# Event Weights for Monte Carlo Samples

## Introduction to Event Weights

When a Monte Carlo (MC) sample is generated the size of the sample is determined by requesting the generation of a certain number of events. The cross section of the sample is a fixed quantity dependent on the process generated. Since number of events, sample size, and luminosity are related according to σ = NEvents/L, the luminosity of a MC sample varies according to the number of events generated and the cross section of the process.

The amount of data collected in an experiment is expressed in terms of luminosity since this quantity can be determined from known properties of the colliding beams. In order to perform a simulation of the data at given luminosity, it is necessary to weight the MC sample to correspond to this luminosity. This allows, for example, to predict the number of top events that will be produced in an amount of data corresponding to that luminosity.

The weighting of the MC can be expressed as N = WN0, where N is the number of weighted events, N0 is the number of events in the original sample, and W is the weight. The weight must be a ratio of the desired luminsoity to the original luminosity of the sample, W = L/L0. Expressing the original luminosity in terms of cross section and number of events,

W = σL/N0.

All histograms are weighted by multiplying the quantity used to fill the histogram (N, pT, eta, etc) by the event weight. In the MSU analysis code, the actual weighting takes place in the method myTH1F::Fill().

### NLO vs. LO

All the MC samples were genereated using a LO cross section prediction. For the single top (s, t, and Wt channels) ttbar processes, the cross sections are known to NLO. In this case the weight is scaled by the ratio of NLO to LO cross sections

WNLO = WNLO / σLO ) = σNLOL/N0

### Branching Ratio

If the MC samples were genereated to produce a certain final state, for example ttbar -> dileptons, then the branching ratio, BR, for that final state must be included in the weight calculation;

W = BRσL/N0

## Sources of information

The information needed to calculate event weights were collected from the following places:

## Weights for v15.5.1

We use weights from this website: https://twiki.cern.ch/twiki/bin/view/AtlasProtected/TopReferences10TeV. Note that the website recommendation is to multiply the cross-section by a factor that includes the k-factor as well as other factors.

## Table of Weights

The following tables list the properties of the MC samples used in the Single Top analysis. The weights for the single top channels (s, t, and Wt) and ttbar channels were calculated using the NLO cross section.

For v13030, the column σ shows σ multiplied by the branching ratio.

### Table for v13030

Run Sample Generator Matrix Element σ (pb) BR NEvents Weight
5200 ttbar->no_had Herwig+Jimmy MC@NLO 833.0 0.555 36708.0 1.25944
5500 Wt Pythia acerMC 66.0 0.333 4000.0 0.54945
5501 s-channel Phythia acerMC 10.65 0.333 10000.0 0.03546
5502 t-channel Phythia acerMC 246.0 0.333 38950.0 0.21032
6410 W->enu+2Jets Herwig+Jimmy Alpgen 826.0 1.0 208000.0 0.39712
6411 W->enu+3Jets Herwig+Jimmy Alpgen 239.0 1.0 43150.0 0.55388
6412 W->enu+4Jets Herwig+Jimmy Alpgen 67.4 1.0 36000.0 0.18722
6413 W->enu+5Jets Herwig+Jimmy Alpgen 24.0 1.0 3000.0 0.80000
6414 W->munu+2Jets Herwig+Jimmy Alpgen 826.0 1.0 212300.0 0.38907
6415 W->munu+3Jets Herwig+Jimmy Alpgen 236.0 1.0 17100.0 1.38012
6416 W->munu+4Jets Herwig+Jimmy Alpgen 68.3 1.0 51950.0 0.13147
6417 W->munu+5Jets Herwig+Jimmy Alpgen 24.3 1.0 0.0 1.00000

In the 121403 MC version, run 1206, the W+Jets weights include branching ratio, alpgen matching efficiency and filtering efficiency.

