Operational mode and input structure

The ALPGEN generator has the following two main running modes:

imode 1: Calculates the matrix elements on parton level for the selected process

using the ALPHA algorithm [49, 50] and produces weighted events – consider- ing phase space information and parton luminosity [47].

For this purpose there are some ”warm-up” cycles3, which are used to examine the distribution of the cross section in the phase space and among the contribut- ing subprocesses [47]. The phase space is parameterized with a multidimen- sional grid and the weight of each bin of this grid is calculated.

After this warm-up phase an optimized cross section information for phase space and subprocesses is available and serves as an input for the actual generation, where a large statistics run is executed and the final integration takes place pro- ducing the matrix element weights which are stored [47].

imode 2: Generates parton level events of unity weight which can be processed

further in MC generators providing shower evolution, hadronization and jet re- construction.

The weighted events are read in and an unweighting is carried out based on the maximum weight of the sample as well as on each event’s weight. The 4-vectors, flavour and colour flow of the events are stored again.

There is also an operational mode 0 where no weighting is available but a total cross section is calculated and histograms can be filled.

The ALPGEN program is steered by means of an input text file containing all infor- mation needed by the event generator. Table 6.3 shows an input file for the generation of a sample of weighted events with six final partons [47].

In this context the variable igrid determines the kind of grid chosen for the next in- tegration. The grid mode can be set to 0 which resets the existing grid and starts a new grid optimization, to 1 which starts a new run with the grid information of the previous warm-up run or it can be set to 2 which starts a run based on the optimized grid information from the end of the last generation run.

For the event generation several runs of ALPGEN have been performed. The random seed has been changed for each run to generate different events.

6.1. ALPGEN 43

Input Meaning

1 Run mode (imode)

sixjet Name of output file

0 Grid mode (igrid)

1000000 6 Number of events to iterate, number of iterations 100000000 Number of events for final integration

njets 6 Number of jets in final state

ih2 1 Collision type (proton-proton)

ebeam 7000 Beam energy in centre-of-mass frame

ickkw 1 Enables parton matching

Uses CKKW scale forαsin matrix element

iqopt 1 Factorization and renormalization scale

ndns 7 Parton density function (CTEQ6M)

ptjmin 20 Minimum pTGeV

for light jets

drjmin 0.699999988 Minimum∆R between two jets etajmax 2.5 Maximum η for light jets

iseed1 15515 Seed of first random number

Table 6.3: Input variables for the generation of a weighted six-parton sample. Note, that within

the ALPGEN program final state partons are referred to as jets.

6.1.3 Jet – parton matching

A very important step in the simulation of the QCD background events is the jet-parton matching, which permits the generation of inclusive samples with any jet multiplicity. A lot of events are lost during the matching procedure and thus, the optimal settings for the simulation have to be found in order to minimize both the loss of events and the time needed for generating a given number of events.

For the matching of partons from the matrix elements with jets, found after applying a parton shower [47], according to the MLM-matching [51] the following steps of event generation were done4:

Samples with weighted events were generated with imode 1, where the para- meter ickkw (see Table 6.3) had to be set to value 1 [47].

With imode 2 unweighted events were created, the ickkw=1 setting is taken again automatically.

The unweighted events were processed through a parton shower generator pro- viding shower evolution. In the case of this study PYTHIA 6.2 [13] was used 4_{For the MLM-matching the default configurations E}

Tclus

ptjmin and Rclus ∆R jet jet

for the generation of the parton shower. The events were clustered with a jet al- gorithm5and the jet-parton matching6was performed before hadronization took place.

A jet can only be matched to one parton. Events which fail the matching are rejected, where ”fail” means that the matching in either energy or direction of the parton and the parton jet fails.

In the inclusive case an event is kept if all matrix element partons are allocated to jets. If two partons match to the same jet or if one parton does not match the event is rejected [52].

For exclusive samples7 all partons have to match to jets [53]. When there is an extra jet which is not matched to any parton [52] the event is discarded.

In this context it should be mentioned that the routine UPVETO in ALPGEN (alpsho.f) has been modified. To increase the number of accepted events in exclusive mode, each rejected event was offered several times to the parton shower generator8. This way a sufficient number of QCD events could be generated within an acceptable period of time. However, this method implies that certain areas of the phase space are weighted too high. Thus, each event has to be reweighted by a factor of _{Number of offers}1 (we are grateful to [54] for pointing this out). Nevertheless, this factor can be neglected if the number of events with more than one additional offer is small, which is indeed the case (see Figure 6.3).

Further information concerning this topic can be found in Section 7.1.

rej_incl_shortened Entries 50000 Mean 2.071 RMS 2.763 Underflow 0 Overflow 0 # offers 0 2 4 6 8 10 12 14 # 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 rej_incl_shortened Entries 50000 Mean 2.071 RMS 2.763 Underflow 0 Overflow 0

Figure 6.3: Number of offers in inclusive QCD 6-jet events. The predominant fraction of

events was accepted after one iteration.

5_{The matching procedure is designed for jets which are clustered with the Cone algorithm.}

6_{For the jet-parton matching PYTHIA version 6.322 was linked as in PYTHIA 6.2 the matching} procedure is not yet implemented.

7_{In this context exclusive means that the jet multiplicity of the sample exactly corresponds to the} number of partons from the matrix element.

6.2. PYTHIA 6.2 45

The matching procedure has been carried out for the production of the QCD multi- jet background events where different samples with three to six partons9 have been created. The further processing of the background events as well as the simulation of fully hadronic t¯t events with the PYTHIA Monte Carlo generator is outlined in the following section.

6.2

PYTHIA 6.2

The PYTHIA Monte Carlo generator [13] is a multipurpose generator, which is com- monly used for the simulation of hadronic processes. It can generate detailed events which can then be compared to real data [13].

PYTHIA is a leading-order (LO) generator, which means that all events are calculated in leading and lowest order. Higher corrections can only be considered via the leading- log parton shower. Next-to-leading-order (NLO) calculations are not implemented, thus, the 4-vectors of the QCD multijet background events – which are proportional to higher orders of the strong coupling constantαs– were simulated in ALPGEN. The

matrix element for the fully hadronic t¯t events, however, is proportional toα_s2and thus, the fully hadronic t¯t events were completely simulated with PYTHIA.