Gismo Simulation of the Next Linear Collider Detector

Abstract

Calorimetry for a proposed the Next Linear Collider Detector (NLC/NLD) is outlined. Consequences of this new design are discussed in terms of gross energy resolution of charged particles and neutral detection goals. The Monte Carlo simulation package GISMO is introduced and compared to GEANT3: a package used to simulate the Stanford Large Detector (SLD). GEANT3 is used to validate GISMO calorimetry and to establish GISMO as a reliable source of detector performance studies.

Table of Contents

• Introduction
• Theory
• Methods
• Data
• Discussion
• Conclusion
• References
• Appendices

Introduction

The Next Linear Collider (NLC) is an instrument proposed by physicists to study electroweak symmetry breaking in the Standard Model (SM). If it is built it will play an important role in the search for a possible fundamental Higgs field and supersymmetric (SUSY) particles, as well as possible new physics at the TeV scale. NLC will take advantage of advances made in accelerator physics and the understanding of high-energy e+e- annihilations. The detector design discussed here was originally proposed at a conference in Snowmass Colorado, 1996 [6].

GISMO is a Monte Carlo simulation package used to study the NLC detector (NLD). As a collection of C++ library functions GISMO provides a backbone for detector development[5]. Detector projects such as NLD interface with a suite of GISMO simulation tools.

Though still at a very early conceptual stage this detector layout does address some basic requirements for study of e+e- annihilation at high energy. GISMO provides an opportunity to explore the feasibility of a compact calorimeter design featuring W-Si em and Fe-scintillator hadron sections. These detector specifications represent a starting point for a detector of this kind.

Calorimetry plays an important role in identifying high energy particles generated in modern accelerators. When atoms in the calorimeter are ionized, the freed electrons provide an observable charged particle energy loss. The nature of this process limits the detector in that only charged particles are visible to the instrumentation. Energy lost due to neutral particles becomes implicit in the gross energy loss logged by the detector. After charged particle contributions are determined, any outstanding energy is assumed to be the neutral contribution. When used in combination with the Tracking system, calorimeters can yield a great deal of information concerning ALL players in an event.

This process of neutral detection puts a premium on detector resolution, particularly on hadronic resolution. Accurate determination of charged particle energies implies accurate measurement of neutral energy loss in the system. NLD will have to distinguish neutral from charged particles if it is to reconstruct non-SM Higgs production and study SUSY at the weak interaction scale. A model-independent search for the Higgs boson will rely on good momentum resolution and two-track separation of the tracking system [6]. The energy resolution of the calorimeter subsystems will be discussed here as well as short-term development issues.

Theory

Moderately relativistic charged particles incident on a material lose energy primarily through ionization (ignoring radiative processes at very high energies). The mean rate of energy loss is given by the Bethe-Bloch equation [4]:

where Z = Atomic number of medium, A = atomic mass of medium, ze = charge of incident particle, bc = particle velocity, m_ec² = e- mass x c², I = intensity of incoming electrons, d = density effect correction factor, and T_max = maximum kinetic energy imparted to a free e- in a single collision. The units are chosen so that dx is measured in mass/unit area (eg. g cm^-2 ). The incident particle energy is defined as E = gMc², where M = incident particle mass.

The rate of energy loss in a material depends on the atomic properties of that material. The radiation length (X₀) of a material can be defined in terms of the fundamental processes at work in a detecting medium. Radiation length is the mean distance over which a high-energy electron loses all but 1/e of its energy by bremsstrahlung.

When a high-energy electron or photon is incident on a material it generates an electromagnetic cascade of lower energy electrons and photons. This process is a combination of bremsstrahlung and pair production in the absorber and active materials of the detector. An electron losses energy through bremsstrahlung at a rate approximately proportional to it’s incident energy E. The ionization rate varies according to log(E). The E where ionization and bremsstrahlung rates are in equal proportion is often quoted as the critical energy (E_c) of a material [1]. When shower electron energies fall below E_c, the ionization rate steadily increases taking over as the primary loss mechanism.

