 r1	manage	25.2 K	2008-09-02 - 13:49	PedroSilva
png	btagMult_mediumpt_minv_swap.png	r2 r1	manage	27.7 K	2008-09-02 - 13:50	PedroSilva
png	btagMult_mediumpt_mt_flip.png	r2 r1	manage	26.4 K	2008-09-02 - 13:50	PedroSilva
png	btagMult_mediumpt_mt_swap.png	r2 r1	manage	26.9 K	2008-09-02 - 13:51	PedroSilva
png	btag_mult_0_chi2_mT.png	r4 r3 r2 r1	manage	21.6 K	2008-07-25 - 10:09	PedroSilva
png	btag_mult_0_chi2_mT_bckg.png	r3 r2 r1	manage	22.8 K	2008-07-25 - 10:10	PedroSilva
png	btag_mult_0_chi2_minv.png	r4 r3 r2 r1	manage	20.5 K	2008-07-25 - 10:10	PedroSilva
png	btag_mult_0_chi2_minv_bckg.png	r3 r2 r1	manage	21.3 K	2008-07-25 - 10:10	PedroSilva
png	btag_mult_1_chi2_mT.png	r4 r3 r2 r1	manage	21.3 K	2008-07-25 - 10:11	PedroSilva
png	btag_mult_1_chi2_mT_bckg.png	r3 r2 r1	manage	24.2 K	2008-07-25 - 10:12	PedroSilva
png	btag_mult_1_chi2_minv.png	r4 r3 r2 r1	manage	20.7 K	2008-07-25 - 10:12	PedroSilva
png	btag_mult_1_chi2_minv_bckg.png	r4 r3 r2 r1	manage	22.3 K	2008-07-25 - 10:15	PedroSilva
png	btag_mult_2_chi2_mT.png	r4 r3 r2 r1	manage	19.9 K	2008-07-25 - 10:14	PedroSilva
png	btag_mult_2_chi2_mT_bckg.png	r3 r2 r1	manage	22.0 K	2008-07-25 - 10:15	PedroSilva
png	btag_mult_2_chi2_minv.png	r4 r3 r2 r1	manage	20.7 K	2008-07-25 - 10:14	PedroSilva
png	btag_mult_2_chi2_minv_bckg.png	r3 r2 r1	manage	20.2 K	2008-07-25 - 10:15	PedroSilva
png	btag_mult_3_chi2_mT.png	r4 r3 r2 r1	manage	18.3 K	2008-07-25 - 10:16	PedroSilva
png	btag_mult_3_chi2_mT_bckg.png	r3 r2 r1	manage	18.9 K	2008-07-25 - 10:16	PedroSilva
png	btag_mult_3_chi2_minv.png	r4 r3 r2 r1	manage	18.9 K	2008-07-25 - 10:17	PedroSilva
png	btag_mult_3_chi2_minv_bckg.png	r3 r2 r1	manage	17.7 K	2008-07-25 - 10:17	PedroSilva
png	btag_mult_loose_chi2_mT.png	r2 r1	manage	15.3 K	2008-07-25 - 10:53	PedroSilva
png	btag_mult_loose_chi2_mT_bckg.png	r2 r1	manage	14.9 K	2008-07-25 - 10:18	PedroSilva
png	btag_mult_loose_chi2_minv.png	r2 r1	manage	16.0 K	2008-07-25 - 10:34	PedroSilva
png	btag_mult_loose_chi2_minv_bckg.png	r2 r1	manage	15.4 K	2008-07-25 - 10:20	PedroSilva
png	btag_mult_medium_chi2_mT.png	r2 r1	manage	15.6 K	2008-07-25 - 10:54	PedroSilva
png	btag_mult_medium_chi2_mT_bckg.png	r2 r1	manage	15.0 K	2008-07-25 - 10:24	PedroSilva
png	btag_mult_medium_chi2_minv.png	r3 r2 r1	manage	15.4 K	2008-07-25 - 10:47	PedroSilva
png	btag_mult_medium_chi2_minv_bckg.png	r2 r1	manage	15.0 K	2008-07-25 - 10:25	PedroSilva
png	chi2_bckg_mTql.png	r3 r2 r1	manage	20.5 K	2008-07-25 - 10:25	PedroSilva
png	chi2_bckg_mTql_lin.png	r3 r2 r1	manage	20.8 K	2008-07-25 - 10:34	PedroSilva
png	chi2_bckg_minvql.png	r3 r2 r1	manage	21.5 K	2008-07-25 - 10:26	PedroSilva
png	chi2_bckg_minvql_lin.png	r3 r2 r1	manage	20.6 K	2008-07-25 - 10:26	PedroSilva
