3.5.  Hadronic Physics

3.5.1.  Introduction

Optimal exploitation of hadronic final states played a key role in successes of all recent collider experiment in HEP, and the ability to use hadronic final states will continue to be one of the decisive issues during the analysis phase of the LHC experiments. Monte Carlo programs like Geant4 facilitate the use of hadronic final states, and have been developed for many years.

We give an overview of the Object Oriented frameworks for hadronic generators in Geant4, and illustrate the physics models underlying hadronic shower simulation on examples, including the three basic types of modeling; data-driven, parametrisation-driven, and theory-driven modeling, and their possible realisations in the Object Oriented component system of Geant4. We put particular focus on the level of extendibility that can and has been achieved by our Russian dolls approach to Object Oriented design, and the role and importance of the frameworks in a component system.

3.5.2.  Principal Considerations

The purpose of this section is to explain the implementation frameworks used in and provided by Geant4 for hadronic shower simulation as in the 1.1 release of the program. The implementation frameworks follow the Russian dolls approach to implementation framework design. A top-level, very abstracting implementation framework provides the basic interface to the other Geant4 categories, and fulfils the most general use-case for hadronic shower simulation. It is refined for more specific use-cases by implementing a hierarchy of implementation frameworks, each level implementing the common logic of a particular use-case package in a concrete implementation of the interface specification of one framework level above, this way refining the granularity of abstraction and delegation. This defines the Russian dolls architectural pattern. Abstract classes are used as the delegation mechanism [1] .

All framework functional requirements were obtained through use-case analysis. In the following we present for each framework level the compressed use-cases, requirements, designs including the flexibility provided, and illustrate the framework functionality with examples. All design patterns cited are to be read as defined in [ Gamma1995 ].

3.5.3.  Level 1 Framework - processes

There are two principal use-cases of the level 1 framework. A user will want to choose the processes used for his particular simulation run, and a physicist will want to write code for processes of his own and use these together with the rest of the system in a seamless manner.

Requirements

  1. Provide a standard interface to be used by process implementations.

  2. Provide registration mechanisms for processes.

Design and interfaces

Both requirements are implemented in a sub-set of the tracking-physics interface in Geant4}. The class diagram is shown in Figure 3.1.

Level 1 implementation framework of the hadronic category of GEANT4.

Figure 3.1.  Level 1 implementation framework of the hadronic category of GEANT4.


All processes have a common base-class G4VProcess, from which a set of specialised classes are derived. Three of them are used as base classes for hadronic processes for particles at rest (G4VRestProcess), for interactions in flight (G4VDiscreteProcess), and for processes like radioactive decay where the same implementation can represent both these extreme cases (G4VRestDiscrete-Process).

Each of these classes declares two types of methods; one for calculating the time to interaction or the physical interaction length, allowing tracking to request the information necessary to decide on the process responsible for final state production, and one to compute the final state. These are pure virtual methods, and have to be implemented in each individual derived class, as enforced by the compiler.

Framework functionality

The functionality provided is through the use of process base-class pointers in the tracking-physics interface, and the G4Process-Manager. All functionality is implemented in abstract, and registration of derived process classes with the G4Process-Manager of an individual particle allows for arbitrary combination of both Geant4 provided processes, and user-implemented processes. This registration mechanism is a modification on a Chain of Responsibility. It is outside the scope of the current paper, and its description is available from G4Manual.

3.5.4.  Level 2 Framework - Cross Sections and Models

At the next level of abstraction, only processes that occur for particles in flight are considered. For these, it is easily observed that the sources of cross sections and final state production are rarely the same. Also, different sources will come with different restrictions. The principal use-cases of the framework are addressing these commonalities. A user might want to combine different cross sections and final state or isotope production models as provided by Geant4, and a physicist might want to implement his own model for particular situation, and add cross-section data sets that are relevant for his particular analysis to the system in a seamless manner.

Requirements

  1. Flexible choice of inclusive scattering cross-sections.

  2. Ability to use different data-sets for different parts of the simulation, depending on the conditions at the point of interaction.

  3. Ability to add user-defined data-sets in a seamless manner.

  4. Flexible, unconstrained choice of final state production models.

  5. Ability to use different final state production codes for different parts of the simulation, depending on the conditions at the point of interaction.

  6. Ability to add user-defined final state production models in a seamless manner.

  7. Flexible choice of isotope production models, to run in parasitic mode to any kind of transport models.

  8. Ability to use different isotope production codes for different parts of the simulation, depending on the conditions at the point of interaction.