Hadronic showers involve em energy mechanisms but are substantially more complicated due to strong interaction and more exotic particle production. A high-energy hadron will interact strongly with calorimeter materials, usually producing mesons. The excited nuclei will release g's and nucleons which in turn may lose energy through ionization. These secondary particles (mesons, nucleons, g's) form other particles that interact electromagnetically, such as p₀ and h. Energy dissipated through the release of nucleons is lost to the detector. This invisible energy can be recouped through neutron capture but has resulted in a detector signal degradation of up to 40% [4].

The number of particles contributing to a hadron signal (the number of em shower particles) is therefore smaller than that of a purely electromagnetic event. The ratio of particles produced varies widely and leads to a statistical interpretation of the detecting device.

Two fundamental measures of detector performance are response and resolution. The response of a detector is its measurement of visible (charged particle) energy. In a sampling detector (eg. NLD) an ionizing particle produces a signal as it traverses the active material (Si in the EM, Polystyrene in the hadronic module) and the response is that signal divided by a sampling fraction (s.f). Consider the theoretical calculation for a Si-W cell (neglecting Air and G10 seating for Si) in the NLD em calorimeter. Given an active layer thickness (0.03cm of Si) and a radiating layer thickness (0.45cm of W), the energy lost in the active medium can be calculated:

and for W:

The s.f for this em calorimeter can then be written:

The resolution of a detector reflects the statistical nature of the particle shower process. Each e- that enters a given detector may produce a slightly different ionization charge. The width of a detector signal distribution (s_s) is related to the number of fundamental, independent processes (n) contributing to the signal (S). For monoenergetic particles of energy E: s_s/S ~ n^½/n, leads to s_s/E = c/E^½ [4]. Fluctuations in the number of fundamental processes set an upper limit on the resolution of a detector. Although resolution improves at higher energy, there is also a rise in alternate fluctuations which may or may not be Gaussian. This may in turn lead to deviations from the 1/E^½ scaling rule and degrade performance of the detector.

Methods

For large batch farm jobs GISMO parses the command line for detector specifications and event running conditions. A user can specify the number of monoenergetic particles to process, their incident energy, and the initial vector to be used for each particle relative to the interaction point (IP or global origin). Particle names are enumerated according to the Particle Data Group (PDG) numbering scheme [1]. Energy is specified in GeVs and the initial vector is given in cylindrical coordinates: (cosq, f, z). NLD configured executables are submitted to the SLAC rs6000 batch farm for processing.

The analysis of GISMO event output is a 2 step process from output file format to analysis format. GISMO produces an ASCII file containing event data which is then converted to a PAW NTUPLE [9] using the NTUPLER utility [5]. NTUPLER output is then converted into ROOT branches [7] for analysis within the ROOT environment.

A GISMO executable was configured to generate the progeny of a primary interacting hadron and to break having interacted that particle for first time. Progeny identities and the energies imparted to them were stored and the shower stack cleared ending an event before the progeny themselves could interact. The data was written to disk, processed and analyzed.

SLD GEANT data was generated similarly on VMS/VAX. GISMO was configured to simulate events in an SLD Liquid Argon Calorimeter (LAC) and Luminosity Monitor (LUM) [2]. The SLD monte carlo is obviously much more mature than GISMO and conducts a much more robust simulation. Many aspects of GEANT's simulation were omitted for the sake of simplicity and to match it’s initial conditions as closely as possible with the GISMO version [3].

Data

GISMO was configured for full shower simulation of NLD em and hadronic subsystems. Jobs consisted of 500 20GeV e- events, 5000 4GeV p+ events and 5000 20GeV p+ events. These events ran for the better part of 3 days where e- events took <26hrs and the 20GeV hadrons >50hrs.

The em and hadronic responses can be compared in terms of amplitude, width and mean.

These histograms indicate a p+ width ~4x that of the e- with a mean ~10% lower with respect to incident energy. The hadron signal contains a very pronounced non-Gaussian tail. This tail can be observed for both 4 and 20GeV events given the larger sample size of each.

