Monte Carlo Samples

5.2 Monte Carlo Samples

5.2.1 Monte Carlo generator and samples The ALPGEN version 2.05 [52] fixed-order matrix element (FOME) generator was used to generate

signal t¯ t samples and background W +jets and Z+jets samples. The background samples consist of vector bosons with light partons (W +Nlp, Z+Nlp) and heavy flavors (W c¯ c, W b¯b, Zc¯ c, Zb¯b). The factorization scale chosen was

(5.1) where V refers to the vector boson type (W or Z). The MLM jet-matching algorithm was applied

Q 2 =M 2 V +p 2 T (V )

during sample generation [53, 54]. Pythia version 6.323 [55] is then used to add parton-level shower and hadronization. Since Pythia can add a b¯b and/or c¯ c pair during the showering and hadronization processes, events in which Pythia has added b¯b and/or c¯ c pair are removed. This is important to ensure that all heavy flavor pairs are coming from ALPGEN.

The decays of tau leptons and B mesons are not handled properly by Pythia. The TAUOLA version 2.5 library [56] is used to decay tau leptons. This library offers the following advanced features in simulating tau decays: availability of about twenty tau lepton decay modes, electroweak radiative corrections in leptonic decays, and precise treatment of hadronic decay matrix elements. The EvtGen version 00-00-17 library [57] is used to decay B hadrons. The library includes CP −violating decay modes and provides better simulation of angular correlation of B hadron decay products in cascade decays.

5.2.2 Heavy flavor K-factor Higher-order calculation shows that the ratio of heavy-flavor jets to light flavor jets in W +jets and

Z+jets production changed compared to leading-order calculation [58, 59]. We correct the heavy flavor to light flavor ratio in ALPGEN W +jets and Z+jets Monte Carlo by applying a relative scale factor to W/Z + b¯b and W/Z + c¯ c samples before combining them with W/Z + N lp sample.

The factor for W +jets sample was determined by members of the DØ collaboration [60] to be

(5.2) For Z+jets sample, we refer to ZH → eeb¯b and ZH → µµb¯b analyses [61] which used the value

K HF = 1.17 ± 0.18.

K HF = 1.1 ± 0.17.

5.2.3 Trigger efficiency corrections in Monte Carlo The trigger efficiency corrections for Monte Carlo samples are done by weighting each Monte Carlo

event with its probability to fire any of the triggers used during the data taking period. Efficiency turn-on curves are measured from unbiased data to determine the efficiency of physics objects to fire triggers at all trigger levels. For this analysis the relevant physics objects are the muon and jet, and the relevant triggers are muon triggers and jet triggers.

The muon and jet triggers are independent of each other, therefore the probability of an event to fire a muon+jets trigger can be written as the product of the probability to fire each trigger separately, that is:

(5.4) The efficiency of muons(jets) to fire the three-level trigger system can be broken down into products

P (µ + jets trigger) = P (µ trigger) × P (jet trigger)

of the probabilities of the muons(jets) to fire the muon(jets) trigger at each trigger level, P (µ trigger) = P (L1 µ) × P (L2 µ|L1 µ) × P (L3 µ|L2 µ & L1 µ)

(5.6) where P (X|Y ) denotes the probability of X given a condition Y .

P (jet trigger) = P (L1 jet) × P (L2 jet|L1 jet) × P (L3 jet|L2 jet & L1 jet)

For each Monte Carlo event that passes the selection cuts, we calculate the probabilities that the event will fire each trigger listed in Table 5.2. The trigger probabilities for all triggers are then averaged by weighting the probability for each trigger by its respective recorded luminosity. The final probability for each Monte Carlo event is the probability that the event will fire any of the listed triggers during the data taking period. The value of the final trigger efficiency is about