## final states

The final states of the produced in an event can be grouped by the different decay channels of the W. We group the final states according to the decays of the W into light leptons (e, ), s and quarks (jets). For the special care must be taken to account for the leptonic decays which will yield final states indistinguishable from the ones resulting from W decays into light leptons. From the Particle Data Group we have the following branching ratios:

We can easily build the branching ratios for the final states of the system starting from the W and branching ratios:

This yields the following final states:

Expected rates for final states in the SM
Final state Branching ratio Value Approx.
di-leptonic (DIL)   0.065 0.002 5/81
+ lepton   0.036 0.001 3/81
lepton + jets (L+J)   0.344 0.004 28/81

## Kinematics

For the introductory study of the event kinematics we make use of the All b samples generated with Madgraph + PYTHIA6. We try to extract the signal of the top decay with two leptonic + 2 jets final states. Below you can find several plots related to the kinematics of the top decay products as given by the generator.

### 10 TeV

kinematics at 10 TeV (L=25/pb, , generator level)

#### Background modeling (data-driven)

We discuss (at Monte-Carlo level) possible strategies to model background in a data-driven way. Altough background for the dilepton channel is expected to be small () it can increase my mis-reconstruction or mis-selection of the jets coming from each top decay. We call this jet misassignment. The simplest way to test if a jet is coming from a top decay is to correlate it kinematically with a lepton from the same top decay. The plot below shows the distribution for the invariant mass of the jet+lepton pairs in two cases:

• signal - both jet and lepton come from the same top decay
• background - the jet comes from radiation (ISR/FSR) or matrix element generated parton

| | |

From the signal distribution one can build the following to test each jet+lepton:

In the equation above is the median and is the standard deviation of the signal distribution for the invariant mass of the jet+lepton pairs. We test this using 3 types of pseudo-events (or solution-like events) generated from the MC event (instead of the partons we make use of the matched kT6GenJet):

• signal events: two jet+lepton pairs correctly assigned
• 1 misassignment events: one jet+lepton pair correctly assigned and one jet+lepton pair with a jet not matched to the parton from top decay
• background or 2 misassignment events: two jet+lepton pairs where the jets are not matched to the partons from the top decay
We expect that signal pairs to have lower with respect to background pairs. The distributions of the and are shown below and are in accordance with expectation.

distributions (generator level)
single (2 entries/event) sum of single (1 entry/event)

Background can be modelled as follows:

• flip method: invert the 3 momentum of the leptons and recompute the
• swap method: retrieve jets from a different event and recompute the for the same leptons
Both these procedures should model independently combinatorial background. The plots below show the ratio between the distribution for background and for these models.

Background models (generator level)
single (2 entries/event) sum of single (1 entry/event)

We see that the flip model does not model so well the background shape for high values. However we shall use it for comparison and as an estimate for systematic uncertainty on the background model. The background level estimate is done by plotting the for the data and the for the background model and finding the ratio between the areas of each one of the distributions, as function of the cut used to compute the area. We expect that for large the distribution is background dominated and as so the ratio yields the background level of the selected events. The procedure is shown in the following table.

Background levels from assignments with different background models
Flip model Swap model
single (2 entries/event) sum of single (1 entry/event) single (2 entries/event) sum of single (1 entry/event)

### 14 TeV

Top decay kinematics
spectrum
top top childs W-boson childs
Angles of emission
wrt to b between lepton and neutrino wrt to W boost, measured in the W CM frame
charged leptons with respect to b
Invariant masses
b and lepton lepton and neutrino

From the distributions of the W decay products we conclude that the particles with have a slightly harder spectrum than the ones with because they are preferentially emitted along the hemisphere where the W is propagating to in the laboratory. This is seen in the distribution of the angle of emission of the lepton and neutrino with respect to the W propagation direction, measured in the CM frame. The angular distribution of the charged leptons is theoretically given by (see R.K. Ellis et. al., QCD and Collider Physics ):