png	chi2_eff_bckg_mTql.png	r2 r1	manage	16.5 K	2008-07-25 - 10:27	PedroSilva
png	chi2_eff_bckg_minvql.png	r2 r1	manage	15.8 K	2008-07-25 - 10:29	PedroSilva
png	chi2_eff_signal_mTql.png	r2 r1	manage	15.6 K	2008-07-25 - 10:28	PedroSilva
png	chi2_eff_signal_minvql.png	r2 r1	manage	15.4 K	2008-07-25 - 10:28	PedroSilva
png	chi2_mT_compared.png	r1	manage	58.1 K	2008-09-02 - 10:55	PedroSilva
png	chi2_minv_bckg_compared.png	r1	manage	39.2 K	2008-09-02 - 12:06	PedroSilva
png	chi2_minv_signal_compared.png	r1	manage	49.9 K	2008-09-02 - 12:07	PedroSilva
png	chi2_mt_bckg_compared.png	r1	manage	36.8 K	2008-09-02 - 12:07	PedroSilva
png	chi2_mt_signal_compared.png	r1	manage	49.9 K	2008-09-02 - 12:08	PedroSilva
png	chi2_signal_mTql.png	r4 r3 r2 r1	manage	20.6 K	2008-07-25 - 10:28	PedroSilva
png	chi2_signal_mTql_lin.png	r2 r1	manage	19.8 K	2008-07-25 - 10:25	PedroSilva
png	chi2_signal_minvql.png	r4 r3 r2 r1	manage	21.3 K	2008-07-25 - 10:29	PedroSilva
png	chi2_signal_minvql_lin.png	r2 r1	manage	19.8 K	2008-07-25 - 10:29	PedroSilva
png	e_EoverP.png	r1	manage	23.1 K	2008-07-04 - 20:53	PedroSilva
png	e_caloIso.png	r2 r1	manage	24.3 K	2008-07-04 - 20:53	PedroSilva
png	e_d0sig.png	r2 r1	manage	23.8 K	2008-07-04 - 20:53	PedroSilva
png	e_emf.png	r1	manage	18.3 K	2008-07-04 - 21:47	PedroSilva
png	e_eta.png	r2 r1	manage	23.9 K	2008-07-04 - 20:54	PedroSilva
png	e_pT.png	r2 r1	manage	24.7 K	2008-07-04 - 21:37	PedroSilva
png	e_sel.png	r1	manage	15.0 K	2008-07-07 - 10:42	PedroSilva
png	e_trackerIso.png	r2 r1	manage	24.6 K	2008-07-04 - 20:54	PedroSilva
png	evSel_CSA07.png	r1	manage	15.4 K	2008-07-01 - 22:16	PedroSilva
png	event_sel.png	r2 r1	manage	17.6 K	2008-07-28 - 13:01	PedroSilva
png	evsel.png	r1	manage	17.3 K	2008-09-02 - 12:26	PedroSilva
png	jetCombLR.png	r1	manage	71.9 K	2008-09-02 - 10:50	PedroSilva
png	jetCombLR_eff.png	r1	manage	37.3 K	2008-09-02 - 10:51	PedroSilva
png	jet_btag.png	r2 r1	manage	24.9 K	2008-07-04 - 13:03	PedroSilva
png	jet_combLR.png	r2 r1	manage	21.8 K	2008-07-04 - 13:04	PedroSilva
png	jet_emf.png	r2 r1	manage	22.6 K	2008-07-04 - 13:04	PedroSilva
png	jet_eta.png	r3 r2 r1	manage	22.6 K	2008-07-04 - 21:16	PedroSilva
png	jet_eta_SandB.png	r1	manage	45.6 K	2008-09-02 - 10:45	PedroSilva
png	jet_eta_corr.png	r1	manage	58.5 K	2008-09-02 - 10:35	PedroSilva
png	jet_eta_f.png	r1	manage	36.0 K	2008-09-02 - 10:35	PedroSilva
png	jet_etdens_SandB.png	r1	manage	53.2 K	2008-09-02 - 10:46	PedroSilva
png	jet_etdens_corr.png	r1	manage	29.3 K	2008-09-02 - 10:36	PedroSilva
png	jet_etdens_f.png	r1	manage	44.0 K	2008-09-02 - 10:37	PedroSilva
png	jet_ijet_SandB.png	r1	manage	46.7 K	2008-09-02 - 10:47	PedroSilva
png	jet_ijet_corr.png	r1	manage	14.6 K	2008-09-02 - 10:46	PedroSilva
