Particle Interaction Modelling in High Energy Physics

We review the software tools and models used in High Energy Physics to describe elementary particle interactions, with emphasis on those which would be most appropriate for application to the field of Cosmic Ray Physics. We discuss the standard Monte Carlo programs in common use and various specialised modifications, ranging from the modelling of very high energy interactions to softer processes of importance in simulating detector performance. The possibilities for a unified framework of common software suitable for high energy and cosmic ray physics is discussed. INTRODUCTION The modelling of high energy interactions using Monte Carlo techniques is invaluable in High Energy Physics (HEP) for understanding the signatures of processes of interest, the backgrounds from processes of lesser interest, or the response of detectors to various particles which traverse them. The tasks of interest may be divided into two categories: high energy processes and low energy processes, where the latter are generally pertinent to studies of the detector response. We describe how each of these categories is handled and the two programs used which are of most relevance to the field of cosmic ray physics. The programs discussed are part of the CERN program library1 and are freely available from the CERN IT division. HIGH ENERGY INTERACTIONS The traditional focus of much of High Energy Physics has been to try to reach the highest centreof-mass energies possible by colliding point-like particles such as electrons and positrons, or the point-like constituents (quarks, antiquarks, and gluons) of hadrons such as protons and antiprotons. A large fraction of these collisions result in rather small momentum transfers such that particles scatter through small angles. The collisions deemed of greatest interest are usually those where a large energy is available for the production of new particles, due either to the exchange of gauge bosons (such as photons, gluons, W and Z0) in the Standard (SU(3)c SU(2)L U(1)Y ) Model or to point-like interactions which are usually assumed to be approximations to interactions involving more massive particles in some grander theory. A variety of programs exist to handle processes of the hard collision of one particle with another and the production of particles from that interaction. The program most prevalently used to simulate hadron collisions is PYTHIA (Sjöstrand, 1986, Sjöstrand and Bengtsson, 1987, Bengtsson and Sjöstrand, 1987, and Sjöstrand, 1993). PYTHIA is a Fortran 77 program which simulates a wide variety of particle collisions. Of particular interest to the field of cosmic rays are the hadron-hadron collision processes. Most effort has been dedicated to the complete and accurate simulation of high Q2 processes, although low Q2 processes, such as diffractive and elastic scattering of (anti-)protons are included. While PYTHIA is not really aimed at modelling the wide range of possible nucleus-nucleus interactions, it includes hooks which facilitate the addition of arbitrary processes and many parameters which may be adjusted to reproduce experimental data. PYTHIA handles events in the following manner: Two particles are coming in towards each other. Each particle is characterised by a set of parton distribution functions, which defines the partonic substructure in terms of flavour composition and 1See http://wwwinfo.cern.ch/asd/ on the World Wide Web. energy sharing. One parton from each shower starts a branching involving, for example, the radiation of gluons or photons. One incoming parton from each of the two showers participates in the hard process, and a number of outgoing partons are produced. This constitutes the “interesting” part of the event for a typical high energy physicist. The outgoing partons may emit particles as did the incoming ones, to build up final-state showers. When the initial parton is taken out of an initial particle, a remnant is left behind. This remnant may have an internal structure, and a colour charge that relates it to the rest of the final state. The PYTHIA modelling of the QCD confinement mechanism ensures that outgoing quarks, and gluons from both the hard scatter and the soft remnants fragment to form colour-neutral hadrons. Many of the hadrons produced are unstable and decay further. PYTHIA uses comprehensive tables containing the properties of the known particles and resonances such as mass, spin-parity, branching fractions, lifetimes, etc. The word “parton” has been used somewhat loosely in the above, and includes quarks, gluons, leptons, and photons. The word “shower” in this context refers to a group of particles originating from a common source and going roughly in the same direction (not an air shower!). By default, all of these steps are carried out within the Standard Model. PYTHIA also includes many optional processes beyond the Standard Model as well as a straightforward way of adding arbitrary new processes, be they Standard Model processes which are neglected by PYTHIA or new physics processes. Low energy processes are typically neglected, so that, for example, the emission of photons of a few eV is neglected completely. The hard scattering processes have in general a firm theoretical basis. The most heuristic part of the whole procedure is in the final stages where QCD provides no means calculating fragmentation, hadronisation, and decay, and recourse must be had to “QCD-inspired” models, such as string fragmentation, and hand-insertion of measured quantities such as the ratios of vector to pseudoscalar production etc. A choice must be made of how far down in energy to follow perturbative QCD for these processes before handing over the task to phenomenological models. Finally, even the distributions of partons in hadrons, such as protons is not known in a model-independent way. Recently there has been a re-awakening of interest (e.g. Eggert and Taylor, 1996) in the kinematic regions in which perturbative QCD is difficult to apply, but where some of the tools of Regge theory are applicable. As interest in the high energy community grows, there is every reason to expect models incorporating this physics to be developed with increasing enthusiasm, incorporating the best of present and future knowledge in this kinematic regime. Despite these caveats, PYTHIA has been subjected to demanding comparisons with data from numerous experiments such that, after some tuning, it performs impressively for a wide range of soft and hard processes (frequently agreeing with the data to better than 1%). While PYTHIA does not include all of the processes