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For the simulation of the interactions of the particles created during the collision with the detector matter, Geant4 is used. Geant4 (Geometry and Tracking, [56, 57]) is a

library that is widely used even outside of particle physics.

It provides the ability to implement the geometry of a detector as well as many different processes for the interaction of particles with matter. These include ionization by MIP-like particles as well as electromagnetic and hadronic cascades.

The simulation itself is performed by tracking the individual particles from one step to another throughout the detector material. At each step a list of possible interactions with the matter is generated and one of them is randomly chosen based on their respective cross sections. If daughter particles are created, they in turn are added to the list of tracked particles. In order to avoid infrared divergences and limit the computing time to a feasible amount, all particles are only tracked down until their energy drops below a certain threshold. Particles below this threshold will deposit their energy in an instant at their current position and hence will not be tracked any longer. In Geant4 these cuts are implemented as a minimal range cut the particles

have to be able to travel in that material. Thus by adjusting this cut the accuracy of the simulation can be exchanged for computing time, as during most steps secondary mostly low energetic particles are created. After all tracked particles dropped below the range cut threshold or have left the considered volume, the simulation of the single event is stopped. At this point Geant4 provides information of how much energy was

deposited in which detector volume.

While the simulation of electromagnetic processes is well understood and can reach accuracies on the sub-percent level, hadronic cascades are more challenging as they involve QCD processes and nuclear reactions. Due to the running of the strong coupling constantαs, only high energy QCD processes can be calculated (asymptotic freedom). At lower energies, however, the underlying perturbation theory collapses.

Therefore, various theoretical and data parametrized models are used instead. These are only valid for certain energy ranges and types of particles and cover only specific subsets of processes during the collision. These range from energy exchange, including the creation of new particles, de-excitation and evaporation of excited nuclei over to the tracking of low energy neutrons.

The most important models are [58–60]:

Parametrized Models The low energy parametrized (LEP) respectively high en-

ergy parametrized (HEP) data set. These are the only data driven models in

Geant4 and are essentially an adaptation of the GEISHA model [61] used in Geant3.

Parton String Models These models are valid for higher energies (E > 10 GeV),

where the interaction is mainly between the incoming particle and the partons of one of the nucleons of the struck nucleus. These models build a string between two quarks, one of the struck nucleon and one from the incident particle. While enough energy is left, new quark-antiquark pairs are created from the string. In

Geant4 two different models are available which differ in the way of string

formation and splitting. One is the Quark-Gluon-String (QGS, [62]) model, which uses Pomerons to mediate the scattering process. The other one is the Fritiof (FTF, [63]) model, which describes the diffractive hadronic interactions of the

projectile with a nucleon via momentum exchange.

Intra-nuclear Cascade Models These models are valid for collisions at lower energy

(E < 10 GeV), where the substructure of the nucleons is neglected and the

interaction forms an intra-nuclear cascade. Within the Geant4 models the

nucleus is treated as a Fermi gas of nucleons, where all nucleons fill all possible energy states under the consideration of the Pauli exclusion principle. Collisions lead to excitations, which are handled by the specific models. In Geant4 two

different models exist: The Bertini cascade (BERT, [64]) differs from the binary cascade (BIC, [65]) in their modeling of the Fermi-gas and thus the creation of the particles. The Bertini cascade includes a complete de-excitation description, whereas the Binary cascade leaves the de-excitation step to an external model.

Precompound A model for the de-excitation of the nucleus. Used for the residual

excited nuclei of models such as FTF and BIC.

High Precision Neutron Tracking At low energies (E < 20 MeV) the thermal

motion becomes relevant for the cross-section and angular distribution calculations. The high precision (HP) neutron tracking model is based on experimental data and simulates the neutron capture. This model is very CPU intensive and thus only used if the low energy neutron part is relevant.

As the different models are only valid for specific energy regions, several models are combined to a physics list covering a larger energy range. At the overlapping regions a linear interpolation between the two lists in question is performed by randomly choosing one of the two models on an event-by-event basis.

LHEP A combination of the LEP and the HEP models, with a transition region from 25 GeV to 50 GeV. It is known to be less accurate than newer models, but is included here to provide an indication of the progress achieved with more recent codes.

QGSP BERT Uses the QGS model followed by the Precompound (P) and evaporation

model for the de-excitation of nuclei for energies above 12 GeV. The Bertini cascade is used for energies below 9.9 GeV. In the intermediate region between those two models in the range from 9.5 GeV to 25 GeV the LEP model is used.

FTFP BERT Uses the FTF model followed by a Reggeon cascade and the Precom-

pound evaporation (P) model for energies higher than 4 GeV. Below 5 GeV the Bertini cascade is used. This physics list uses the same cross section model as the QGSP BERT list.

QGS BIC This list is identical to QGSP BERT for energies above 12 GeV. However,

for lower energies the Bertini cascade is replaced by a combination of the LEP model and the binary cascade (BIC), with a transition between 1.2 GeV and 1.3 GeV.

QGSP BERT HP Same list as QGSP BERT, but uses the high precision neutron

tracking in addition.

QBBC A combination of various models depending on the energy and particle type. For pions BERT is used below 5 GeV, FTFP is used in the range of 4₋25 GeV and finally QGSP is used above 12.5 GeV. It has its own implementation of low energy neutron tracking which is similar to the high precision model (HP), but significantly faster.

The simulation of hadronic showers based on the physics lists above is in reasonable agreement with data acquired during beam tests. Most of the shower observables such as energy deposition, density, transversal and longitudinal size are often within 15% [59] or better, depending on the observable, the process and the physics list. However, further validation is still necessary to improve the various models. The prototypes of imaging calorimeters of the CALICE collaboration with their so far unmet fine granularity are therefore a rich source of information.