png	jet_ijet_f.png	r1	manage	38.3 K	2008-09-02 - 10:47	PedroSilva
png	jet_minDRjj.png	r2 r1	manage	20.1 K	2008-07-04 - 21:18	PedroSilva
png	jet_mindetajl_SandB.png	r1	manage	42.1 K	2008-09-02 - 10:48	PedroSilva
png	jet_mindetajl_f.png	r1	manage	43.2 K	2008-09-02 - 10:47	PedroSilva
png	jet_multiplicity.png	r2 r1	manage	15.6 K	2008-07-04 - 13:07	PedroSilva
png	jet_n90_SandB.png	r1	manage	48.1 K	2008-09-02 - 10:50	PedroSilva
png	jet_n90_corr.png	r1	manage	39.6 K	2008-09-02 - 10:49	PedroSilva
png	jet_n90_f.png	r1	manage	43.3 K	2008-09-02 - 10:49	PedroSilva
png	jet_pT.png	r3 r2 r1	manage	24.3 K	2008-07-04 - 13:41	PedroSilva
png	jet_sel.png	r1	manage	16.6 K	2008-07-07 - 10:43	PedroSilva
png	jet_selection_efficiencies.png	r1	manage	10.6 K	2008-06-30 - 10:49	PedroSilva
png	jet_selection_efficiency.png	r2 r1	manage	13.4 K	2008-06-30 - 11:21	PedroSilva
png	jet_towerET.png	r2 r1	manage	24.5 K	2008-07-04 - 13:47	PedroSilva
png	jet_trackpT.png	r2 r1	manage	25.5 K	2008-07-04 - 13:47	PedroSilva
png	jet_zMaxTowers.png	r3 r2 r1	manage	22.4 K	2008-07-04 - 21:17	PedroSilva
png	jet_zMaxTracks.png	r3 r2 r1	manage	27.2 K	2008-07-04 - 21:18	PedroSilva
png	jets_mult.png	r1	manage	31.0 K	2008-09-02 - 10:54	PedroSilva
png	likelihood_distributions.png	r1	manage	11.4 K	2008-06-30 - 10:49	PedroSilva
png	mT.png	r1	manage	16.7 K	2008-07-07 - 10:29	PedroSilva
png	mT_ql.png	r2 r1	manage	18.3 K	2008-07-21 - 18:01	PedroSilva
png	met.png	r1	manage	42.5 K	2008-09-02 - 10:54	PedroSilva
png	minv_ql.png	r2 r1	manage	16.9 K	2008-07-21 - 18:23	PedroSilva
png	minv_ql_compared_gen.png	r1	manage	42.4 K	2008-09-02 - 11:05	PedroSilva
png	mu_EoverP.png	r1	manage	17.6 K	2008-07-04 - 20:54	PedroSilva
png	mu_caloIso.png	r2 r1	manage	20.8 K	2008-07-04 - 20:55	PedroSilva
png	mu_d0sig.png	r2 r1	manage	25.5 K	2008-07-04 - 20:56	PedroSilva
png	mu_emf.png	r1	manage	21.1 K	2008-07-04 - 21:17	PedroSilva
png	mu_eta.png	r2 r1	manage	24.4 K	2008-07-04 - 21:02	PedroSilva
png	mu_pT.png	r2 r1	manage	24.8 K	2008-07-04 - 21:37	PedroSilva
png	mu_sel.png	r1	manage	16.1 K	2008-07-07 - 10:42	PedroSilva
png	mu_trackerIso.png	r2 r1	manage	22.9 K	2008-07-04 - 20:56	PedroSilva
png	observable1.png	r1	manage	18.3 K	2008-06-30 - 10:47	PedroSilva
png	observable11.png	r1	manage	23.1 K	2008-06-30 - 10:48	PedroSilva
png	observable19.png	r1	manage	19.4 K	2008-06-30 - 10:48	PedroSilva
png	observable23.png	r1	manage	22.2 K	2008-06-30 - 10:48	PedroSilva
png	observable4.png	r1	manage	19.7 K	2008-06-30 - 10:48	PedroSilva
png	sqmt_ql_compared_gen.png	r1	manage	43.1 K	2008-09-02 - 11:05	PedroSilva
png	triggerEfficiency_reco.png	r1	manage	15.7 K	2008-07-03 - 12:07	PedroSilva

Topic revision: r53 - 2008-11-19 - PedroSilva

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