### Table for Version 121403, weights calculated for 100pb-1

Run Sample Generator Version Matrix_Ele σLO(pb) σNLO(pb) BR NEvents Weight
5200 ttbar->no_had Herwig+Jimmy 12000601 MC@NLO 830.63 833.0 0.555 401336.0 0.11519
52001 ttbar->lep+jets Herwig+Jimmy 12000601 MC@NLO 830.63 833.0 0.444 321720.0 0.11496
52002 ttbar->dilep Herwig+Jimmy 12000601 MC@NLO 830.63 833.0 0.111 79616.0 0.11614
5500 Wt Pythia 12000601 acerMC 80.1 66.0 0.333 48350.0 0.04546
5501 s-channel Phythia 12000601 acerMC 9.9 10.65 0.333 48300.0 0.00734
5502 t-channel Phythia 12000601 acerMC 243.9 246.6 0.333 41428.68 0.19821
6210 W+0Jets Herwig+Jimmy 12000604 Alpgen 731.62 0.0 0.0 364950.0 0.20047
6211 W+1Jets Herwig+Jimmy 12000604 Alpgen 6249.0 0.0 0.0 896949.0 0.69670
6212 W+2Jets Herwig+Jimmy 12000604 Alpgen 2021.45 0.0 0.0 630834.0 0.32044
6213 W+3Jets Herwig+Jimmy 12000604 Alpgen 818.0 0.0 0.0 133046.0 0.61482

### Table for Version 1214

Run Sample Generator Version Matrix_Ele σLO(pb) σNLO(pb) NEvents Lumi(pb-1) Weight
005500 Wt Pythia 11000505 acerMC - 26.7 22.0 1.00E+04 3.75E+002 72600 2.197253
005501 s-channel Phythia 11004209 acerMC - 3.3 3.55 1.00E+04 3.03E+003 82950 0.355036
005502 t-channel Phythia 11004207 acerMC - 81.3 82.2 1.00E+04 1.23E+002 8400 8.220082
005223 W->ev(2parton_exe) Herwig+Jimmy 11004206 ALPGEN - 504 - 1.50E+04 8.24E+003 4000 0.121359
005224 W->ev(3parton_exe) Herwig+Jimmy 11004206 ALPGEN - 122 - 1.50E+04 6.58E+003 15200 0.151976
005225 W->ev(4parton_exe) Herwig+Jimmy 11004206 ALPGEN - 28.4 - 1.50E+04 16.3E+003 15200 0.061350
005226 W->ev(5patron_inc) Hewwig+Jimmy 11004206 ALPGEN - 6.1 - 1.50E+04 10.0E+003 7000 0.100000
008203 W->mv(3parton_exe) Herwig+Jimmy 11004206 ALPGEN - 122 - 1.50E+04 7.91E+003 5000 0.126422
008204 W->mv(4parton_exe) Herwig+Jimmy 11004206 ALPGEN - 28.4 - 1.50E+04 16.2E+003 18050 0.061728
005204 ttbar->all_had Herwig+Jimmy 11004206 MC@NLO 0.46 369 - 2.00E+05 5.42E+002 77600 1.845018
005001 minBias Phythia 11004103 - - 80 - 5.00E+05 6.25E-06 5000 160000000.0
005200 ttbar->no_had Herwig+Jimmy 11000505 MC@NLO 0.54 461 - 5.00E+05 1.08E+003 598700 0.925926
005205 ttbar->lep+jet Pythia 11004206 acerMC - 460 - 5.00E+05 - 434650 -

### Table for Version 1213

File Sample Cross Section Branching Ratio Luminosity(pb-1) MC Events Weight
5200 t-tbar -> lepton + jets and dilepton 872.8 0.555 100 592300 0.08178356
5200 t-tbar -> dilepton 872.8 0.111 100 117516 0.08244052
5200 t-bar -> lepton + jets 872.8 0.444 100 474784 0.08162095
5500 Wt 62.1 1/3 100 48350 0.0428128
5501 s-channel (tb) 10.65 1/3 100 48050 0.0073881
5502 t-channel (tq) 246.6 1/3 100 43950 0.1870307

-- PatRyan - 19 Feb 2007, -- JennyHolzbauer - 01 Aug 2007-- JennyHolzbauer - 30 Jan 2008
Topic revision: r23 - 21 Nov 2009, JennyHolzbauer

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