  9. Ability to add user-defined isotope production models in a seamless manner.

Design and interfaces

The above requirements are implemented in three framework components, one for cross-sections, final state production, and isotope production each. The class diagrams are shown in Figure 3.2 for the cross-section aspects, Figure 3.3 for the final state production aspects, and figure Figure 3.4 for the isotope production aspects.

Level 2 implementation framework of the hadronic category of Geant4; cross-section aspect.

Figure 3.2.  Level 2 implementation framework of the hadronic category of Geant4; cross-section aspect.


Level 2 implementation framework of the hadronic category of Geant4; final state production aspect.

Figure 3.3.  Level 2 implementation framework of the hadronic category of Geant4; final state production aspect.


Level 2 implementation framework of the hadronic category of Geant4; isotope production aspect

Figure 3.4.  Level 2 implementation framework of the hadronic category of Geant4; isotope production aspect


The three parts are integrated in the G4Hadronic-Process class, that serves as base-class for all hadronic processes of particles in flight.

Cross-sections

Each hadronic process is derived from G4Hadronic-Process}, which holds a list of ``cross section data sets''. The term ``data set'' is representing an object that encapsulates methods and data for calculating total cross sections for a given process in a certain range of validity. The implementations may take any form. It can be a simple equation as well as sophisticated parameterisations, or evaluated data. All cross section data set classes are derived from the abstract class G4VCrossSection-DataSet}, which declares methods that allow the process inquire, about the applicability of an individual data-set through IsApplicable(const G4DynamicParticle*, const G4Element*), and to delegate the calculation of the actual cross-section value through GetCrossSection(const G4DynamicParticle*, const G4Element*).

Final state production

The G4HadronicInteraction base class is provided for final state generation. It declares a minimal interface of only one pure virtual method: G4VParticleChange* ApplyYourself(const G4Track &, G4Nucleus &)}. G4HadronicProcess provides a registry for final state production models inheriting from G4Hadronic-Interaction. Again, final state production model is meant in very general terms. This can be an implementation of a quark gluon string model [QGSM], a sampling code for ENDF/B data formats [ ENDFForm ], or a parametrisation describing only neutron elastic scattering off Silicon up to 300~MeV.

Isotope production

For isotope production, a base class (G4VIsotope-Production) is provided. It declares a method G4IsoResult * GetIsotope(const G4Track &, const G4Nucleus &) that calculates and returns the isotope production information. Any concrete isotope production model will inherit from this class, and implement the method. Again, the modeling possibilities are not limited, and the implementation of concrete production models is not restricted in any way. By convention, the GetIsotope method returns NULL, if the model is not applicable for the current projectile target combination.

Framework functionality:

Cross Sections

G4HadronicProcess provides registering possibilities for data sets. A default is provided covering all possible conditions to some approximation. The process stores and retrieves the data sets through a data store that acts like a FILO stack (a Chain of Responsibility with a First In Last Out decision strategy). This allows the user to map out the entire parameter space by overlaying cross section data sets to optimise the overall result. Examples are the cross sections for low energy neutron transport. If these are registered last by the user, they will be used whenever low energy neutrons are encountered. In all other conditions the system falls back on the default, or data sets with earlier registration dates. The fact that the registration is done through abstract base classes with no side-effects allows the user to implement and use his own cross sections. Examples are special reaction cross sections of κ0-nuclear interactions that might be used for ∊/∊' analysis at LHC to control the systematic error.

Final state production

The G4HadronicProcess class provides a registration service for classes deriving from G4Hadronic-Interaction, and delegates final state production to the applicable model. G4Hadronic-Interactionprovides the functionality needed to define and enforce the applicability of a particular model. Models inheriting from G4Hadronic-Interaction can be restricted in applicability in projectile type and energy, and can be activated/deactivated for individual materials and elements. This allows a user to use final state production models in arbitrary combinations, and to write his own models for final state production. The design is a variant of a Chain of Responsibility. An example would be the likely CMS scenario - the combination of low energy neutron transport with a quantum molecular dynamics [QMD], invariant phase space decay [CHIPS], and fast parametrised models for calorimeter materials, with user defined modeling of interactions of spallation nucleons with the most abundant tracker and calorimeter materials.