#### Preliminary studies (2007)

• Preliminary studies (sub-page kept for reference from the prelimiary studies from Nov. - Dec. 2007)

-- PedroSilva - 14 May 2008

Topic attachments
I Attachment History Action Size Date Who Comment
png BckgLevelsChi2SumwFlipModel.png r1 manage 14.8 K 2008-11-18 - 15:56 PedroSilva
png BckgLevelsChi2SumwSwapEvModel.png r1 manage 15.4 K 2008-11-18 - 15:57 PedroSilva
png BckgLevelsChi2wFlipModel.png r1 manage 14.5 K 2008-11-18 - 15:57 PedroSilva
png BckgLevelsChi2wSwapEvModel.png r1 manage 15.2 K 2008-11-18 - 15:57 PedroSilva
png Chi2BckgModels_ratio.png r1 manage 12.9 K 2008-11-18 - 15:58 PedroSilva
png Chi2Sum.png r1 manage 17.4 K 2008-11-18 - 15:58 PedroSilva
png Chi2Sum_log.png r1 manage 15.4 K 2008-11-18 - 15:58 PedroSilva
png JetLeptonKinematics.png r1 manage 15.4 K 2008-11-18 - 16:31 PedroSilva
png JetLeptonKinematics_SoverSpB.png r1 manage 14.6 K 2008-11-18 - 16:31 PedroSilva
png SingleChi2.png r1 manage 14.2 K 2008-11-18 - 15:59 PedroSilva
png SingleChi2_log.png r1 manage 12.6 K 2008-11-18 - 15:59 PedroSilva
png SumChi2BckgModels_ratio.png r1 manage 13.5 K 2008-11-18 - 16:08 PedroSilva
png dR_bl.png r1 manage 8.4 K 2008-05-29 - 16:00 PedroSilva
png deta_bl.png r1 manage 14.2 K 2008-05-29 - 15:59 PedroSilva
png dphi_bl.png r1 manage 12.4 K 2008-05-29 - 19:26 PedroSilva
png s_bl.png r2 r1 manage 10.2 K 2008-05-29 - 16:00 PedroSilva
png s_lnu.png r1 manage 17.4 K 2008-05-14 - 15:56 PedroSilva
png theta_lnu.png r1 manage 11.1 K 2008-05-14 - 15:56 PedroSilva
png theta_tob.png r1 manage 14.3 K 2008-05-14 - 15:56 PedroSilva
png theta_tow_cm.png r1 manage 18.8 K 2008-05-14 - 15:57 PedroSilva
png top_childs_pT.png r1 manage 17.0 K 2008-05-14 - 15:57 PedroSilva
png top_eta.png r1 manage 19.8 K 2008-11-10 - 11:44 PedroSilva
png top_eta_comp.png r1 manage 10.5 K 2008-11-10 - 11:46 PedroSilva
png top_pT.png r1 manage 13.5 K 2008-05-14 - 15:57 PedroSilva
png top_pt.png r1 manage 16.3 K 2008-11-10 - 11:46 PedroSilva
png top_pt_comp.png r1 manage 10.0 K 2008-11-10 - 11:45 PedroSilva
png ttbar_deta.png r1 manage 18.5 K 2008-11-10 - 11:47 PedroSilva
png ttbar_deta_comp.png r1 manage 11.0 K 2008-11-10 - 11:48 PedroSilva
png ttbar_dphi.png r1 manage 16.8 K 2008-11-10 - 11:49 PedroSilva
png ttbar_dphi_comp.png r1 manage 8.9 K 2008-11-10 - 11:52 PedroSilva
png ttbar_minv.png r1 manage 17.0 K 2008-11-10 - 11:50 PedroSilva
png ttbar_minv_comp.png r1 manage 10.4 K 2008-11-10 - 11:52 PedroSilva
png w_childs_pT.png r1 manage 16.4 K 2008-05-14 - 15:57 PedroSilva
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