--Barison 14:10, 12 Oct 2005 (MET DST)

Chapter 5 Event Generation and Reconstruction

The startup of the LHC machine will take place in April 2007, and few months will pass before a data sample is ready for analysis. In the meantime, simulations of the physics processes can be used to tune the physical analysis and forecast the results. Simulation software is composed by a chain of different elements:

Monte Carlo Event Generators, which compute the matrix elements of the partonic scattering at fixed order;
Parton Shower Algorithms, which hadronise the scattered partons and simulate the emission of soft gluons and photons in the non-perturbative regime;
Detector Simulations, which reproduce the effects of the finite resolution of the detector instrumentation on the observables. Detector simulations are of two types:
- Fast Detector Simulations, where the momenta of the particles are convoluted with parametrised smearing functions;
- Full Detector Simulations, where the interaction of particles with the detector is simulated at the microscopic scale --- resulting in, for example, realistic electromagnetic shower shapes, multiple scattering, etc.

The ATLAS collaboration organizes every two years a conference to discuss issues and results of the prospective physics analyses. In preparation for the 2005 conference, held in Rome, a sample of five million events was produced with full detector simulation. As member of the ATLAS Top Physics Working Group, I had the task to generate a fraction of this sample, dedicated to single top production. In this Chapter I will outline the software framework for the simulation of physics processes in ATLAS, the systematic uncertainties in the use of fixed-order Monte Carlo generators, and the data sample for the ATLAS Physics Workshop 2005.

5.1 Monte Carlo Generators

5.1.1 TopReX

The Monte Carlo generator was written with the specific intent of treating top production and decay []. provides production processes not implemented in popular Monte Carlo packages such as Pythia or Herwig. In particular, implements both the Feynman diagrams associated with W-gluon fusion and takes into account the spin polarization of the decay products of the top quark.

As alread explained in Section 1.3.2, the W-gluon fusion channel is described by the interference of LO and NLO diagrams. The NLO diagram features an extra b quark in the final state; however, this extra quark could be produced at LO by initial state radiation. In order to avoid the double-counting of events and produce a cross-section consistent with theory, introduces two cut-off parameters k₀~20 GeV and p₀~10 GeV. For each simulated event, the program generates the transverse momentum k_T of the light quark in the final state. If k_T<k₀, the 2→2 process is used; otherwise the 2→3 process is used. For the generated event to be accepted, a check is performed on the transverse momentum p_T(b) of the b quark. In the 2→2 process, the b is produced by soft gluon splitting, so it is required that p_T(b)<p₀. In the 2→3 process it is required that p_T(b)>p₀.

The resulting sample is the sum of the two contributions []:

N(pp→ tX)_t-channel	=	N^{2→ 2}(pp→ tqb; k_T<k₀; p_T(b)<p₀)
	+	N^{2→ 3}(pp→ tqb; k_T>k₀; p_T(b)>p₀)

The spectrum of the extra b obtained by using the cut-offs is shown in Figure 5.1.

The hadronisation of the partons generated by is handled by an interface with Pythia.

Figure 5.1: p_T spectrum of the additional b in the LO 2→2 (dotted curve) and the NLO 2→3 (dashed curve) W-gluon process. The full line shows the spectrum generated by mixing the 2→2 spectrum below the 10 GeV threshold with the 2→3 spectrum above the threshold [].

5.1.2 Comparison with NLO calculation

The output of generators needs to be checked with theory in order to validate the Monte Carlo simulation. In a paper from Z.Sullivan, the events generated with Pythia and were checked against the NLO calculations of the ZTOP package [97]. Since both MC generators implement only the LO diagram for t-channel single top production, the p_T spectrum of the additional b in the generated sample is softer than the spectrum predicted by the NLO calculation.

Using the same ZTOP results, I performed a comparison between the NLO calculations and the results. First of all, I ran ZTOP, generating the differential distributions for the t-channel. The selected set parton distribution functions was CTEQ5M and the factorization and renormalization scales were set to Q² for light quarks and Q²+m_t² for the top quark. The final state included the top quark --- ZTOP does not simulate top decay --- and at least one reconstructed jet with p_T>10 GeV, |h|<5.

The sample was composed of 20000 events generated with the CTEQ5L PDF (which is better suited for LO distributions), and with factorization and renormalization scales set to m_t. Since the cross-section calculated by ZTOP is for kT jets, not particles, I ran a jet algorithm on the particle list output by +Pythia. I used a kT algorithm with cut parameter D=0.54 --- which is equivalent to a cone of R=0.4 for cone algorithms --- and with a energy threshold of 10 GeV. Then, I proceeded to identify the jets in the list: a jet was tagged as a b-jet if a b-quark from the MC truth was found inside the jet cone. The b-jet from the top decay was discarded, and the p_T spectra of the additional b-jet and the light jet were compared with the ZTOP results.