For event populations <1000 the non-Gaussian fit is much more subtle even for incident E>20GeV. The hadron tails were approximated with a 3^o polynomial.

A plot of NLD hadronic resolution demonstrates a E^-½ scaling trend.  This resolution indicates an improvement of ~25% over recent SLD values [5].

When the products of a primary interaction are examined for both SLD GEANT and SLD GISMO, the two algorithms seem to produce nearly identical types.

The numbering scheme follows GEANT3 guidelines (see Appendix I). The momentum distributions generated by the two packages can be compared.

Discussion

GISMO produces exceptional hadronic resolution, there's no question of that when one considers detectors to date [8]. The barrel and endcap algorithms have been cross-checked against GEANT: a working, realistic model which has successfully reproduced SLD data for years. The em performance was expected in the Snowmass report and came as no surprise, but the hadronic response does seem high and the resolution too good.

The non-Gaussian shape of the hadronic response is not really surprising given that NLD is a non-compensating detector: material specs and detector dimensions don't make up for lost visibility of hadronic events (em/hadronic response > 1) [4]. This can be minimized as it is in SLD where hadronic events are parameterized to expedite the process of their simulation.

GISMO production of hadronic shower particles is in very good agreement with GEANT in both energy and type. If GISMO were creating a large number of p⁰'s for example, this might lead to a more substantial em shower contribution. Such ‘em weighted’ showers would result in an increased response, but there doesn't appear to be any favoritism on the part of GISMO. GEANT produces many of the same particles that GISMO does and the two of them seem to agree on the energy imparted to them. This fact clears the GISMO interface to EGS and GHEISHA packages used by both for em and hadronic monte carlo calculations.

Evidence supporting a GISMO miscalculation of hadronic events does not seem overwhelming. There isn't much reason to doubt that it's telling the truth about NLD, other than historical reasons that suggest the resolution is too good by about 20%. The GEANT picture of SLD has been validated by data collected over the past 10 years. GISMO gives a similar picture of SLD. There is little reason to doubt the GISMO picture of NLD. Any further validation of GISMO would have to come from the device itself.

Conclusions

GISMO gives an accurate picture of NLD: 15% em resolution, 47% hadronic. The first stage of a two part development of GISMO particle identification is complete. The calorimetry has been validated and believed to be detecting an appropriate energy loss for incident particles. The tracking system can now be integrated with the calorimetry to accurately measure charged particle momenta, and to infer neutral contributions. The exceptional hadronic resolution should make neutral ids a snap. We should be able to narrow down neutral/charged masses in a jet quite effectively and perhaps find an increased confidence in individual neutral masses.

Appendix I

SLD uses generated particle types enumerated according to an SLD GEANT scheme. The Particle Data Group later standardized this practice but SLD GEANT development was already too far along to convert. GISMO uses a table look-up to resolve particle identities returned by other EGS and GHEISHA. The versions of these packages used in GISMO currently follow the GEANT convention and have to be "fixed" for future compatability.

For the purposes of this study PDG/GEANT look-up was disabled and enumerated types were written directly from the interface.

References

[1] APS, Phys. Rev. D 50, 3 (1994)

[2] Colgur C. and Dubois R., http://sldnt17.slac.stanford.edu/nld/studies/study.htm

[3] Colgur C. and Dubois R., http://sldnt17.slac.stanford.edu/nld/studies/geant.htm

[4] Hollebeek R., ASI 275 (1991)

[5] NLD Working Group, http://sldnt17.slac.stanford.edu/nld/default.htm

[6] NLC ZDR Design and Physics Working Groups, SLAC Report 485 (1996)

[7] ROOT Analysis Studio, http://root.cern.ch

[8] Sandler P.H. et al., Phys. Rev. D 42, 3 (1990)

[9] SLD Offline Processing, http://www-sld.slac.stanford.edu/sldwww/sld-working.html

Chad Colgur

01/13/04