required to simulate high energy cosmic ray interactions and atmospheric showers, it does contain a wealth of pertinent and reliably simulated physics processes which could be profitably exploited to facilitate the development of simulation programs used in cosmic ray physics. LOW ENERGY INTERACTIONS (DETECTOR SIMULATION) By low energy interactions, we mean the interactions of the particles arising from high energy interactions which survive long enough to travel macroscopic distances to physical devices for their detection. These are typically either tracking devices which try to reconstruct their trajectories as they lose only small amounts of energy, or calorimeters, which try to determine their energies by forcing them to stop in some volume which is sensitive to the energy they lose. Here an alternative approach to PYTHIA is taken, and the most common Monte Carlo program in use is GEANT (Brun, 1987), which is a Fortran 77 program. Originally designed for the High Energy Physics experiments, GEANT has today found applications also outside this domain in areas such as medical and biological sciences, radio-protection, and astronautics. Here the emission of soft (low energy) particles such as photons of a few eV or thermal neutrons may be of great importance, and the idea is to simulate not just one high energy collision, but very many low energy collisions as a particle traverses the material volumes of a detector. GEANT may optionally include other shower simulation code such as GHEISHA (Fesefeldt, 1985), FLUKA (Brun, 1987), and CALOR (Zeitnitz, 1994). The GEANT program simulates the passage of particles through matter, with the following principal functions: the transport of particles through an experimental setup, of arbitrary geometry, materials, and magnetic field configuration; the simulation of particle decays and interactions with the detector elements, with subsequent tracking of secondary particles; the simulation of the detector response to primary, secondary, tertiary, etc. particles; the graphical representation of the detector setup and of the particle trajectories. Given an input particle or set of particles, GEANT will follow them through the given materials and simulate the physics processes, which include (but are not limited to): pair creation; positron annihilation; Compton scattering; photoelectric effect; photofission; Rayleigh scattering; Čerenkov photons; Molière scattering; ionisation; delta-ray production; bremsstrahlung; and particle decays. Detector elements may be defined as sensitive volumes of various types. For example, for a calorimeter sensitive volume, GEANT will integrate the energies deposited by all particles passing through the volume. When desired, for example for hits in a tracker volume, GEANT can store information such as the spatial and time coordinates. The program can run in both batch and interactive modes, and provides a set of graphics tools to enable one to view detector and the passage of particles through it. GEANT has been used to simulate numerous, highly complex2, High Energy Physics experiments for two decades. It is now a very mature and comprehensive program for the simulation of particle interactions in matter. GEANT could be profitably used, with little or no modifications, to simulate many of the detectors used in the field of cosmic ray physics. OUTLOOK The current Fortran 77 version of GEANT, known as GEANT3, is now a stable package with essentially no new developments foreseen. In preparation for future HEP experiments, which will be using an Object-Oriented paradigm for their software, CERN initiated the GEANT4 project (Giani, 1996 and Allison, 1996) with the aim of completely rewriting GEANT in C++. The GEANT4 collaboration, which consists of approximately 100 physicists throughout the world, does not aim merely to translate the code from Fortran to C++. Rather, GEANT4 constitutes a complete redesign of the software to address many of shortcomings of the procedural approach inherent in Fortran programs. The main similarities of GEANT4 with GEANT3 will be the Monte Carlo philosophy of tracking particles and their interactions in material volumes, and the breadth and reliability of the physics processes included. Given the complexity and high particle multiplicities of future experiments, considerable emphasis has been placed on performance. For example, the algorithms for particle tracking through arbitrary geometrical configurations have been improved using input from fields as distinct 2For example, the LHC experiments typically have 106 distinct detector components. from HEP as robotic manufacturing. Care has been taken to avoid uncertainties due to the propagation of results with insufficient precision. For example, GEANT3 is limited to 1μm precision over 1 m. The procedures for the definition of detector configurations, novel physics processes, and visualisation have also been improved. GEANT4 has recently been released as an Alpha version with a public release anticipated within a year or so. While GEANT3 is already a powerful tool for the simulation of detectors in cosmic ray experiments, we believe that the impact of GEANT4 could be much greater. Firstly, GEANT4 aims to maintain precision over arbitrary scales (from microns to mega parsecs). Secondly, the modular design greatly facilitates the addition of arbitrary physics processes, which may be of particular interest to cosmic ray physicists. Thirdly, the ability to replace full step-by-step tracking and simulation of interactions with fast parametrisations in selected arbitrary volumes is built in. One might conceive of using the GEANT4 framework (with the addition of some missing physics processes) to simulate a cosmic shower experiment at multiple levels: the individual detectors; the full array of detectors; and the interactions of the particles in the atmosphere (allowing for the geomagnetic field) either in layers with intermediate storage of results in “shower libraries” or using the in-built GEANT4 hooks for parametrised interactions. One might say that “the sky’s the limit” but perhaps the GEANT4 framework could even be used to track particles through the universe, allowing for the galactic magnetic field and interactions in the interstellar medium. ACKNOWLEDGEMENTSWe would like to thank our colleagues in the L3, CMS, and Auger collaborations and in the CERNcomputing division for useful discussions. REFERENCESAllison., J., Graphics for GEANT4. In L. Taylor and C. Vandoni, ed. Proceedings of the HEPVIS 96Workshop, CERN, Geneva, Switzerland, September 2-4 (1996). 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