To proceed with the comparison, first of all a multiplying factor was applied to all histograms, in order to obtain the same cross-section between and ZTOP:

K=

s_ZTOP

s_TopReX

=

247.6 pb

251.4 pb

~0.985

The p_T and h distributions of the generated top quark are shown in Figures 5.2 and 5.3. The distributions agree with the ZTOP previsions.

Figure 5.2: p_T distribution of the top quark by NLO predictions (grey) and . The histograms are normalized to the NLO cross-section.

Figure 5.3: h distribution of the top quark by NLO predictions (grey) and . The histograms are normalized to the NLO cross-section.

The p_T spectra for light jets and b-jets are shown respectively in Figures 5.4 and 5.5. The light jet spectrum is roughly consistent with the NLO predictions, but the b-jet spectrum has an integrated cross-section which is considerably considerably lower than the NLO predictions. The cross-section for b-jets with p_T>50 GeV is 26% lower than the corresponding cross-section from NLO; after applying a scaling factor to compensate for the different cross-section, the eta spectrum is compatible with the NLO predictions. Thus, the presence of an additional b-jet in the data sample is underestimated. Since the selection cuts for the t-channel sample require the presence of only one b-jet with p_T>50 GeV (see Section ??), the selection efficiency from real data could be lower than from the MC sample.

Figure 5.4: p_T distribution of light jets by NLO predictions (grey) and . The histograms are normalized to the NLO cross-section.

p_T distribution of b-jets by NLO predictions (grey) and . The histograms are normalized to the NLO cross-section.

Figure 5.5:

5.2 Parton Shower Algorithms

Pythia. Brief description of the string model

5.3 Fast simulation

5.3.1 ATLFAST

Atlfast algorithm chain:

Cell Maker and Clu. All particles are divided in cells of granularity 0.1×0.1 for the barrel and 0.2×0.2 for the endcap. The f angle is smeared according to two parametrizations of the magnetic fields in the barrel and in the endcap. All cells with E_t>1.5 GeV are selected as cluster seeds and listed in descending order. For each seed, all cells inside a cone of D R<0.4 belong to the cluster. A cluster is accepted if the total E_t is higher than 10 GeV and the cells used are removed from the list; thus jet energy sharing is not implemented. Atlfast can also be instr ucted to use kT or sliding window algorithms.
Isolator. The isolator algorithm associates each reconstructed cluster with a particle of the MC truth. The associated particle must have |h|<2.5, p_t>10 GeV and with a separation D R<0.1 from the cluster baricenter. The particle is declared as isolated if the associated cluster is atleast D R>0.4 away from the closest reconstructed cluster and the transverse energy deposited in a cone D R<0.2 around the particle is lower than 10 GeV. Photons, Electron and Muons follow the same procedure. Muons have a lower p_T threshold (6 GeV) and, in addition, receive a p_T smearing. The smearing in the Inner Detector is given by

δ p_T

p_T
=5×10^-4⊕0.012
The smearing in the Muon Spectrometer is not documented.
Jet Maker. Unidentified clusters are treated as hadron jets and smeared with the following (low-luminosity):

δ E

E
=

0.5

E
⊕0.03 (barrel)

δ E

E
=

1.0

E
⊕0.07 (endcap)
For high luminosity, a pile-up term of 7.5 GeV E_t is added to non-empty cells. Non-isolated muons are added to jet energy too. If the total E_t exceeds 15 GeV, the hadron jet is accepted.
Missing E_t. The total E_t of the event is computed by summing the transverse momenta of identified isolated particles, hadronic jets, non-isolated muons and unused clusters and cells. The missing E_t is obtained by balancing the total E_t. Thus it contains neutrinos, SUSY particles (if any) and muons outside the detector acceptance. Since by construction ATLFAST does not add pileup to empty cells, the Missing energy might be a little higher than the true value. .
Atlfast-B. This algorithm calibrates the jet energy of b-jets, on the premise that b-jets have usually a lower energy than the originating b-quark, because of the presence of leptons (and hence neutrinos) in the decay chain. This algorithm, moreover, provides a realistic b-tagging and c-tagging efficiency, as opposed to the next to 100% efficiency of the standard ATLFAST algorithm.

5.4 Full Simulation

(Very brief, just an outline on GEANT4 and the Rome Layout)

5.5 ATHENA and the ATLAS Data Model

File:Atlas EDM.gif

Figure 5.6:

What do I find inside an AOD?

5.6 The Rome Data Challenge

5 Million events of various nature. Single top samples:

100k W-gluon fusion
40k+40k Associated production
60k s-channel
25k+25k W-gluon fusion with FCNC decays

W+2jets
W+3jets
W+4jets
Wbb
tt MC@NLO

Chapter V

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