Isotope production

The G4HadronicProcess by default calculates the isotope production information from the final state given by the transport model. In addition, it provides a registering mechanism for isotope production models that run in parasitic mode to the transport models and inherit from G4VIsotope-Production. The registering mechanism behaves like a FILO stack, again based on Chain of Responsibility. The models will be asked for isotope production information in inverse order of registration. The first model that returns a non-NULL value will be applied. In addition, the G4Hadronic-Process provides the basic infrastructure for accessing and steering of isotope-production information. It allows to enable and disable the calculation of isotope production information globally, or for individual processes, and to retrieve the isotope production information through the G4IsoParticleChange * GetIsotopeProductionInfo()} method at the end of each step. The G4HadronicProcess is a finite state machine that will ensure the GetIsotope-ProductionInfo returns a non-zero value only at the first call after isotope production occurred. An example of the use of this functionality is the study of activation of a Germanium detector in a high precision, low background experiment.

3.5.5.  Level 3 Framework - Theoretical Models

Level 3 implementation framework of the hadronic category of Geant4; theoretical model aspect.

Figure 3.5.  Level 3 implementation framework of the hadronic category of Geant4; theoretical model aspect.


Geant4 provides at present one implementation framework for theory driven models. The main use-case is that of a user wishing to use theoretical models in general, and to use various intra-nuclear transport or pre-compound models together with models simulating the initial interactions at very high energies.

Requirements

  1. Allow to use or adapt any string-parton or parton transport [VNI],

  2. Allow to adapt event generators, ex. [PYTHIA7], state production in shower simulation.

  3. Allow for combination of the above with any intra-nuclear transport (INT).

  4. Allow stand-alone use of intra-nuclear transport.

  5. Allow for combination of the above with any pre-compound model.

  6. Allow stand-alone use of any pre-compound model.

  7. Allow for use of any evaporation code.

  8. Allow for seamless integration of user defined components for any of the above.

Design and interfaces

To provide the above flexibility, the following abstract base classes have been implemented:

  • G4VHighEnergyGenerator

  • G4VIntranuclearTransportModel

  • G4VPreCompoundModel

  • G4VExcitationHandler

In addition, the class G4TheoFS-Generator is provided to orchestrate interactions between these classes. The class diagram is shown in Figure 3.5.

G4VHighEnergy-Generator serves as base class for parton transport or parton string models, and for Adapters to event generators. This class declares two methods, Scatter, and GetWoundedNucleus.

The base class for INT inherits from G4Hadronic-Interaction, making any concrete implementation usable as a stand-alone model. In doing so, it re-declares the ApplyYourself interface of G4Hadronic-Interaction, and adds a second interface, Propagate, for further propagation after high energy interactions. Propagate takes as arguments a three-dimensional model of a wounded nucleus, and a set of secondaries with energies and positions.

The base class for pre-equilibrium decay models, G4VPre-CompoundModel, inherits from G4Hadronic-Interaction, again making any concrete implementation usable as stand-alone model. It adds a pure virtual DeExcite method for further evolution of the system when intra-nuclear transport assumptions break down. DeExcite takes a G4Fragment, the Geant4 representation of an excited nucleus, as argument.

The base class for evaporation phases, G4VExcitation-Handler, declares an abstract method, BreakItUP(), for compound decay.

Framework functionality

The G4TheoFSGenerator class inherits from G4Hadronic-Interaction, and hence can be registered as a model for final state production with a hadronic process. It allows a concrete implementation of G4VIntranuclear-TransportModel and G4VHighEnergy-Generator to be registered, and delegates initial interactions, and intra-nuclear transport of the corresponding secondaries to the respective classes. The design is a complex variant of a Strategy. The most spectacular application of this pattern is the use of parton-string models for string excitation, quark molecular dynamics for correlated string decay, and quantum molecular dynamics for transport, a combination which promises to result in a coherent description of quark gluon plasma in high energy nucleus-nucleus interactions.

The class G4VIntranuclearTransportModel provides registering mechanisms for concrete implementations of G4VPreCompound-Model, and provides concrete intra-nuclear transports with the possibility of delegating pre-compound decay to these models.

G4VPreCompoundModel provides a registering mechanism for compound decay through the G4VExcitation-Handler interface, and provides concrete implementations with the possibility of delegating the decay of a compound nucleus.

