Given the complexity of the experimental setup, precise event simulations play an essen-tial role in understanding the data collected by ATLAS. The simulation is carried out by means of Monte Carlo (MC) techniques, where the entire available knowledge of the physics processes involved as well as the experiment components and its geometry are taken into account. The purpose of the simulation is to reproduce the recorded outcome of proton proton collisions in the most possibly realistic way. Such detailed prediction is necessary in order to determine the selection efficiencies and assess the discovery potential of ATLAS in terms of the most important physics signatures, design the most suitable trigger system and optimise the algorithms for the offline reconstruction of physics events. The common ATLAS framework called Athena [A+05] is used, among many purposes, to embed in a shared and centrally controlled fashion the canonical three steps of the event simulation procedure: Event Generation, Detector Simulation and Event Reconstruction.
A brief description of the simulation steps is given in the following, while the reconstruction of physics objects in the events is described in detail in Sec.3.5. In order to assess the impact of systematic effects related to the choice of the PDF set used for the generation of events, the technique of PDF re-weighting described in Sec. 7.1.1 is used.
3.3.1. Event Generation
The first phase of the event generation process is performed using physics event generators.
The generators simulate the collisions of protons at the centre-of-mass energy of 7 TeV. The input needed by the generator generally contains the design beam energy, the PDFs set that fixes the proton composition, the tables of decay probabilities for all known particles that enter the simulation, the specific particle interaction models and eventually the particle composition of the desired final state.
Generators are able to produce lists of simulated particles emerging from the interac-tion region for any desired physics interacinterac-tion model provided to the program. The out-put is a collection of events which serve as inout-put to the following simulation step. For each particle object generated in the event it is then possible to retrieve the particle-type, the electric charge, the initial vertex position, as well as the four-momentum vectors. To simulate high energy physics processes, several Monte Carlo packages are available that implement either leading or next-to-leading order terms of the matrix elements. The op-timal choice of the specific generator to be used for the production of each physics pro-cess is driven by their ability to describe the data. For this reason several MC pack-ages with different generating procedures are used to produce the simulations, in
accor-dance with the studies performed inside the entire ATLAS collaboration. Monte Carlo packages used for this analysis that simulate physics interactions at leading order preci-sion are AcerMC [KRW04] and Alpgen [MMP+03],Pythia [SMS06, A+11b] and Her-wig[C+01], while for next-to-leading order precision simulations the processes are generated with Mc@NLO [Nas04, LGH+10, FW02] and PowHeg [FNO07]. The final states gener-ated with MC generators include the effect of QCD corrections at perturbative level only.
This is done by fixing the QCD renormalisation scale cutoff parameter, ΛQCD. Its setting is crucial since it affects directly the hard parton composition of the initial and final state radiation (I/FSR) in the event.
Event generators of short distance processes do not reproduce the effects of hadronisation and formation of the underlying event (UE), for which no unique model based on first prin-ciples is available. Hadronisation and UE formation are non-perturbative QCD phenomena that occur on a timescale that is longer than the high energy process and much shorter than the time needed for the final state particles to reach detection. For this reason the event generation is carried out in a modular way, and the final states of the fundamental interaction simulation of the above must be interfaced with further packages, dedicated to correctly simulate the parton fragmentation and their hadronisation. The lists of physics objects resulting at the end of the event generation process are stored in the HepMC event record.
Hadronisation Models
Hadronisation models are used to reproduce the population of particle jets and their stable hadrons composition that is seen in real data. This simulation step involves the physics of the so called parton showering (PS) processes. Two main algorithms were developed in the latest years to reproduce the parton fragmentation and are interfaced with the event generators used to simulate ATLAS data. These are the Lund string and the Cluster, which are implemented in the Pythia and Herwig event generators respectively. 3 The two models, which differ in the parametrisation of the form factors of the radiation emission are equally reliable and developed independently from each other. For this reason a comparison between the two is used later to assess the systematic effects arising from the approximations and the assumptions of the chosen hadronisation model.
After the generation of leading order hard processes, higher order effects are added in the form of a parton shower, where simulated parton objects are allowed to subsequently split into pairs of other partons, until a cut-off energy threshold is reached. The shower components are then grouped into colour-singlets to form the hadrons. By means of the decay tables short-lived hadrons are allowed to decay according to the known rates. To
3ThePythiaandHerwigtools are software packages. These can be interfaced with the other generators in order to simulate the parton shower, but they also include private matrix event generators, which are often used for the simulation of Multijet events.
reproduce as closely as possible the experimental results, the hadronisation models and their parameters are tuned to ATLAS data that were collected at the beginning of the collisions phase and in beam conditions that were as similar as possible to the periods when physics data was being recorded.
Underlying Event
In a last step the underlying event structure is adjusted with the aid of dedicated tools such as the Jimmy [BFS96]. Objects that are not produced either in the “hard” event or in the hadronisation phase are added to the event. These can be originated in the interactions undergone by beam remnants and as a result of additional interactions between the partons that do not represent initial states to the “hard” event.
Pile-up
To describe the effect of pile-up events in the simulated samples, minimum bias events generated with Pythia are added to the initial events at the digitisation step before the reconstruction.
3.3.2. Detector Simulation And Digitisation
For each generated event, the HepMCparticle lists are passed through the ATLAS detector simulation. At this step, the interaction of each particle with the traversed material is simulated within the Geant4[A+03b] framework. For simulating the particle propagation, detailed information on the detector geometry, matter composition across the subdetectors layers and the most precise map of the embedded magnetic field are used. During this step, the decay of long lived particles is taken into account. As a very last step, the simulated events are digitised simulating the subdetectors response and readout. The simulated events are recorded in raw data objects (RDO) format.
The lengthy full simulation (FS) chain described so far is applied to all samples necessary to the main physics analyses inside ATLAS. For assessing the impact of systematics arising from the uncertainties related to the intrinsic limits of physics modelling, a comparison between samples simulated with different packages is carried out. In order to reduce the usage of computing resources, the alternative and faster simulation chain available within the Athena framework AtlFastII [Luk12], is used for the production for the comparison samples. These tools make use of simplified parametrisations and smearing routines, and adopt detailed look-up tables of average detector response that reduce very sensibly the size and the computation time of the samples. The data description provided by theAtlFastII simulation has been shown to be in very good agreement with the one provided by the full simulation package [A+12l, Bil12].