The concrete scenario of G4TheoFS-Generator using a dual parton model and a classical cascade, which in turn uses an exciton pre-compound model that delegates to an evaporation phase, would be the following: G4TheoFS-Generator receives the conditions of the interaction; a primary particle and a nucleus. It asks the dual parton model to perform the initial scatterings, and return the final state, along with the by then damaged nucleus. The nucleus records all information on the damage sustained. G4TheoFS-Generator forwards all information to the classical cascade, that propagates the particles in the already damaged nucleus, keeping track of interactions, further damage to the nucleus, etc.. Once the cascade assumptions break down, the cascade will collect the information of the current state of the hadronic system, like excitation energy and number of excited particles, and interpret it as a pre-compound system. It delegates the decay of this to the exciton model. The exciton model will take the information provided, and calculate transitions and emissions, until the number of excitons in the system equals the mean number of excitons expected in equilibrium for the current excitation energy. Then it hands over to the evaporation phase. The evaporation phase decays the residual nucleus, and the Chain of Command rolls back to G4TheoFS-Generator, accumulating the information produced in the various levels of delegation.

3.5.6.  Level 4 Frameworks - String Parton Models and Intra-Nuclear Cascade

Level 4 implementation framework of the hadronic category of Geant4; parton string aspect.

Figure 3.6.  Level 4 implementation framework of the hadronic category of Geant4; parton string aspect.


Level 4 implementation framework of the hadronic category of Geant4; intra-nuclear transport aspect.

Figure 3.7.  Level 4 implementation framework of the hadronic category of Geant4; intra-nuclear transport aspect.


The use-cases of this level are related to commonalities and detailed choices in string-parton models and cascade models. They are use-cases of an expert user wishing to alter details of a model, or a theoretical physicist, wishing to study details of a particular model.

Requirements

  1. Allow to select string decay algorithm

  2. Allow to select string excitation.

  3. Allow the selection of concrete implementations of three-dimensional models of the nucleus

  4. Allow the selection of concrete implementations of final state and cross sections in intra-nuclear scattering.

Design and interfaces

To fulfil the requirements on string models, two abstract classes are provided, the G4VParton-StringModel and the G4VString-Fragmentation. The base class for parton string models, G4VParton-StringModel, declares the GetStrings() pure virtual method. G4VString-Fragmentation, the pure abstract base class for string fragmentation, declares the interface for string fragmentation.

To fulfill the requirements on intra-nuclear transport, two abstract classes are provided, G4V3DNucleus, and G4VScatterer. At this point in time, the usage of these intra-nuclear transport related classes by concrete codes is not enforced by designs, as the details of the cascade loop are still model dependent, and more experience has to be gathered to achieve standardisation. It is within the responsibility of the implementers of concrete intra-nuclear transport codes to use the abstract interfaces as defined in these classes.

The class diagram is shown in Figure 3.6 for the string parton model aspects, and in Figure 3.7 for the intra-nuclear transport.

Framework functionality

Again variants of Strategy, Bridge and Chain of Responsibility are used. G4VParton-StringModel implements the initialisation of a three-dimensional model of a nucleus, and the logic of scattering. It delegates secondary production to string fragmentation through a G4VString-Fragmentation pointer. It provides a registering service for the concrete string fragmentation, and delegates the string excitation to derived classes. Selection of string excitation is through selection of derived class. Selection of string fragmentation is through registration.

3.5.7.  Level 5 Framework - String De-excitation}

Level 5 implementation framework of the hadronic category of Geant4; string fragmentation aspect.

Figure 3.8.  Level 5 implementation framework of the hadronic category of Geant4; string fragmentation aspect.


The use-case of this level is that of a user or theoretical physicist wishing to understand the systematic effects involved in combining various fragmentation functions with individual types of string fragmentation. Note that this framework level is meeting the current state of the art, making extensions and changes of interfaces in subsequent releases likely.

Requirements

  1. Allow the selection of fragmentation function.

Design and interfaces

A base class for fragmentation functions, G4VFragmentation-Function}, is provided. It declares the GetLightConeZ() interface.

Framework functionality

The design is a basic Strategy. The class diagram is shown in Figure 3.8. At this point in time, the usage of the G4VFragmentation-Function is not enforced by design, but made available from the G4VString-Fragmentation to an implementer of a concrete string decay. G4VString-Fragmentation provides a registering mechanism for the concrete fragmentation function. It delegates the calculation of zf of the hadron to split of the string to the concrete implementation. Standardisation in this area is expected.



[1] The same can be achieved with template specialisations with slightly improved CPU performance but at the cost of significantly more complex designs and, with present compilers, significantly reduced portability.